id	sid	tid	token	lemma	pos
ijassa-1367	1	1	adv	adv	PROPN
ijassa-1367	1	2	syst	syst	PROPN
ijassa-1367	1	3	sci	sci	PROPN
ijassa-1367	1	4	appl	appl	PROPN
ijassa-1367	1	5	2023	2023	NUM
ijassa-1367	1	6	;	;	PUNCT
ijassa-1367	1	7	01:35–49	01:35–49	NUM
ijassa-1367	1	8	published	publish	VERB
ijassa-1367	1	9	online	online	ADV
ijassa-1367	1	10	at	at	ADP
ijassa-1367	1	11	https://ijassa.ipu.ru	https://ijassa.ipu.ru	ADV
ijassa-1367	1	12	.	.	PUNCT
ijassa-1367	2	1	piecewise	piecewise	NOUN
ijassa-1367	2	2	constant	constant	ADJ
ijassa-1367	2	3	functions	function	NOUN
ijassa-1367	2	4	in	in	ADP
ijassa-1367	2	5	dynamic	dynamic	ADJ
ijassa-1367	2	6	optimization	optimization	NOUN
ijassa-1367	2	7	problems	problem	NOUN
ijassa-1367	2	8	olga	olga	PROPN
ijassa-1367	2	9	e.	e.	PROPN
ijassa-1367	2	10	orel1	orel1	PROPN
ijassa-1367	2	11	*	*	PROPN
ijassa-1367	2	12	,	,	PUNCT
ijassa-1367	2	13	evgeny	evgeny	PROPN
ijassa-1367	2	14	n.	n.	PROPN
ijassa-1367	2	15	orel2	orel2	PROPN
ijassa-1367	3	1	1moscow	1moscow	NUM
ijassa-1367	3	2	institute	institute	PROPN
ijassa-1367	3	3	of	of	ADP
ijassa-1367	3	4	physics	physics	PROPN
ijassa-1367	3	5	and	and	CCONJ
ijassa-1367	3	6	technology	technology	NOUN
ijassa-1367	3	7	(	(	PUNCT
ijassa-1367	3	8	state	state	NOUN
ijassa-1367	3	9	university	university	NOUN
ijassa-1367	3	10	)	)	PUNCT
ijassa-1367	3	11	,	,	PUNCT
ijassa-1367	3	12	dolgoprudnyi	dolgoprudnyi	PROPN
ijassa-1367	3	13	,	,	PUNCT
ijassa-1367	3	14	russia	russia	PROPN
ijassa-1367	3	15	2financial	2financial	PROPN
ijassa-1367	3	16	university	university	NOUN
ijassa-1367	3	17	under	under	ADP
ijassa-1367	3	18	the	the	DET
ijassa-1367	3	19	government	government	NOUN
ijassa-1367	3	20	of	of	ADP
ijassa-1367	3	21	the	the	DET
ijassa-1367	3	22	russian	russian	PROPN
ijassa-1367	3	23	federation	federation	PROPN
ijassa-1367	3	24	,	,	PUNCT
ijassa-1367	3	25	moscow	moscow	PROPN
ijassa-1367	3	26	,	,	PUNCT
ijassa-1367	3	27	russia	russia	PROPN
ijassa-1367	3	28	abstract	abstract	NOUN
ijassa-1367	3	29	:	:	PUNCT
ijassa-1367	3	30	we	we	PRON
ijassa-1367	3	31	consider	consider	VERB
ijassa-1367	3	32	a	a	DET
ijassa-1367	3	33	direct	direct	ADJ
ijassa-1367	3	34	method	method	NOUN
ijassa-1367	3	35	of	of	ADP
ijassa-1367	3	36	dynamic	dynamic	ADJ
ijassa-1367	3	37	optimization	optimization	NOUN
ijassa-1367	3	38	to	to	PART
ijassa-1367	3	39	approximate	approximate	VERB
ijassa-1367	3	40	the	the	DET
ijassa-1367	3	41	global	global	ADJ
ijassa-1367	3	42	extremum	extremum	NOUN
ijassa-1367	3	43	.	.	PUNCT
ijassa-1367	4	1	this	this	DET
ijassa-1367	4	2	method	method	NOUN
ijassa-1367	4	3	is	be	AUX
ijassa-1367	4	4	based	base	VERB
ijassa-1367	4	5	on	on	ADP
ijassa-1367	4	6	splitting	split	VERB
ijassa-1367	4	7	the	the	DET
ijassa-1367	4	8	state	state	NOUN
ijassa-1367	4	9	space	space	NOUN
ijassa-1367	4	10	into	into	ADP
ijassa-1367	4	11	classes	class	NOUN
ijassa-1367	4	12	(	(	PUNCT
ijassa-1367	4	13	cells	cell	NOUN
ijassa-1367	4	14	)	)	PUNCT
ijassa-1367	4	15	and	and	CCONJ
ijassa-1367	4	16	constructing	construct	VERB
ijassa-1367	4	17	piecewise	piecewise	NOUN
ijassa-1367	4	18	constant	constant	ADJ
ijassa-1367	4	19	functions	function	NOUN
ijassa-1367	4	20	on	on	ADP
ijassa-1367	4	21	the	the	DET
ijassa-1367	4	22	partition	partition	NOUN
ijassa-1367	4	23	.	.	PUNCT
ijassa-1367	5	1	such	such	DET
ijassa-1367	5	2	an	an	DET
ijassa-1367	5	3	approach	approach	NOUN
ijassa-1367	5	4	leads	lead	VERB
ijassa-1367	5	5	to	to	ADP
ijassa-1367	5	6	a	a	DET
ijassa-1367	5	7	generalization	generalization	NOUN
ijassa-1367	5	8	of	of	ADP
ijassa-1367	5	9	the	the	DET
ijassa-1367	5	10	euler	euler	ADJ
ijassa-1367	5	11	polygonal	polygonal	ADJ
ijassa-1367	5	12	method	method	NOUN
ijassa-1367	5	13	and	and	CCONJ
ijassa-1367	5	14	makes	make	VERB
ijassa-1367	5	15	it	it	PRON
ijassa-1367	5	16	possible	possible	ADJ
ijassa-1367	5	17	to	to	PART
ijassa-1367	5	18	use	use	VERB
ijassa-1367	5	19	shortest	short	ADJ
ijassa-1367	5	20	path	path	NOUN
ijassa-1367	5	21	algorithms	algorithm	NOUN
ijassa-1367	5	22	on	on	ADP
ijassa-1367	5	23	graphs	graph	NOUN
ijassa-1367	5	24	.	.	PUNCT
ijassa-1367	6	1	in	in	ADP
ijassa-1367	6	2	the	the	DET
ijassa-1367	6	3	suggested	suggest	VERB
ijassa-1367	6	4	algorithm	algorithm	NOUN
ijassa-1367	6	5	,	,	PUNCT
ijassa-1367	6	6	for	for	ADP
ijassa-1367	6	7	each	each	DET
ijassa-1367	6	8	class	class	NOUN
ijassa-1367	6	9	we	we	PRON
ijassa-1367	6	10	construct	construct	VERB
ijassa-1367	6	11	a	a	DET
ijassa-1367	6	12	path	path	NOUN
ijassa-1367	6	13	from	from	ADP
ijassa-1367	6	14	an	an	DET
ijassa-1367	6	15	initial	initial	ADJ
ijassa-1367	6	16	point	point	NOUN
ijassa-1367	6	17	to	to	ADP
ijassa-1367	6	18	this	this	DET
ijassa-1367	6	19	class	class	NOUN
ijassa-1367	6	20	.	.	PUNCT
ijassa-1367	7	1	note	note	VERB
ijassa-1367	7	2	that	that	SCONJ
ijassa-1367	7	3	the	the	DET
ijassa-1367	7	4	program	program	NOUN
ijassa-1367	7	5	remembers	remember	VERB
ijassa-1367	7	6	only	only	ADV
ijassa-1367	7	7	the	the	DET
ijassa-1367	7	8	terminal	terminal	ADJ
ijassa-1367	7	9	point	point	NOUN
ijassa-1367	7	10	of	of	ADP
ijassa-1367	7	11	the	the	DET
ijassa-1367	7	12	path	path	NOUN
ijassa-1367	7	13	,	,	PUNCT
ijassa-1367	7	14	functional	functional	ADJ
ijassa-1367	7	15	value	value	NOUN
ijassa-1367	7	16	along	along	ADP
ijassa-1367	7	17	the	the	DET
ijassa-1367	7	18	path	path	NOUN
ijassa-1367	7	19	and	and	CCONJ
ijassa-1367	7	20	number	number	NOUN
ijassa-1367	7	21	of	of	ADP
ijassa-1367	7	22	the	the	DET
ijassa-1367	7	23	preceding	precede	VERB
ijassa-1367	7	24	class	class	NOUN
ijassa-1367	7	25	.	.	PUNCT
ijassa-1367	8	1	if	if	SCONJ
ijassa-1367	8	2	one	one	NUM
ijassa-1367	8	3	found	find	VERB
ijassa-1367	8	4	another	another	DET
ijassa-1367	8	5	path	path	NOUN
ijassa-1367	8	6	with	with	ADP
ijassa-1367	8	7	the	the	DET
ijassa-1367	8	8	same	same	ADJ
ijassa-1367	8	9	boundary	boundary	ADJ
ijassa-1367	8	10	conditions	condition	NOUN
ijassa-1367	8	11	but	but	CCONJ
ijassa-1367	8	12	less	less	ADV
ijassa-1367	8	13	functional	functional	ADJ
ijassa-1367	8	14	value	value	NOUN
ijassa-1367	8	15	(	(	PUNCT
ijassa-1367	8	16	for	for	ADP
ijassa-1367	8	17	the	the	DET
ijassa-1367	8	18	minimization	minimization	NOUN
ijassa-1367	8	19	problem	problem	NOUN
ijassa-1367	8	20	)	)	PUNCT
ijassa-1367	8	21	,	,	PUNCT
ijassa-1367	8	22	this	this	DET
ijassa-1367	8	23	path	path	NOUN
ijassa-1367	8	24	would	would	AUX
ijassa-1367	8	25	become	become	VERB
ijassa-1367	8	26	the	the	DET
ijassa-1367	8	27	current	current	ADJ
ijassa-1367	8	28	approximation	approximation	NOUN
ijassa-1367	8	29	.	.	PUNCT
ijassa-1367	9	1	we	we	PRON
ijassa-1367	9	2	prove	prove	VERB
ijassa-1367	9	3	that	that	SCONJ
ijassa-1367	9	4	if	if	SCONJ
ijassa-1367	9	5	the	the	DET
ijassa-1367	9	6	partition	partition	NOUN
ijassa-1367	9	7	is	be	AUX
ijassa-1367	9	8	sufficiently	sufficiently	ADV
ijassa-1367	9	9	small	small	ADJ
ijassa-1367	9	10	,	,	PUNCT
ijassa-1367	9	11	then	then	ADV
ijassa-1367	9	12	,	,	PUNCT
ijassa-1367	9	13	by	by	ADP
ijassa-1367	9	14	using	use	VERB
ijassa-1367	9	15	our	our	PRON
ijassa-1367	9	16	method	method	NOUN
ijassa-1367	9	17	,	,	PUNCT
ijassa-1367	9	18	we	we	PRON
ijassa-1367	9	19	obtain	obtain	VERB
ijassa-1367	9	20	the	the	DET
ijassa-1367	9	21	optimal	optimal	ADJ
ijassa-1367	9	22	polygon	polygon	NOUN
ijassa-1367	9	23	.	.	PUNCT
ijassa-1367	10	1	the	the	DET
ijassa-1367	10	2	suggested	suggest	VERB
ijassa-1367	10	3	approach	approach	NOUN
ijassa-1367	10	4	can	can	AUX
ijassa-1367	10	5	also	also	ADV
ijassa-1367	10	6	be	be	AUX
ijassa-1367	10	7	applied	apply	VERB
ijassa-1367	10	8	to	to	ADP
ijassa-1367	10	9	problems	problem	NOUN
ijassa-1367	10	10	of	of	ADP
ijassa-1367	10	11	dynamic	dynamic	ADJ
ijassa-1367	10	12	optimization	optimization	NOUN
ijassa-1367	10	13	with	with	ADP
ijassa-1367	10	14	incomplete	incomplete	ADJ
ijassa-1367	10	15	information	information	NOUN
ijassa-1367	10	16	(	(	PUNCT
ijassa-1367	10	17	differential	differential	NOUN
ijassa-1367	10	18	games	game	NOUN
ijassa-1367	10	19	,	,	PUNCT
ijassa-1367	10	20	control	control	NOUN
ijassa-1367	10	21	of	of	ADP
ijassa-1367	10	22	systems	system	NOUN
ijassa-1367	10	23	with	with	ADP
ijassa-1367	10	24	unknown	unknown	ADJ
ijassa-1367	10	25	dynamics	dynamic	NOUN
ijassa-1367	10	26	)	)	PUNCT
ijassa-1367	10	27	.	.	PUNCT
ijassa-1367	11	1	in	in	ADP
ijassa-1367	11	2	addition	addition	NOUN
ijassa-1367	11	3	,	,	PUNCT
ijassa-1367	11	4	some	some	DET
ijassa-1367	11	5	results	result	NOUN
ijassa-1367	11	6	of	of	ADP
ijassa-1367	11	7	numerical	numerical	ADJ
ijassa-1367	11	8	solutions	solution	NOUN
ijassa-1367	11	9	of	of	ADP
ijassa-1367	11	10	optimal	optimal	ADJ
ijassa-1367	11	11	control	control	NOUN
ijassa-1367	11	12	problems	problem	NOUN
ijassa-1367	11	13	and	and	CCONJ
ijassa-1367	11	14	differential	differential	NOUN
ijassa-1367	11	15	games	game	NOUN
ijassa-1367	11	16	are	be	AUX
ijassa-1367	11	17	given	give	VERB
ijassa-1367	11	18	.	.	PUNCT
ijassa-1367	12	1	keywords	keyword	NOUN
ijassa-1367	12	2	:	:	PUNCT
ijassa-1367	12	3	global	global	ADJ
ijassa-1367	12	4	extremum	extremum	ADJ
ijassa-1367	12	5	,	,	PUNCT
ijassa-1367	12	6	optimal	optimal	ADJ
ijassa-1367	12	7	control	control	NOUN
ijassa-1367	12	8	,	,	PUNCT
ijassa-1367	12	9	euler	euler	NOUN
ijassa-1367	12	10	polygonal	polygonal	ADJ
ijassa-1367	12	11	method	method	NOUN
ijassa-1367	12	12	,	,	PUNCT
ijassa-1367	12	13	differential	differential	NOUN
ijassa-1367	12	14	games	game	NOUN
ijassa-1367	12	15	,	,	PUNCT
ijassa-1367	12	16	splitting	split	VERB
ijassa-1367	12	17	into	into	ADP
ijassa-1367	12	18	classes	class	NOUN
ijassa-1367	12	19	,	,	PUNCT
ijassa-1367	12	20	piecewise	piecewise	NOUN
ijassa-1367	12	21	constant	constant	ADJ
ijassa-1367	12	22	function	function	NOUN
ijassa-1367	12	23	1	1	NUM
ijassa-1367	12	24	.	.	PUNCT
ijassa-1367	12	25	introduction	introduction	NOUN
ijassa-1367	12	26	in	in	ADP
ijassa-1367	12	27	[	[	X
ijassa-1367	12	28	11	11	NUM
ijassa-1367	12	29	]	]	PUNCT
ijassa-1367	12	30	,	,	PUNCT
ijassa-1367	12	31	[	[	X
ijassa-1367	12	32	12	12	NUM
ijassa-1367	12	33	]	]	PUNCT
ijassa-1367	12	34	,	,	PUNCT
ijassa-1367	12	35	[	[	X
ijassa-1367	12	36	9	9	NUM
ijassa-1367	12	37	]	]	PUNCT
ijassa-1367	12	38	to	to	PART
ijassa-1367	12	39	solve	solve	VERB
ijassa-1367	12	40	optimal	optimal	ADJ
ijassa-1367	12	41	control	control	NOUN
ijassa-1367	12	42	problems	problem	NOUN
ijassa-1367	12	43	we	we	PRON
ijassa-1367	12	44	used	use	VERB
ijassa-1367	12	45	an	an	DET
ijassa-1367	12	46	approach	approach	NOUN
ijassa-1367	12	47	based	base	VERB
ijassa-1367	12	48	on	on	ADP
ijassa-1367	12	49	construction	construction	NOUN
ijassa-1367	12	50	of	of	ADP
ijassa-1367	12	51	piecewise	piecewise	NOUN
ijassa-1367	12	52	constant	constant	ADJ
ijassa-1367	12	53	functions	function	NOUN
ijassa-1367	12	54	that	that	PRON
ijassa-1367	12	55	are	be	AUX
ijassa-1367	12	56	approximations	approximation	NOUN
ijassa-1367	12	57	of	of	ADP
ijassa-1367	12	58	a	a	DET
ijassa-1367	12	59	bellman	bellman	NOUN
ijassa-1367	12	60	function	function	NOUN
ijassa-1367	12	61	b(x	b(x	NOUN
ijassa-1367	12	62	)	)	PUNCT
ijassa-1367	12	63	or	or	CCONJ
ijassa-1367	12	64	a	a	DET
ijassa-1367	12	65	dual	dual	ADJ
ijassa-1367	12	66	function	function	NOUN
ijassa-1367	12	67	a(x	a(x	NOUN
ijassa-1367	12	68	)	)	PUNCT
ijassa-1367	12	69	(	(	PUNCT
ijassa-1367	12	70	i.e.	i.e.	X
ijassa-1367	12	71	,	,	PUNCT
ijassa-1367	12	72	a	a	DET
ijassa-1367	12	73	bellman	bellman	NOUN
ijassa-1367	12	74	function	function	NOUN
ijassa-1367	12	75	with	with	ADP
ijassa-1367	12	76	time	time	NOUN
ijassa-1367	12	77	reversal	reversal	NOUN
ijassa-1367	12	78	)	)	PUNCT
ijassa-1367	12	79	.	.	PUNCT
ijassa-1367	13	1	in	in	ADP
ijassa-1367	13	2	the	the	DET
ijassa-1367	13	3	paper	paper	NOUN
ijassa-1367	13	4	,	,	PUNCT
ijassa-1367	13	5	we	we	PRON
ijassa-1367	13	6	show	show	VERB
ijassa-1367	13	7	that	that	SCONJ
ijassa-1367	13	8	such	such	DET
ijassa-1367	13	9	an	an	DET
ijassa-1367	13	10	approach	approach	NOUN
ijassa-1367	13	11	is	be	AUX
ijassa-1367	13	12	universal	universal	ADJ
ijassa-1367	13	13	and	and	CCONJ
ijassa-1367	13	14	can	can	AUX
ijassa-1367	13	15	be	be	AUX
ijassa-1367	13	16	applied	apply	VERB
ijassa-1367	13	17	to	to	ADP
ijassa-1367	13	18	various	various	ADJ
ijassa-1367	13	19	problems	problem	NOUN
ijassa-1367	13	20	of	of	ADP
ijassa-1367	13	21	dynamic	dynamic	ADJ
ijassa-1367	13	22	optimization	optimization	NOUN
ijassa-1367	13	23	when	when	SCONJ
ijassa-1367	13	24	we	we	PRON
ijassa-1367	13	25	face	face	VERB
ijassa-1367	13	26	different	different	ADJ
ijassa-1367	13	27	types	type	NOUN
ijassa-1367	13	28	of	of	ADP
ijassa-1367	13	29	uncertainty	uncertainty	NOUN
ijassa-1367	13	30	.	.	PUNCT
ijassa-1367	14	1	most	most	ADJ
ijassa-1367	14	2	general	general	ADJ
ijassa-1367	14	3	consideration	consideration	NOUN
ijassa-1367	14	4	of	of	ADP
ijassa-1367	14	5	optimal	optimal	ADJ
ijassa-1367	14	6	control	control	NOUN
ijassa-1367	14	7	problems	problem	NOUN
ijassa-1367	14	8	is	be	AUX
ijassa-1367	14	9	given	give	VERB
ijassa-1367	14	10	in	in	ADP
ijassa-1367	14	11	[	[	X
ijassa-1367	14	12	18	18	NUM
ijassa-1367	14	13	]	]	PUNCT
ijassa-1367	14	14	.	.	PUNCT
ijassa-1367	15	1	to	to	PART
ijassa-1367	15	2	solve	solve	VERB
ijassa-1367	15	3	a	a	DET
ijassa-1367	15	4	particular	particular	ADJ
ijassa-1367	15	5	problem	problem	NOUN
ijassa-1367	15	6	,	,	PUNCT
ijassa-1367	15	7	we	we	PRON
ijassa-1367	15	8	must	must	AUX
ijassa-1367	15	9	split	split	VERB
ijassa-1367	15	10	the	the	DET
ijassa-1367	15	11	state	state	NOUN
ijassa-1367	15	12	space	space	NOUN
ijassa-1367	15	13	into	into	ADP
ijassa-1367	15	14	a	a	DET
ijassa-1367	15	15	finite	finite	ADJ
ijassa-1367	15	16	number	number	NOUN
ijassa-1367	15	17	of	of	ADP
ijassa-1367	15	18	subsets	subset	NOUN
ijassa-1367	15	19	,	,	PUNCT
ijassa-1367	15	20	which	which	PRON
ijassa-1367	15	21	are	be	AUX
ijassa-1367	15	22	called	call	VERB
ijassa-1367	15	23	classes	class	NOUN
ijassa-1367	15	24	,	,	PUNCT
ijassa-1367	15	25	or	or	CCONJ
ijassa-1367	15	26	cells	cell	NOUN
ijassa-1367	15	27	.	.	PUNCT
ijassa-1367	16	1	the	the	DET
ijassa-1367	16	2	space	space	NOUN
ijassa-1367	16	3	of	of	ADP
ijassa-1367	16	4	functions	function	NOUN
ijassa-1367	16	5	that	that	PRON
ijassa-1367	16	6	take	take	VERB
ijassa-1367	16	7	constant	constant	ADJ
ijassa-1367	16	8	values	value	NOUN
ijassa-1367	16	9	on	on	ADP
ijassa-1367	16	10	classes	class	NOUN
ijassa-1367	16	11	is	be	AUX
ijassa-1367	16	12	finite	finite	ADJ
ijassa-1367	16	13	dimensional	dimensional	ADJ
ijassa-1367	16	14	.	.	PUNCT
ijassa-1367	17	1	thus	thus	ADV
ijassa-1367	17	2	the	the	DET
ijassa-1367	17	3	values	value	NOUN
ijassa-1367	17	4	of	of	ADP
ijassa-1367	17	5	the	the	DET
ijassa-1367	17	6	functions	function	NOUN
ijassa-1367	17	7	could	could	AUX
ijassa-1367	17	8	be	be	AUX
ijassa-1367	17	9	computed	compute	VERB
ijassa-1367	17	10	and	and	CCONJ
ijassa-1367	17	11	stored	store	VERB
ijassa-1367	17	12	in	in	ADP
ijassa-1367	17	13	computer	computer	NOUN
ijassa-1367	17	14	memory	memory	NOUN
ijassa-1367	17	15	.	.	PUNCT
ijassa-1367	18	1	splitting	split	VERB
ijassa-1367	18	2	the	the	DET
ijassa-1367	18	3	space	space	NOUN
ijassa-1367	18	4	into	into	ADP
ijassa-1367	18	5	classes	class	NOUN
ijassa-1367	18	6	does	do	AUX
ijassa-1367	18	7	not	not	PART
ijassa-1367	18	8	mean	mean	VERB
ijassa-1367	18	9	that	that	SCONJ
ijassa-1367	18	10	we	we	PRON
ijassa-1367	18	11	impose	impose	VERB
ijassa-1367	18	12	the	the	DET
ijassa-1367	18	13	restriction	restriction	NOUN
ijassa-1367	18	14	to	to	PART
ijassa-1367	18	15	get	get	VERB
ijassa-1367	18	16	into	into	ADP
ijassa-1367	18	17	points	point	NOUN
ijassa-1367	18	18	of	of	ADP
ijassa-1367	18	19	the	the	DET
ijassa-1367	18	20	predetermined	predetermine	VERB
ijassa-1367	18	21	lattice	lattice	NOUN
ijassa-1367	18	22	.	.	PUNCT
ijassa-1367	19	1	our	our	PRON
ijassa-1367	19	2	approach	approach	NOUN
ijassa-1367	19	3	is	be	AUX
ijassa-1367	19	4	a	a	DET
ijassa-1367	19	5	direct	direct	ADJ
ijassa-1367	19	6	method	method	NOUN
ijassa-1367	19	7	and	and	CCONJ
ijassa-1367	19	8	is	be	AUX
ijassa-1367	19	9	not	not	PART
ijassa-1367	19	10	related	relate	VERB
ijassa-1367	19	11	to	to	ADP
ijassa-1367	19	12	necessary	necessary	ADJ
ijassa-1367	19	13	and	and	CCONJ
ijassa-1367	19	14	/	/	SYM
ijassa-1367	19	15	or	or	CCONJ
ijassa-1367	19	16	sufficient	sufficient	ADJ
ijassa-1367	19	17	conditions	condition	NOUN
ijassa-1367	19	18	of	of	ADP
ijassa-1367	19	19	extremum	extremum	NOUN
ijassa-1367	19	20	.	.	PUNCT
ijassa-1367	20	1	sometimes	sometimes	ADV
ijassa-1367	20	2	,	,	PUNCT
ijassa-1367	20	3	the	the	DET
ijassa-1367	20	4	process	process	NOUN
ijassa-1367	20	5	of	of	ADP
ijassa-1367	20	6	search	search	NOUN
ijassa-1367	20	7	and	and	CCONJ
ijassa-1367	20	8	construction	construction	NOUN
ijassa-1367	20	9	of	of	ADP
ijassa-1367	20	10	piecewise	piecewise	NOUN
ijassa-1367	20	11	constant	constant	ADJ
ijassa-1367	20	12	functions	function	NOUN
ijassa-1367	20	13	resembles	resemble	VERB
ijassa-1367	20	14	imitation	imitation	NOUN
ijassa-1367	20	15	modelling	modelling	NOUN
ijassa-1367	20	16	when	when	SCONJ
ijassa-1367	20	17	the	the	DET
ijassa-1367	20	18	scenario	scenario	NOUN
ijassa-1367	20	19	of	of	ADP
ijassa-1367	20	20	future	future	ADJ
ijassa-1367	20	21	behavior	behavior	NOUN
ijassa-1367	20	22	of	of	ADP
ijassa-1367	20	23	the	the	DET
ijassa-1367	20	24	system	system	NOUN
ijassa-1367	20	25	is	be	AUX
ijassa-1367	20	26	played	play	VERB
ijassa-1367	20	27	repeatedly	repeatedly	ADV
ijassa-1367	20	28	.	.	PUNCT
ijassa-1367	21	1	during	during	ADP
ijassa-1367	21	2	this	this	DET
ijassa-1367	21	3	process	process	NOUN
ijassa-1367	21	4	,	,	PUNCT
ijassa-1367	21	5	the	the	DET
ijassa-1367	21	6	behavior	behavior	NOUN
ijassa-1367	21	7	of	of	ADP
ijassa-1367	21	8	the	the	DET
ijassa-1367	21	9	system	system	NOUN
ijassa-1367	21	10	is	be	AUX
ijassa-1367	21	11	being	be	AUX
ijassa-1367	21	12	improved	improve	VERB
ijassa-1367	21	13	step	step	NOUN
ijassa-1367	21	14	-	-	PUNCT
ijassa-1367	21	15	by	by	ADP
ijassa-1367	21	16	-	-	PUNCT
ijassa-1367	21	17	step	step	NOUN
ijassa-1367	21	18	and	and	CCONJ
ijassa-1367	21	19	eventually	eventually	ADV
ijassa-1367	21	20	we	we	PRON
ijassa-1367	21	21	get	get	VERB
ijassa-1367	21	22	a	a	DET
ijassa-1367	21	23	trajectory	trajectory	NOUN
ijassa-1367	21	24	that	that	PRON
ijassa-1367	21	25	approximates	approximate	VERB
ijassa-1367	21	26	the	the	DET
ijassa-1367	21	27	global	global	ADJ
ijassa-1367	21	28	extremum	extremum	NOUN
ijassa-1367	21	29	.	.	PUNCT
ijassa-1367	22	1	to	to	PART
ijassa-1367	22	2	show	show	VERB
ijassa-1367	22	3	the	the	DET
ijassa-1367	22	4	relationship	relationship	NOUN
ijassa-1367	22	5	between	between	ADP
ijassa-1367	22	6	the	the	DET
ijassa-1367	22	7	global	global	ADJ
ijassa-1367	22	8	extremum	extremum	NOUN
ijassa-1367	22	9	and	and	CCONJ
ijassa-1367	22	10	its	its	PRON
ijassa-1367	22	11	approximation	approximation	NOUN
ijassa-1367	22	12	,	,	PUNCT
ijassa-1367	22	13	we	we	PRON
ijassa-1367	22	14	consider	consider	VERB
ijassa-1367	22	15	some	some	DET
ijassa-1367	22	16	well	well	ADV
ijassa-1367	22	17	-	-	PUNCT
ijassa-1367	22	18	known	know	VERB
ijassa-1367	22	19	problems	problem	NOUN
ijassa-1367	22	20	,	,	PUNCT
ijassa-1367	22	21	which	which	PRON
ijassa-1367	22	22	were	be	AUX
ijassa-1367	22	23	investigated	investigate	VERB
ijassa-1367	22	24	earlier	early	ADV
ijassa-1367	22	25	(	(	PUNCT
ijassa-1367	22	26	see	see	VERB
ijassa-1367	22	27	,	,	PUNCT
ijassa-1367	22	28	for	for	ADP
ijassa-1367	22	29	example	example	NOUN
ijassa-1367	22	30	,	,	PUNCT
ijassa-1367	22	31	[	[	X
ijassa-1367	22	32	3	3	NUM
ijassa-1367	22	33	]	]	NUM
ijassa-1367	22	34	)	)	PUNCT
ijassa-1367	22	35	.	.	PUNCT
ijassa-1367	23	1	for	for	ADP
ijassa-1367	23	2	these	these	DET
ijassa-1367	23	3	∗corresponding	∗corresponde	VERB
ijassa-1367	23	4	author	author	NOUN
ijassa-1367	23	5	:	:	PUNCT
ijassa-1367	23	6	orel.oe@phystech.edu	orel.oe@phystech.edu	PROPN
ijassa-1367	23	7	36	36	NUM
ijassa-1367	23	8	o.	o.	PROPN
ijassa-1367	23	9	e.	e.	PROPN
ijassa-1367	23	10	orel	orel	PROPN
ijassa-1367	23	11	,	,	PUNCT
ijassa-1367	23	12	e.	e.	PROPN
ijassa-1367	23	13	n.	n.	PROPN
ijassa-1367	23	14	orel	orel	PROPN
ijassa-1367	23	15	problems	problem	NOUN
ijassa-1367	23	16	,	,	PUNCT
ijassa-1367	23	17	the	the	DET
ijassa-1367	23	18	detailed	detailed	ADJ
ijassa-1367	23	19	study	study	NOUN
ijassa-1367	23	20	of	of	ADP
ijassa-1367	23	21	various	various	ADJ
ijassa-1367	23	22	characteristic	characteristic	NOUN
ijassa-1367	23	23	of	of	ADP
ijassa-1367	23	24	switching	switch	VERB
ijassa-1367	23	25	surfaces	surface	NOUN
ijassa-1367	23	26	,	,	PUNCT
ijassa-1367	23	27	universal	universal	ADJ
ijassa-1367	23	28	and	and	CCONJ
ijassa-1367	23	29	equivocal	equivocal	ADJ
ijassa-1367	23	30	surfaces	surface	NOUN
ijassa-1367	23	31	,	,	PUNCT
ijassa-1367	23	32	barriers	barrier	NOUN
ijassa-1367	23	33	,	,	PUNCT
ijassa-1367	23	34	etc	etc	X
ijassa-1367	23	35	.	.	X
ijassa-1367	23	36	was	be	AUX
ijassa-1367	23	37	carried	carry	VERB
ijassa-1367	23	38	out	out	ADP
ijassa-1367	23	39	.	.	PUNCT
ijassa-1367	24	1	however	however	ADV
ijassa-1367	24	2	,	,	PUNCT
ijassa-1367	24	3	sometimes	sometimes	ADV
ijassa-1367	24	4	the	the	DET
ijassa-1367	24	5	solution	solution	NOUN
ijassa-1367	24	6	was	be	AUX
ijassa-1367	24	7	not	not	PART
ijassa-1367	24	8	complete	complete	ADJ
ijassa-1367	24	9	.	.	PUNCT
ijassa-1367	25	1	in	in	ADP
ijassa-1367	25	2	what	what	PRON
ijassa-1367	25	3	follows	follow	VERB
ijassa-1367	25	4	,	,	PUNCT
ijassa-1367	25	5	we	we	PRON
ijassa-1367	25	6	will	will	AUX
ijassa-1367	25	7	compare	compare	VERB
ijassa-1367	25	8	the	the	DET
ijassa-1367	25	9	results	result	NOUN
ijassa-1367	25	10	achieved	achieve	VERB
ijassa-1367	25	11	by	by	ADP
ijassa-1367	25	12	analytic	analytic	ADJ
ijassa-1367	25	13	and	and	CCONJ
ijassa-1367	25	14	numerical	numerical	ADJ
ijassa-1367	25	15	methods	method	NOUN
ijassa-1367	25	16	and	and	CCONJ
ijassa-1367	25	17	establish	establish	VERB
ijassa-1367	25	18	the	the	DET
ijassa-1367	25	19	approximate	approximate	ADJ
ijassa-1367	25	20	boundaries	boundary	NOUN
ijassa-1367	25	21	of	of	ADP
ijassa-1367	25	22	their	their	PRON
ijassa-1367	25	23	applications	application	NOUN
ijassa-1367	25	24	.	.	PUNCT
ijassa-1367	26	1	the	the	DET
ijassa-1367	26	2	suggested	suggest	VERB
ijassa-1367	26	3	approach	approach	NOUN
ijassa-1367	26	4	enables	enable	VERB
ijassa-1367	26	5	to	to	PART
ijassa-1367	26	6	avoid	avoid	VERB
ijassa-1367	26	7	use	use	NOUN
ijassa-1367	26	8	of	of	ADP
ijassa-1367	26	9	moiseev	moiseev	ADJ
ijassa-1367	26	10	“	"	PUNCT
ijassa-1367	26	11	elementary	elementary	ADJ
ijassa-1367	26	12	operation	operation	NOUN
ijassa-1367	26	13	”	"	PUNCT
ijassa-1367	26	14	due	due	ADP
ijassa-1367	26	15	to	to	ADP
ijassa-1367	26	16	moving	move	VERB
ijassa-1367	26	17	from	from	ADP
ijassa-1367	26	18	cell	cell	NOUN
ijassa-1367	26	19	to	to	ADP
ijassa-1367	26	20	cell	cell	NOUN
ijassa-1367	26	21	rather	rather	ADV
ijassa-1367	26	22	than	than	ADP
ijassa-1367	26	23	from	from	ADP
ijassa-1367	26	24	point	point	NOUN
ijassa-1367	26	25	to	to	ADP
ijassa-1367	26	26	point	point	NOUN
ijassa-1367	26	27	(	(	PUNCT
ijassa-1367	26	28	for	for	ADP
ijassa-1367	26	29	example	example	NOUN
ijassa-1367	26	30	,	,	PUNCT
ijassa-1367	26	31	vertices	vertex	NOUN
ijassa-1367	26	32	of	of	ADP
ijassa-1367	26	33	a	a	DET
ijassa-1367	26	34	lattice	lattice	NOUN
ijassa-1367	26	35	)	)	PUNCT
ijassa-1367	26	36	.	.	PUNCT
ijassa-1367	27	1	the	the	DET
ijassa-1367	27	2	method	method	NOUN
ijassa-1367	27	3	of	of	ADP
ijassa-1367	27	4	piecewise	piecewise	NOUN
ijassa-1367	27	5	constant	constant	ADJ
ijassa-1367	27	6	functions	function	NOUN
ijassa-1367	27	7	originates	originate	NOUN
ijassa-1367	27	8	from	from	ADP
ijassa-1367	27	9	the	the	DET
ijassa-1367	27	10	euler	euler	ADJ
ijassa-1367	27	11	polygonal	polygonal	ADJ
ijassa-1367	27	12	method	method	NOUN
ijassa-1367	27	13	,	,	PUNCT
ijassa-1367	27	14	with	with	ADP
ijassa-1367	27	15	which	which	PRON
ijassa-1367	27	16	we	we	PRON
ijassa-1367	27	17	start	start	VERB
ijassa-1367	27	18	.	.	PUNCT
ijassa-1367	28	1	the	the	DET
ijassa-1367	28	2	euler	euler	PROPN
ijassa-1367	28	3	polygonal	polygonal	ADJ
ijassa-1367	28	4	method	method	NOUN
ijassa-1367	28	5	plays	play	VERB
ijassa-1367	28	6	an	an	DET
ijassa-1367	28	7	important	important	ADJ
ijassa-1367	28	8	role	role	NOUN
ijassa-1367	28	9	not	not	PART
ijassa-1367	28	10	only	only	ADV
ijassa-1367	28	11	in	in	ADP
ijassa-1367	28	12	the	the	DET
ijassa-1367	28	13	applied	apply	VERB
ijassa-1367	28	14	but	but	CCONJ
ijassa-1367	28	15	also	also	ADV
ijassa-1367	28	16	in	in	ADP
ijassa-1367	28	17	the	the	DET
ijassa-1367	28	18	pure	pure	ADJ
ijassa-1367	28	19	mathematics	mathematic	NOUN
ijassa-1367	28	20	[	[	X
ijassa-1367	28	21	2	2	NUM
ijassa-1367	28	22	]	]	PUNCT
ijassa-1367	28	23	:	:	PUNCT
ijassa-1367	28	24	it	it	PRON
ijassa-1367	28	25	is	be	AUX
ijassa-1367	28	26	used	use	VERB
ijassa-1367	28	27	to	to	PART
ijassa-1367	28	28	solve	solve	VERB
ijassa-1367	28	29	differential	differential	ADJ
ijassa-1367	28	30	equations	equation	NOUN
ijassa-1367	28	31	as	as	ADV
ijassa-1367	28	32	well	well	ADV
ijassa-1367	28	33	as	as	ADP
ijassa-1367	28	34	to	to	PART
ijassa-1367	28	35	derive	derive	VERB
ijassa-1367	28	36	euler	euler	NOUN
ijassa-1367	28	37	–	–	PUNCT
ijassa-1367	28	38	lagrange	lagrange	NOUN
ijassa-1367	28	39	equation	equation	NOUN
ijassa-1367	28	40	and	and	CCONJ
ijassa-1367	28	41	to	to	PART
ijassa-1367	28	42	prove	prove	VERB
ijassa-1367	28	43	the	the	DET
ijassa-1367	28	44	existence	existence	NOUN
ijassa-1367	28	45	theorem	theorem	VERB
ijassa-1367	28	46	in	in	ADP
ijassa-1367	28	47	the	the	DET
ijassa-1367	28	48	calculus	calculus	NOUN
ijassa-1367	28	49	of	of	ADP
ijassa-1367	28	50	variations	variation	NOUN
ijassa-1367	28	51	.	.	PUNCT
ijassa-1367	29	1	in	in	ADP
ijassa-1367	29	2	the	the	DET
ijassa-1367	29	3	paper	paper	NOUN
ijassa-1367	29	4	,	,	PUNCT
ijassa-1367	29	5	we	we	PRON
ijassa-1367	29	6	consider	consider	VERB
ijassa-1367	29	7	the	the	DET
ijassa-1367	29	8	application	application	NOUN
ijassa-1367	29	9	of	of	ADP
ijassa-1367	29	10	the	the	DET
ijassa-1367	29	11	euler	euler	ADJ
ijassa-1367	29	12	polygonal	polygonal	ADJ
ijassa-1367	29	13	method	method	NOUN
ijassa-1367	29	14	to	to	ADP
ijassa-1367	29	15	numerical	numerical	ADJ
ijassa-1367	29	16	solution	solution	NOUN
ijassa-1367	29	17	of	of	ADP
ijassa-1367	29	18	a	a	DET
ijassa-1367	29	19	variational	variational	ADJ
ijassa-1367	29	20	problem	problem	NOUN
ijassa-1367	29	21	.	.	PUNCT
ijassa-1367	30	1	as	as	ADP
ijassa-1367	30	2	a	a	DET
ijassa-1367	30	3	result	result	NOUN
ijassa-1367	30	4	we	we	PRON
ijassa-1367	30	5	can	can	AUX
ijassa-1367	30	6	see	see	VERB
ijassa-1367	30	7	that	that	SCONJ
ijassa-1367	30	8	the	the	DET
ijassa-1367	30	9	algorithm	algorithm	NOUN
ijassa-1367	30	10	constructs	construct	VERB
ijassa-1367	30	11	not	not	PART
ijassa-1367	30	12	only	only	ADV
ijassa-1367	30	13	a	a	DET
ijassa-1367	30	14	unique	unique	ADJ
ijassa-1367	30	15	polygonal	polygonal	ADJ
ijassa-1367	30	16	line	line	NOUN
ijassa-1367	30	17	,	,	PUNCT
ijassa-1367	30	18	but	but	CCONJ
ijassa-1367	30	19	also	also	ADV
ijassa-1367	30	20	a	a	DET
ijassa-1367	30	21	family	family	NOUN
ijassa-1367	30	22	of	of	ADP
ijassa-1367	30	23	such	such	ADJ
ijassa-1367	30	24	lines	line	NOUN
ijassa-1367	30	25	that	that	PRON
ijassa-1367	30	26	form	form	VERB
ijassa-1367	30	27	a	a	DET
ijassa-1367	30	28	discrete	discrete	ADJ
ijassa-1367	30	29	central	central	ADJ
ijassa-1367	30	30	field	field	NOUN
ijassa-1367	30	31	of	of	ADP
ijassa-1367	30	32	curves	curve	NOUN
ijassa-1367	30	33	.	.	PUNCT
ijassa-1367	31	1	each	each	DET
ijassa-1367	31	2	curve	curve	NOUN
ijassa-1367	31	3	consists	consist	VERB
ijassa-1367	31	4	of	of	ADP
ijassa-1367	31	5	segments	segment	NOUN
ijassa-1367	31	6	with	with	ADP
ijassa-1367	31	7	constant	constant	ADJ
ijassa-1367	31	8	slopes	slope	NOUN
ijassa-1367	31	9	.	.	PUNCT
ijassa-1367	32	1	in	in	ADP
ijassa-1367	32	2	the	the	DET
ijassa-1367	32	3	optimal	optimal	ADJ
ijassa-1367	32	4	control	control	NOUN
ijassa-1367	32	5	problems	problem	NOUN
ijassa-1367	32	6	,	,	PUNCT
ijassa-1367	32	7	by	by	ADP
ijassa-1367	32	8	a	a	DET
ijassa-1367	32	9	polygonal	polygonal	ADJ
ijassa-1367	32	10	line	line	NOUN
ijassa-1367	32	11	we	we	PRON
ijassa-1367	32	12	mean	mean	VERB
ijassa-1367	32	13	a	a	DET
ijassa-1367	32	14	trajectory	trajectory	NOUN
ijassa-1367	32	15	with	with	ADP
ijassa-1367	32	16	a	a	DET
ijassa-1367	32	17	piecewise	piecewise	NOUN
ijassa-1367	32	18	constant	constant	ADJ
ijassa-1367	32	19	control	control	NOUN
ijassa-1367	32	20	.	.	PUNCT
ijassa-1367	33	1	we	we	PRON
ijassa-1367	33	2	also	also	ADV
ijassa-1367	33	3	consider	consider	VERB
ijassa-1367	33	4	differential	differential	ADJ
ijassa-1367	33	5	games	game	NOUN
ijassa-1367	33	6	and	and	CCONJ
ijassa-1367	33	7	survival	survival	NOUN
ijassa-1367	33	8	problems	problem	NOUN
ijassa-1367	33	9	with	with	ADP
ijassa-1367	33	10	unknown	unknown	ADJ
ijassa-1367	33	11	dynamics	dynamic	NOUN
ijassa-1367	33	12	.	.	PUNCT
ijassa-1367	34	1	to	to	PART
ijassa-1367	34	2	construct	construct	VERB
ijassa-1367	34	3	piecewise	piecewise	NOUN
ijassa-1367	34	4	defined	define	VERB
ijassa-1367	34	5	functions	function	NOUN
ijassa-1367	34	6	,	,	PUNCT
ijassa-1367	34	7	we	we	PRON
ijassa-1367	34	8	can	can	AUX
ijassa-1367	34	9	choose	choose	VERB
ijassa-1367	34	10	various	various	ADJ
ijassa-1367	34	11	approaches	approach	NOUN
ijassa-1367	34	12	,	,	PUNCT
ijassa-1367	34	13	which	which	PRON
ijassa-1367	34	14	depend	depend	VERB
ijassa-1367	34	15	on	on	ADP
ijassa-1367	34	16	a	a	DET
ijassa-1367	34	17	particular	particular	ADJ
ijassa-1367	34	18	problem	problem	NOUN
ijassa-1367	34	19	.	.	PUNCT
ijassa-1367	35	1	the	the	DET
ijassa-1367	35	2	initial	initial	ADJ
ijassa-1367	35	3	points	point	NOUN
ijassa-1367	35	4	at	at	ADP
ijassa-1367	35	5	the	the	DET
ijassa-1367	35	6	self	self	NOUN
ijassa-1367	35	7	-	-	PUNCT
ijassa-1367	35	8	learning	learn	VERB
ijassa-1367	35	9	stage	stage	NOUN
ijassa-1367	35	10	could	could	AUX
ijassa-1367	35	11	be	be	AUX
ijassa-1367	35	12	chosen	choose	VERB
ijassa-1367	35	13	systematically	systematically	ADV
ijassa-1367	35	14	or	or	CCONJ
ijassa-1367	35	15	at	at	ADP
ijassa-1367	35	16	random	random	ADJ
ijassa-1367	35	17	,	,	PUNCT
ijassa-1367	35	18	the	the	DET
ijassa-1367	35	19	process	process	NOUN
ijassa-1367	35	20	could	could	AUX
ijassa-1367	35	21	start	start	VERB
ijassa-1367	35	22	with	with	ADP
ijassa-1367	35	23	a	a	DET
ijassa-1367	35	24	minorant	minorant	NOUN
ijassa-1367	35	25	[	[	X
ijassa-1367	35	26	14	14	NUM
ijassa-1367	35	27	]	]	PUNCT
ijassa-1367	35	28	or	or	CCONJ
ijassa-1367	35	29	with	with	ADP
ijassa-1367	35	30	a	a	DET
ijassa-1367	35	31	majorant	majorant	NOUN
ijassa-1367	35	32	of	of	ADP
ijassa-1367	35	33	the	the	DET
ijassa-1367	35	34	bellman	bellman	NOUN
ijassa-1367	35	35	function	function	NOUN
ijassa-1367	35	36	.	.	PUNCT
ijassa-1367	36	1	one	one	PRON
ijassa-1367	36	2	can	can	AUX
ijassa-1367	36	3	proceed	proceed	VERB
ijassa-1367	36	4	with	with	ADP
ijassa-1367	36	5	the	the	DET
ijassa-1367	36	6	breadth	breadth	NOUN
ijassa-1367	36	7	-	-	PUNCT
ijassa-1367	36	8	first	first	ADJ
ijassa-1367	36	9	or	or	CCONJ
ijassa-1367	36	10	depth	depth	NOUN
ijassa-1367	36	11	-	-	PUNCT
ijassa-1367	36	12	first	first	ADV
ijassa-1367	36	13	backtracking	backtrack	VERB
ijassa-1367	36	14	search	search	NOUN
ijassa-1367	36	15	[	[	X
ijassa-1367	36	16	10	10	NUM
ijassa-1367	36	17	]	]	PUNCT
ijassa-1367	36	18	,	,	PUNCT
ijassa-1367	36	19	[	[	X
ijassa-1367	36	20	15	15	NUM
ijassa-1367	36	21	]	]	PUNCT
ijassa-1367	36	22	.	.	PUNCT
ijassa-1367	37	1	finally	finally	ADV
ijassa-1367	37	2	,	,	PUNCT
ijassa-1367	37	3	in	in	ADP
ijassa-1367	37	4	the	the	DET
ijassa-1367	37	5	problems	problem	NOUN
ijassa-1367	37	6	with	with	ADP
ijassa-1367	37	7	incomplete	incomplete	ADJ
ijassa-1367	37	8	information	information	NOUN
ijassa-1367	37	9	on	on	ADP
ijassa-1367	37	10	phase	phase	NOUN
ijassa-1367	37	11	limitations	limitation	NOUN
ijassa-1367	37	12	,	,	PUNCT
ijassa-1367	37	13	one	one	PRON
ijassa-1367	37	14	can	can	AUX
ijassa-1367	37	15	use	use	VERB
ijassa-1367	37	16	a	a	DET
ijassa-1367	37	17	heuristic	heuristic	ADJ
ijassa-1367	37	18	function	function	NOUN
ijassa-1367	37	19	to	to	PART
ijassa-1367	37	20	speed	speed	VERB
ijassa-1367	37	21	up	up	ADP
ijassa-1367	37	22	the	the	DET
ijassa-1367	37	23	process	process	NOUN
ijassa-1367	37	24	.	.	PUNCT
ijassa-1367	38	1	the	the	DET
ijassa-1367	38	2	algorithms	algorithm	NOUN
ijassa-1367	38	3	and	and	CCONJ
ijassa-1367	38	4	programs	program	NOUN
ijassa-1367	38	5	are	be	AUX
ijassa-1367	38	6	demonstrated	demonstrate	VERB
ijassa-1367	38	7	on	on	ADP
ijassa-1367	38	8	the	the	DET
ijassa-1367	38	9	base	base	NOUN
ijassa-1367	38	10	of	of	ADP
ijassa-1367	38	11	a	a	DET
ijassa-1367	38	12	pseudocode	pseudocode	NOUN
ijassa-1367	38	13	that	that	PRON
ijassa-1367	38	14	is	be	AUX
ijassa-1367	38	15	not	not	PART
ijassa-1367	38	16	completely	completely	ADV
ijassa-1367	38	17	formalized	formalize	VERB
ijassa-1367	38	18	pdl	pdl	NOUN
ijassa-1367	38	19	(	(	PUNCT
ijassa-1367	38	20	program	program	NOUN
ijassa-1367	38	21	design	design	NOUN
ijassa-1367	38	22	language	language	NOUN
ijassa-1367	38	23	)	)	PUNCT
ijassa-1367	38	24	,	,	PUNCT
ijassa-1367	38	25	where	where	SCONJ
ijassa-1367	38	26	we	we	PRON
ijassa-1367	38	27	use	use	VERB
ijassa-1367	38	28	elements	element	NOUN
ijassa-1367	38	29	of	of	ADP
ijassa-1367	38	30	pascal	pascal	NOUN
ijassa-1367	38	31	.	.	PUNCT
ijassa-1367	39	1	2	2	X
ijassa-1367	39	2	.	.	X
ijassa-1367	39	3	euler	euler	NOUN
ijassa-1367	39	4	field	field	NOUN
ijassa-1367	39	5	of	of	ADP
ijassa-1367	39	6	optimal	optimal	ADJ
ijassa-1367	39	7	polygonal	polygonal	ADJ
ijassa-1367	39	8	lines	line	NOUN
ijassa-1367	39	9	consider	consider	VERB
ijassa-1367	39	10	the	the	DET
ijassa-1367	39	11	variational	variational	ADJ
ijassa-1367	39	12	problem	problem	NOUN
ijassa-1367	39	13	j(x	j(x	PROPN
ijassa-1367	39	14	(	(	PUNCT
ijassa-1367	39	15	.	.	PUNCT
ijassa-1367	39	16	)	)	PUNCT
ijassa-1367	39	17	)	)	PUNCT
ijassa-1367	40	1	=	=	SYM
ijassa-1367	40	2	∫	∫	PROPN
ijassa-1367	40	3	t1	t1	PROPN
ijassa-1367	40	4	t0	t0	PROPN
ijassa-1367	40	5	l(t	l(t	PROPN
ijassa-1367	40	6	,	,	PUNCT
ijassa-1367	40	7	x(t	x(t	PROPN
ijassa-1367	40	8	)	)	PUNCT
ijassa-1367	40	9	,	,	PUNCT
ijassa-1367	40	10	ẋ(t)dt	ẋ(t)dt	PROPN
ijassa-1367	40	11	→	→	SYM
ijassa-1367	40	12	min	min	PROPN
ijassa-1367	40	13	,	,	PUNCT
ijassa-1367	40	14	t0	t0	PROPN
ijassa-1367	40	15	<	<	X
ijassa-1367	40	16	t1	t1	PROPN
ijassa-1367	40	17	,	,	PUNCT
ijassa-1367	40	18	x(t0	x(t0	PROPN
ijassa-1367	40	19	)	)	PUNCT
ijassa-1367	41	1	=	=	SYM
ijassa-1367	41	2	x0	x0	PROPN
ijassa-1367	41	3	,	,	PUNCT
ijassa-1367	41	4	x(t1	x(t1	X
ijassa-1367	41	5	)	)	PUNCT
ijassa-1367	42	1	=	=	SYM
ijassa-1367	42	2	x1	x1	PROPN
ijassa-1367	42	3	(	(	PUNCT
ijassa-1367	42	4	for	for	ADP
ijassa-1367	42	5	simplicity	simplicity	NOUN
ijassa-1367	42	6	,	,	PUNCT
ijassa-1367	42	7	we	we	PRON
ijassa-1367	42	8	consider	consider	VERB
ijassa-1367	42	9	one	one	NUM
ijassa-1367	42	10	-	-	PUNCT
ijassa-1367	42	11	dimensional	dimensional	ADJ
ijassa-1367	42	12	case	case	NOUN
ijassa-1367	42	13	,	,	PUNCT
ijassa-1367	42	14	however	however	ADV
ijassa-1367	42	15	all	all	DET
ijassa-1367	42	16	the	the	DET
ijassa-1367	42	17	results	result	NOUN
ijassa-1367	42	18	can	can	AUX
ijassa-1367	42	19	easily	easily	ADV
ijassa-1367	42	20	be	be	AUX
ijassa-1367	42	21	generalized	generalize	VERB
ijassa-1367	42	22	to	to	ADP
ijassa-1367	42	23	the	the	DET
ijassa-1367	42	24	case	case	NOUN
ijassa-1367	42	25	x	x	X
ijassa-1367	42	26	∈	∈	PROPN
ijassa-1367	42	27	rn	rn	PROPN
ijassa-1367	42	28	)	)	PUNCT
ijassa-1367	42	29	.	.	PUNCT
ijassa-1367	43	1	to	to	PART
ijassa-1367	43	2	construct	construct	VERB
ijassa-1367	43	3	polygonal	polygonal	ADJ
ijassa-1367	43	4	lines	line	NOUN
ijassa-1367	43	5	,	,	PUNCT
ijassa-1367	43	6	we	we	PRON
ijassa-1367	43	7	divide	divide	VERB
ijassa-1367	43	8	the	the	DET
ijassa-1367	43	9	time	time	NOUN
ijassa-1367	43	10	the	the	DET
ijassa-1367	43	11	segment	segment	NOUN
ijassa-1367	43	12	[	[	X
ijassa-1367	43	13	t0	t0	NOUN
ijassa-1367	43	14	,	,	PUNCT
ijassa-1367	43	15	t1	t1	PROPN
ijassa-1367	43	16	]	]	PUNCT
ijassa-1367	43	17	into	into	ADP
ijassa-1367	43	18	m	m	PROPN
ijassa-1367	43	19	equal	equal	ADJ
ijassa-1367	43	20	parts	part	NOUN
ijassa-1367	43	21	and	and	CCONJ
ijassa-1367	43	22	pick	pick	VERB
ijassa-1367	43	23	n	n	PRON
ijassa-1367	43	24	points	point	NOUN
ijassa-1367	43	25	with	with	ADP
ijassa-1367	43	26	a	a	DET
ijassa-1367	43	27	fixed	fix	VERB
ijassa-1367	43	28	step	step	NOUN
ijassa-1367	43	29	on	on	ADP
ijassa-1367	43	30	the	the	DET
ijassa-1367	43	31	ox	ox	NOUN
ijassa-1367	43	32	-	-	NOUN
ijassa-1367	43	33	axis	axis	NOUN
ijassa-1367	43	34	.	.	PUNCT
ijassa-1367	44	1	thus	thus	ADV
ijassa-1367	44	2	a	a	DET
ijassa-1367	44	3	regular	regular	ADJ
ijassa-1367	44	4	lattice	lattice	NOUN
ijassa-1367	44	5	(	(	PUNCT
ijassa-1367	44	6	τi	τi	PROPN
ijassa-1367	44	7	,	,	PUNCT
ijassa-1367	44	8	xj	xj	NOUN
ijassa-1367	44	9	)	)	PUNCT
ijassa-1367	44	10	appears	appear	VERB
ijassa-1367	44	11	in	in	ADP
ijassa-1367	44	12	the	the	DET
ijassa-1367	44	13	plane	plane	NOUN
ijassa-1367	44	14	.	.	PUNCT
ijassa-1367	45	1	after	after	ADP
ijassa-1367	45	2	that	that	PRON
ijassa-1367	45	3	we	we	PRON
ijassa-1367	45	4	join	join	VERB
ijassa-1367	45	5	the	the	DET
ijassa-1367	45	6	nodes	node	NOUN
ijassa-1367	45	7	of	of	ADP
ijassa-1367	45	8	the	the	DET
ijassa-1367	45	9	lattice	lattice	NOUN
ijassa-1367	45	10	located	locate	VERB
ijassa-1367	45	11	at	at	ADP
ijassa-1367	45	12	the	the	DET
ijassa-1367	45	13	neighboring	neighboring	NOUN
ijassa-1367	45	14	verticals	vertical	NOUN
ijassa-1367	45	15	by	by	ADP
ijassa-1367	45	16	segments	segment	NOUN
ijassa-1367	45	17	and	and	CCONJ
ijassa-1367	45	18	look	look	VERB
ijassa-1367	45	19	for	for	ADP
ijassa-1367	45	20	the	the	DET
ijassa-1367	45	21	least	least	ADJ
ijassa-1367	45	22	-	-	PUNCT
ijassa-1367	45	23	cost	cost	NOUN
ijassa-1367	45	24	path	path	NOUN
ijassa-1367	45	25	on	on	ADP
ijassa-1367	45	26	this	this	DET
ijassa-1367	45	27	graph	graph	NOUN
ijassa-1367	45	28	,	,	PUNCT
ijassa-1367	45	29	which	which	PRON
ijassa-1367	45	30	has	have	VERB
ijassa-1367	45	31	about	about	ADP
ijassa-1367	45	32	mn	mn	PROPN
ijassa-1367	45	33	nodes	node	NOUN
ijassa-1367	45	34	.	.	PUNCT
ijassa-1367	46	1	computation	computation	NOUN
ijassa-1367	46	2	of	of	ADP
ijassa-1367	46	3	labels	label	NOUN
ijassa-1367	46	4	of	of	ADP
ijassa-1367	46	5	nodes	node	NOUN
ijassa-1367	46	6	goes	go	VERB
ijassa-1367	46	7	from	from	ADP
ijassa-1367	46	8	left	left	NOUN
ijassa-1367	46	9	to	to	ADP
ijassa-1367	46	10	right	right	NOUN
ijassa-1367	46	11	,	,	PUNCT
ijassa-1367	46	12	so	so	CCONJ
ijassa-1367	46	13	it	it	PRON
ijassa-1367	46	14	takes	take	VERB
ijassa-1367	46	15	mn2	mn2	ADJ
ijassa-1367	46	16	macro	macro	ADJ
ijassa-1367	46	17	operations	operation	NOUN
ijassa-1367	46	18	to	to	PART
ijassa-1367	46	19	solve	solve	VERB
ijassa-1367	46	20	the	the	DET
ijassa-1367	46	21	problem	problem	NOUN
ijassa-1367	46	22	.	.	PUNCT
ijassa-1367	47	1	at	at	ADP
ijassa-1367	47	2	the	the	DET
ijassa-1367	47	3	same	same	ADJ
ijassa-1367	47	4	time	time	NOUN
ijassa-1367	47	5	we	we	PRON
ijassa-1367	47	6	construct	construct	VERB
ijassa-1367	47	7	the	the	DET
ijassa-1367	47	8	function	function	NOUN
ijassa-1367	47	9	a	a	DET
ijassa-1367	47	10	(	(	PUNCT
ijassa-1367	47	11	τi	τi	PROPN
ijassa-1367	47	12	,	,	PUNCT
ijassa-1367	47	13	xj	xj	NOUN
ijassa-1367	47	14	)	)	PUNCT
ijassa-1367	47	15	that	that	PRON
ijassa-1367	47	16	is	be	AUX
ijassa-1367	47	17	defined	define	VERB
ijassa-1367	47	18	on	on	ADP
ijassa-1367	47	19	the	the	DET
ijassa-1367	47	20	nodes	node	NOUN
ijassa-1367	47	21	of	of	ADP
ijassa-1367	47	22	the	the	DET
ijassa-1367	47	23	lattice	lattice	NOUN
ijassa-1367	47	24	and	and	CCONJ
ijassa-1367	47	25	is	be	AUX
ijassa-1367	47	26	equal	equal	ADJ
ijassa-1367	47	27	to	to	ADP
ijassa-1367	47	28	the	the	DET
ijassa-1367	47	29	minimum	minimum	ADJ
ijassa-1367	47	30	cost	cost	NOUN
ijassa-1367	47	31	of	of	ADP
ijassa-1367	47	32	a	a	DET
ijassa-1367	47	33	polygonal	polygonal	ADJ
ijassa-1367	47	34	line	line	NOUN
ijassa-1367	47	35	passing	pass	VERB
ijassa-1367	47	36	from	from	ADP
ijassa-1367	47	37	the	the	DET
ijassa-1367	47	38	initial	initial	ADJ
ijassa-1367	47	39	point	point	NOUN
ijassa-1367	47	40	to	to	ADP
ijassa-1367	47	41	the	the	DET
ijassa-1367	47	42	current	current	ADJ
ijassa-1367	47	43	node	node	NOUN
ijassa-1367	47	44	.	.	PUNCT
ijassa-1367	48	1	actually	actually	ADV
ijassa-1367	48	2	,	,	PUNCT
ijassa-1367	48	3	the	the	DET
ijassa-1367	48	4	algorithm	algorithm	NOUN
ijassa-1367	48	5	provides	provide	VERB
ijassa-1367	48	6	not	not	PART
ijassa-1367	48	7	only	only	ADV
ijassa-1367	48	8	one	one	NUM
ijassa-1367	48	9	trajectory	trajectory	NOUN
ijassa-1367	48	10	,	,	PUNCT
ijassa-1367	48	11	but	but	CCONJ
ijassa-1367	48	12	rather	rather	ADV
ijassa-1367	48	13	a	a	DET
ijassa-1367	48	14	discrete	discrete	ADJ
ijassa-1367	48	15	central	central	ADJ
ijassa-1367	48	16	field	field	NOUN
ijassa-1367	48	17	of	of	ADP
ijassa-1367	48	18	euler	euler	NOUN
ijassa-1367	48	19	optimal	optimal	ADJ
ijassa-1367	48	20	polygonal	polygonal	ADJ
ijassa-1367	48	21	lines	line	NOUN
ijassa-1367	48	22	,	,	PUNCT
ijassa-1367	48	23	starting	start	VERB
ijassa-1367	48	24	at	at	ADP
ijassa-1367	48	25	(	(	PUNCT
ijassa-1367	48	26	t0	t0	PROPN
ijassa-1367	48	27	,	,	PUNCT
ijassa-1367	48	28	x0	x0	PROPN
ijassa-1367	48	29	)	)	PUNCT
ijassa-1367	48	30	and	and	CCONJ
ijassa-1367	48	31	terminating	terminate	VERB
ijassa-1367	48	32	at	at	ADP
ijassa-1367	48	33	all	all	DET
ijassa-1367	48	34	other	other	ADJ
ijassa-1367	48	35	nodes	node	NOUN
ijassa-1367	48	36	of	of	ADP
ijassa-1367	48	37	the	the	DET
ijassa-1367	48	38	lattice	lattice	NOUN
ijassa-1367	48	39	,	,	PUNCT
ijassa-1367	48	40	i.e.	i.e.	X
ijassa-1367	48	41	,	,	PUNCT
ijassa-1367	48	42	the	the	DET
ijassa-1367	48	43	optimal	optimal	ADJ
ijassa-1367	48	44	motion	motion	NOUN
ijassa-1367	48	45	is	be	AUX
ijassa-1367	48	46	imitated	imitate	VERB
ijassa-1367	48	47	repeatedly	repeatedly	ADV
ijassa-1367	48	48	.	.	PUNCT
ijassa-1367	49	1	the	the	DET
ijassa-1367	49	2	last	last	ADJ
ijassa-1367	49	3	circumstance	circumstance	NOUN
ijassa-1367	49	4	is	be	AUX
ijassa-1367	49	5	very	very	ADV
ijassa-1367	49	6	important	important	ADJ
ijassa-1367	49	7	because	because	SCONJ
ijassa-1367	49	8	before	before	SCONJ
ijassa-1367	49	9	we	we	PRON
ijassa-1367	49	10	find	find	VERB
ijassa-1367	49	11	one	one	NUM
ijassa-1367	49	12	globally	globally	ADV
ijassa-1367	49	13	optimal	optimal	ADJ
ijassa-1367	49	14	trajectory	trajectory	NOUN
ijassa-1367	49	15	,	,	PUNCT
ijassa-1367	49	16	we	we	PRON
ijassa-1367	49	17	must	must	AUX
ijassa-1367	49	18	pass	pass	VERB
ijassa-1367	49	19	through	through	ADP
ijassa-1367	49	20	all	all	DET
ijassa-1367	49	21	nodes	node	NOUN
ijassa-1367	49	22	to	to	PART
ijassa-1367	49	23	make	make	VERB
ijassa-1367	49	24	sure	sure	ADJ
ijassa-1367	49	25	that	that	SCONJ
ijassa-1367	49	26	there	there	PRON
ijassa-1367	49	27	are	be	VERB
ijassa-1367	49	28	no	no	DET
ijassa-1367	49	29	regions	region	NOUN
ijassa-1367	49	30	,	,	PUNCT
ijassa-1367	49	31	at	at	ADP
ijassa-1367	49	32	which	which	PRON
ijassa-1367	49	33	the	the	DET
ijassa-1367	49	34	cost	cost	NOUN
ijassa-1367	49	35	of	of	ADP
ijassa-1367	49	36	steps	step	NOUN
ijassa-1367	49	37	is	be	AUX
ijassa-1367	49	38	too	too	ADV
ijassa-1367	49	39	low	low	ADJ
ijassa-1367	49	40	or	or	CCONJ
ijassa-1367	49	41	even	even	ADV
ijassa-1367	49	42	negative	negative	ADJ
ijassa-1367	49	43	.	.	PUNCT
ijassa-1367	50	1	by	by	ADP
ijassa-1367	50	2	using	use	VERB
ijassa-1367	50	3	euler	euler	NOUN
ijassa-1367	50	4	polygonal	polygonal	ADJ
ijassa-1367	50	5	lines	line	NOUN
ijassa-1367	50	6	we	we	PRON
ijassa-1367	50	7	significantly	significantly	ADV
ijassa-1367	50	8	simplify	simplify	VERB
ijassa-1367	50	9	the	the	DET
ijassa-1367	50	10	problem	problem	NOUN
ijassa-1367	50	11	and	and	CCONJ
ijassa-1367	50	12	restrict	restrict	VERB
ijassa-1367	50	13	the	the	DET
ijassa-1367	50	14	domain	domain	NOUN
ijassa-1367	50	15	of	of	ADP
ijassa-1367	50	16	search	search	NOUN
ijassa-1367	50	17	.	.	PUNCT
ijassa-1367	51	1	however	however	ADV
ijassa-1367	51	2	,	,	PUNCT
ijassa-1367	51	3	as	as	SCONJ
ijassa-1367	51	4	we	we	PRON
ijassa-1367	51	5	know	know	VERB
ijassa-1367	51	6	,	,	PUNCT
ijassa-1367	51	7	any	any	DET
ijassa-1367	51	8	sufficiently	sufficiently	ADV
ijassa-1367	51	9	smooth	smooth	ADJ
ijassa-1367	51	10	curve	curve	NOUN
ijassa-1367	51	11	can	can	AUX
ijassa-1367	51	12	be	be	AUX
ijassa-1367	51	13	approximated	approximate	VERB
ijassa-1367	51	14	by	by	ADP
ijassa-1367	51	15	such	such	ADJ
ijassa-1367	51	16	polygonal	polygonal	ADJ
ijassa-1367	51	17	lines	line	NOUN
ijassa-1367	51	18	.	.	PUNCT
ijassa-1367	52	1	therefore	therefore	ADV
ijassa-1367	52	2	,	,	PUNCT
ijassa-1367	52	3	if	if	SCONJ
ijassa-1367	52	4	we	we	PRON
ijassa-1367	52	5	want	want	VERB
ijassa-1367	52	6	to	to	PART
ijassa-1367	52	7	obtain	obtain	VERB
ijassa-1367	52	8	more	more	ADV
ijassa-1367	52	9	accurate	accurate	ADJ
ijassa-1367	52	10	approximation	approximation	NOUN
ijassa-1367	52	11	,	,	PUNCT
ijassa-1367	52	12	we	we	PRON
ijassa-1367	52	13	must	must	AUX
ijassa-1367	52	14	consider	consider	VERB
ijassa-1367	52	15	a	a	DET
ijassa-1367	52	16	more	more	ADV
ijassa-1367	52	17	fine	fine	ADJ
ijassa-1367	52	18	lattice	lattice	NOUN
ijassa-1367	52	19	.	.	PUNCT
ijassa-1367	53	1	copyright	copyright	NOUN
ijassa-1367	53	2	©	©	ADP
ijassa-1367	53	3	2023	2023	NUM
ijassa-1367	53	4	assa	assa	NOUN
ijassa-1367	53	5	.	.	PUNCT
ijassa-1367	54	1	adv	adv	PROPN
ijassa-1367	54	2	syst	syst	PROPN
ijassa-1367	54	3	sci	sci	PROPN
ijassa-1367	54	4	appl	appl	PROPN
ijassa-1367	54	5	(	(	PUNCT
ijassa-1367	54	6	2023	2023	NUM
ijassa-1367	54	7	)	)	PUNCT
ijassa-1367	54	8	piecewise	piecewise	NOUN
ijassa-1367	54	9	constant	constant	ADJ
ijassa-1367	54	10	functions	function	NOUN
ijassa-1367	54	11	in	in	ADP
ijassa-1367	54	12	dynamic	dynamic	ADJ
ijassa-1367	54	13	optimization	optimization	NOUN
ijassa-1367	54	14	problems	problem	NOUN
ijassa-1367	54	15	37	37	NUM
ijassa-1367	54	16	fig	fig	NOUN
ijassa-1367	54	17	.	.	PUNCT
ijassa-1367	55	1	2.1	2.1	NUM
ijassa-1367	55	2	.	.	PUNCT
ijassa-1367	56	1	optimal	optimal	ADJ
ijassa-1367	56	2	polygonal	polygonal	ADJ
ijassa-1367	56	3	lines	line	NOUN
ijassa-1367	56	4	on	on	ADP
ijassa-1367	56	5	the	the	DET
ijassa-1367	56	6	standard	standard	ADJ
ijassa-1367	56	7	and	and	CCONJ
ijassa-1367	56	8	distorted	distorted	ADJ
ijassa-1367	56	9	euclidean	euclidean	ADJ
ijassa-1367	56	10	planes	plane	NOUN
ijassa-1367	56	11	the	the	DET
ijassa-1367	56	12	euler	euler	PROPN
ijassa-1367	56	13	polygonal	polygonal	ADJ
ijassa-1367	56	14	method	method	NOUN
ijassa-1367	56	15	was	be	AUX
ijassa-1367	56	16	verified	verify	VERB
ijassa-1367	56	17	by	by	ADP
ijassa-1367	56	18	the	the	DET
ijassa-1367	56	19	authors	author	NOUN
ijassa-1367	56	20	on	on	ADP
ijassa-1367	56	21	the	the	DET
ijassa-1367	56	22	familiar	familiar	ADJ
ijassa-1367	56	23	variational	variational	ADJ
ijassa-1367	56	24	problems	problem	NOUN
ijassa-1367	56	25	,	,	PUNCT
ijassa-1367	56	26	such	such	ADJ
ijassa-1367	56	27	as	as	ADP
ijassa-1367	56	28	the	the	DET
ijassa-1367	56	29	shortest	short	ADJ
ijassa-1367	56	30	curves	curve	NOUN
ijassa-1367	56	31	on	on	ADP
ijassa-1367	56	32	the	the	DET
ijassa-1367	56	33	euclidean	euclidean	ADJ
ijassa-1367	56	34	and	and	CCONJ
ijassa-1367	56	35	lobachevsky	lobachevsky	ADJ
ijassa-1367	56	36	planes	plane	NOUN
ijassa-1367	56	37	,	,	PUNCT
ijassa-1367	56	38	the	the	DET
ijassa-1367	56	39	brachistochrone	brachistochrone	NOUN
ijassa-1367	56	40	curve	curve	NOUN
ijassa-1367	56	41	,	,	PUNCT
ijassa-1367	56	42	and	and	CCONJ
ijassa-1367	56	43	the	the	DET
ijassa-1367	56	44	minimal	minimal	ADJ
ijassa-1367	56	45	surfaces	surface	NOUN
ijassa-1367	56	46	of	of	ADP
ijassa-1367	56	47	revolution	revolution	NOUN
ijassa-1367	56	48	[	[	X
ijassa-1367	56	49	16	16	NUM
ijassa-1367	56	50	]	]	PUNCT
ijassa-1367	56	51	,	,	PUNCT
ijassa-1367	56	52	[	[	X
ijassa-1367	56	53	17	17	NUM
ijassa-1367	56	54	]	]	PUNCT
ijassa-1367	56	55	.	.	PUNCT
ijassa-1367	57	1	in	in	ADP
ijassa-1367	57	2	all	all	DET
ijassa-1367	57	3	cases	case	NOUN
ijassa-1367	57	4	,	,	PUNCT
ijassa-1367	57	5	visually	visually	ADV
ijassa-1367	57	6	it	it	PRON
ijassa-1367	57	7	would	would	AUX
ijassa-1367	57	8	be	be	AUX
ijassa-1367	57	9	difficult	difficult	ADJ
ijassa-1367	57	10	to	to	PART
ijassa-1367	57	11	distinguish	distinguish	VERB
ijassa-1367	57	12	between	between	ADP
ijassa-1367	57	13	the	the	DET
ijassa-1367	57	14	fields	field	NOUN
ijassa-1367	57	15	of	of	ADP
ijassa-1367	57	16	curves	curve	NOUN
ijassa-1367	57	17	constructed	construct	VERB
ijassa-1367	57	18	analytically	analytically	ADV
ijassa-1367	57	19	and	and	CCONJ
ijassa-1367	57	20	numerically	numerically	ADV
ijassa-1367	57	21	.	.	PUNCT
ijassa-1367	58	1	figure	figure	NOUN
ijassa-1367	58	2	2.1	2.1	NUM
ijassa-1367	58	3	represents	represent	VERB
ijassa-1367	58	4	the	the	DET
ijassa-1367	58	5	results	result	NOUN
ijassa-1367	58	6	of	of	ADP
ijassa-1367	58	7	the	the	DET
ijassa-1367	58	8	algorithm	algorithm	NOUN
ijassa-1367	58	9	for	for	ADP
ijassa-1367	58	10	two	two	NUM
ijassa-1367	58	11	related	relate	VERB
ijassa-1367	58	12	problems	problem	NOUN
ijassa-1367	58	13	of	of	ADP
ijassa-1367	58	14	searching	search	VERB
ijassa-1367	58	15	the	the	DET
ijassa-1367	58	16	shortest	short	ADJ
ijassa-1367	58	17	paths	path	NOUN
ijassa-1367	58	18	on	on	ADP
ijassa-1367	58	19	the	the	DET
ijassa-1367	58	20	standard	standard	NOUN
ijassa-1367	58	21	and	and	CCONJ
ijassa-1367	58	22	“	"	PUNCT
ijassa-1367	58	23	distorted	distort	VERB
ijassa-1367	58	24	”	"	PUNCT
ijassa-1367	58	25	euclidean	euclidean	ADJ
ijassa-1367	58	26	planes	plane	NOUN
ijassa-1367	58	27	.	.	PUNCT
ijassa-1367	59	1	the	the	DET
ijassa-1367	59	2	program	program	NOUN
ijassa-1367	59	3	has	have	AUX
ijassa-1367	59	4	constructed	construct	VERB
ijassa-1367	59	5	optimal	optimal	ADJ
ijassa-1367	59	6	polygonal	polygonal	ADJ
ijassa-1367	59	7	lines	line	NOUN
ijassa-1367	59	8	connecting	connect	VERB
ijassa-1367	59	9	the	the	DET
ijassa-1367	59	10	origin	origin	NOUN
ijassa-1367	59	11	o	o	NOUN
ijassa-1367	59	12	to	to	ADP
ijassa-1367	59	13	the	the	DET
ijassa-1367	59	14	points	point	NOUN
ijassa-1367	59	15	of	of	ADP
ijassa-1367	59	16	the	the	DET
ijassa-1367	59	17	line	line	NOUN
ijassa-1367	59	18	ac	ac	PROPN
ijassa-1367	59	19	.	.	PUNCT
ijassa-1367	60	1	on	on	ADP
ijassa-1367	60	2	the	the	DET
ijassa-1367	60	3	“	"	PUNCT
ijassa-1367	60	4	distorted	distorted	ADJ
ijassa-1367	60	5	”	"	PUNCT
ijassa-1367	60	6	plane	plane	NOUN
ijassa-1367	60	7	,	,	PUNCT
ijassa-1367	60	8	the	the	DET
ijassa-1367	60	9	lagrangian	lagrangian	ADJ
ijassa-1367	60	10	function	function	NOUN
ijassa-1367	60	11	is	be	AUX
ijassa-1367	60	12	given	give	VERB
ijassa-1367	60	13	by	by	ADP
ijassa-1367	60	14	l	l	NOUN
ijassa-1367	60	15	=	=	PUNCT
ijassa-1367	60	16	{	{	PUNCT
ijassa-1367	60	17	√	√	NUM
ijassa-1367	60	18	1	1	NUM
ijassa-1367	60	19	+	+	CCONJ
ijassa-1367	60	20	ẋ2	ẋ2	PROPN
ijassa-1367	60	21	,	,	PUNCT
ijassa-1367	60	22	x	x	X
ijassa-1367	60	23	≥	≥	NOUN
ijassa-1367	60	24	0,√	0,√	NUM
ijassa-1367	60	25	1	1	NUM
ijassa-1367	60	26	+	+	X
ijassa-1367	60	27	ẋ2	ẋ2	X
ijassa-1367	60	28	(	(	PUNCT
ijassa-1367	60	29	1−	1−	NUM
ijassa-1367	60	30	(	(	PUNCT
ijassa-1367	60	31	x	x	NOUN
ijassa-1367	60	32	a	a	X
ijassa-1367	60	33	)	)	PUNCT
ijassa-1367	60	34	2	2	NUM
ijassa-1367	60	35	)	)	PUNCT
ijassa-1367	60	36	,	,	PUNCT
ijassa-1367	60	37	−a	−a	VERB
ijassa-1367	60	38	≤	≤	NOUN
ijassa-1367	60	39	x	x	PUNCT
ijassa-1367	60	40	<	<	X
ijassa-1367	60	41	0	0	NUM
ijassa-1367	60	42	,	,	PUNCT
ijassa-1367	60	43	where	where	SCONJ
ijassa-1367	60	44	a	a	DET
ijassa-1367	60	45	>	>	X
ijassa-1367	60	46	0	0	NUM
ijassa-1367	60	47	is	be	AUX
ijassa-1367	60	48	some	some	DET
ijassa-1367	60	49	constant	constant	ADJ
ijassa-1367	60	50	.	.	PUNCT
ijassa-1367	61	1	notice	notice	VERB
ijassa-1367	61	2	that	that	SCONJ
ijassa-1367	61	3	on	on	ADP
ijassa-1367	61	4	the	the	DET
ijassa-1367	61	5	half	half	ADJ
ijassa-1367	61	6	-	-	PUNCT
ijassa-1367	61	7	plane	plane	NOUN
ijassa-1367	61	8	x	x	NOUN
ijassa-1367	61	9	≥	≥	NOUN
ijassa-1367	61	10	0	0	NUM
ijassa-1367	61	11	the	the	DET
ijassa-1367	61	12	lagrangian	lagrangian	ADJ
ijassa-1367	61	13	is	be	AUX
ijassa-1367	61	14	the	the	DET
ijassa-1367	61	15	same	same	ADJ
ijassa-1367	61	16	for	for	ADP
ijassa-1367	61	17	both	both	DET
ijassa-1367	61	18	problems	problem	NOUN
ijassa-1367	61	19	.	.	PUNCT
ijassa-1367	62	1	thus	thus	ADV
ijassa-1367	62	2	the	the	DET
ijassa-1367	62	3	segments	segment	NOUN
ijassa-1367	62	4	om	om	VERB
ijassa-1367	62	5	to	to	ADP
ijassa-1367	62	6	the	the	DET
ijassa-1367	62	7	points	point	NOUN
ijassa-1367	62	8	m	m	AUX
ijassa-1367	62	9	lying	lie	VERB
ijassa-1367	62	10	above	above	ADP
ijassa-1367	62	11	the	the	DET
ijassa-1367	62	12	ot	ot	ADJ
ijassa-1367	62	13	-	-	PUNCT
ijassa-1367	62	14	axis	axis	NOUN
ijassa-1367	62	15	are	be	AUX
ijassa-1367	62	16	extremals	extremal	NOUN
ijassa-1367	62	17	for	for	ADP
ijassa-1367	62	18	the	the	DET
ijassa-1367	62	19	“	"	PUNCT
ijassa-1367	62	20	distorted	distorted	ADJ
ijassa-1367	62	21	”	"	PUNCT
ijassa-1367	62	22	plane	plane	NOUN
ijassa-1367	62	23	as	as	ADV
ijassa-1367	62	24	well	well	ADV
ijassa-1367	62	25	.	.	PUNCT
ijassa-1367	63	1	however	however	ADV
ijassa-1367	63	2	,	,	PUNCT
ijassa-1367	63	3	if	if	SCONJ
ijassa-1367	63	4	m	m	NOUN
ijassa-1367	63	5	is	be	AUX
ijassa-1367	63	6	located	locate	VERB
ijassa-1367	63	7	below	below	ADP
ijassa-1367	63	8	the	the	DET
ijassa-1367	63	9	point	point	NOUN
ijassa-1367	63	10	b	b	NOUN
ijassa-1367	63	11	,	,	PUNCT
ijassa-1367	63	12	the	the	DET
ijassa-1367	63	13	optimal	optimal	ADJ
ijassa-1367	63	14	extremal	extremal	NOUN
ijassa-1367	63	15	will	will	AUX
ijassa-1367	63	16	not	not	PART
ijassa-1367	63	17	be	be	AUX
ijassa-1367	63	18	the	the	DET
ijassa-1367	63	19	standard	standard	ADJ
ijassa-1367	63	20	extremal	extremal	NOUN
ijassa-1367	63	21	represented	represent	VERB
ijassa-1367	63	22	by	by	ADP
ijassa-1367	63	23	the	the	DET
ijassa-1367	63	24	segment	segment	NOUN
ijassa-1367	63	25	om	om	PROPN
ijassa-1367	63	26	,	,	PUNCT
ijassa-1367	63	27	but	but	CCONJ
ijassa-1367	63	28	rather	rather	ADV
ijassa-1367	63	29	a	a	DET
ijassa-1367	63	30	polygonal	polygonal	ADJ
ijassa-1367	63	31	line	line	NOUN
ijassa-1367	63	32	that	that	PRON
ijassa-1367	63	33	moves	move	VERB
ijassa-1367	63	34	down	down	ADP
ijassa-1367	63	35	to	to	ADP
ijassa-1367	63	36	a	a	DET
ijassa-1367	63	37	point	point	NOUN
ijassa-1367	63	38	k	k	NOUN
ijassa-1367	63	39	,	,	PUNCT
ijassa-1367	63	40	next	next	ADV
ijassa-1367	63	41	goes	go	VERB
ijassa-1367	63	42	in	in	ADP
ijassa-1367	63	43	a	a	DET
ijassa-1367	63	44	horizontal	horizontal	ADJ
ijassa-1367	63	45	direction	direction	NOUN
ijassa-1367	63	46	,	,	PUNCT
ijassa-1367	63	47	and	and	CCONJ
ijassa-1367	63	48	finally	finally	ADV
ijassa-1367	63	49	goes	go	VERB
ijassa-1367	63	50	up	up	ADP
ijassa-1367	63	51	rather	rather	ADV
ijassa-1367	63	52	than	than	ADP
ijassa-1367	63	53	.	.	PUNCT
ijassa-1367	64	1	turning	turn	VERB
ijassa-1367	64	2	back	back	ADV
ijassa-1367	64	3	to	to	ADP
ijassa-1367	64	4	the	the	DET
ijassa-1367	64	5	general	general	ADJ
ijassa-1367	64	6	case	case	NOUN
ijassa-1367	64	7	,	,	PUNCT
ijassa-1367	64	8	note	note	VERB
ijassa-1367	64	9	that	that	SCONJ
ijassa-1367	64	10	picking	pick	VERB
ijassa-1367	64	11	points	point	NOUN
ijassa-1367	64	12	xj	xj	PROPN
ijassa-1367	64	13	on	on	ADP
ijassa-1367	64	14	the	the	DET
ijassa-1367	64	15	ox	ox	NOUN
ijassa-1367	64	16	-	-	NOUN
ijassa-1367	64	17	axis	axis	NOUN
ijassa-1367	64	18	,	,	PUNCT
ijassa-1367	64	19	we	we	PRON
ijassa-1367	64	20	divide	divide	VERB
ijassa-1367	64	21	the	the	DET
ijassa-1367	64	22	axis	axis	NOUN
ijassa-1367	64	23	into	into	ADP
ijassa-1367	64	24	n+	n+	ADP
ijassa-1367	64	25	1	1	NUM
ijassa-1367	64	26	sets	set	NOUN
ijassa-1367	64	27	:	:	PUNCT
ijassa-1367	64	28	single	single	ADJ
ijassa-1367	64	29	-	-	PUNCT
ijassa-1367	64	30	element	element	NOUN
ijassa-1367	64	31	sets	set	NOUN
ijassa-1367	64	32	{	{	PUNCT
ijassa-1367	64	33	xj	xj	NOUN
ijassa-1367	64	34	}	}	PUNCT
ijassa-1367	64	35	and	and	CCONJ
ijassa-1367	64	36	all	all	DET
ijassa-1367	64	37	other	other	ADJ
ijassa-1367	64	38	points	point	NOUN
ijassa-1367	64	39	of	of	ADP
ijassa-1367	64	40	the	the	DET
ijassa-1367	64	41	axis	axis	NOUN
ijassa-1367	64	42	.	.	PUNCT
ijassa-1367	65	1	with	with	ADP
ijassa-1367	65	2	this	this	DET
ijassa-1367	65	3	point	point	NOUN
ijassa-1367	65	4	of	of	ADP
ijassa-1367	65	5	view	view	NOUN
ijassa-1367	65	6	,	,	PUNCT
ijassa-1367	65	7	a	a	DET
ijassa-1367	65	8	(	(	PUNCT
ijassa-1367	65	9	τi	τi	PROPN
ijassa-1367	65	10	,	,	PUNCT
ijassa-1367	65	11	xj	xj	NOUN
ijassa-1367	65	12	)	)	PUNCT
ijassa-1367	65	13	can	can	AUX
ijassa-1367	65	14	be	be	AUX
ijassa-1367	65	15	considered	consider	VERB
ijassa-1367	65	16	as	as	ADP
ijassa-1367	65	17	a	a	DET
ijassa-1367	65	18	trivial	trivial	ADJ
ijassa-1367	65	19	piecewise	piecewise	NOUN
ijassa-1367	65	20	constant	constant	ADJ
ijassa-1367	65	21	function	function	NOUN
ijassa-1367	65	22	if	if	SCONJ
ijassa-1367	65	23	we	we	PRON
ijassa-1367	65	24	let	let	VERB
ijassa-1367	65	25	it	it	PRON
ijassa-1367	65	26	be	be	AUX
ijassa-1367	65	27	equal	equal	ADJ
ijassa-1367	65	28	to	to	ADP
ijassa-1367	65	29	+	+	NOUN
ijassa-1367	65	30	∞	∞	PROPN
ijassa-1367	65	31	at	at	ADP
ijassa-1367	65	32	the	the	DET
ijassa-1367	65	33	points	point	NOUN
ijassa-1367	65	34	that	that	PRON
ijassa-1367	65	35	are	be	AUX
ijassa-1367	65	36	not	not	PART
ijassa-1367	65	37	the	the	DET
ijassa-1367	65	38	nodes	node	NOUN
ijassa-1367	65	39	of	of	ADP
ijassa-1367	65	40	the	the	DET
ijassa-1367	65	41	lattice	lattice	PROPN
ijassa-1367	65	42	.	.	PUNCT
ijassa-1367	66	1	nontrivial	nontrivial	PROPN
ijassa-1367	66	2	functions	function	NOUN
ijassa-1367	66	3	a	a	DET
ijassa-1367	66	4	(	(	PUNCT
ijassa-1367	66	5	t	t	PROPN
ijassa-1367	66	6	,	,	PUNCT
ijassa-1367	66	7	x	x	PRON
ijassa-1367	66	8	)	)	PUNCT
ijassa-1367	66	9	will	will	AUX
ijassa-1367	66	10	be	be	AUX
ijassa-1367	66	11	considered	consider	VERB
ijassa-1367	66	12	later	later	ADV
ijassa-1367	66	13	.	.	PUNCT
ijassa-1367	67	1	3	3	X
ijassa-1367	67	2	.	.	PUNCT
ijassa-1367	67	3	fixed	fix	VERB
ijassa-1367	67	4	time	time	NOUN
ijassa-1367	67	5	optimal	optimal	ADJ
ijassa-1367	67	6	control	control	NOUN
ijassa-1367	67	7	problems	problem	NOUN
ijassa-1367	67	8	3.1	3.1	NUM
ijassa-1367	67	9	.	.	PUNCT
ijassa-1367	68	1	generalized	generalize	VERB
ijassa-1367	68	2	polygonal	polygonal	ADJ
ijassa-1367	68	3	lines	line	NOUN
ijassa-1367	68	4	now	now	ADV
ijassa-1367	68	5	consider	consider	VERB
ijassa-1367	68	6	an	an	DET
ijassa-1367	68	7	optimal	optimal	ADJ
ijassa-1367	68	8	control	control	NOUN
ijassa-1367	68	9	problem	problem	NOUN
ijassa-1367	68	10	j	j	PROPN
ijassa-1367	68	11	(	(	PUNCT
ijassa-1367	68	12	[	[	X
ijassa-1367	68	13	t0	t0	NOUN
ijassa-1367	68	14	,	,	PUNCT
ijassa-1367	68	15	t1	t1	PROPN
ijassa-1367	68	16	]	]	X
ijassa-1367	68	17	,	,	PUNCT
ijassa-1367	68	18	x	x	X
ijassa-1367	68	19	(	(	PUNCT
ijassa-1367	68	20	.	.	PUNCT
ijassa-1367	68	21	)	)	PUNCT
ijassa-1367	68	22	,	,	PUNCT
ijassa-1367	68	23	u	u	NOUN
ijassa-1367	68	24	(	(	PUNCT
ijassa-1367	68	25	.	.	PUNCT
ijassa-1367	68	26	)	)	PUNCT
ijassa-1367	68	27	)	)	PUNCT
ijassa-1367	69	1	=	=	SYM
ijassa-1367	69	2	∫	∫	PROPN
ijassa-1367	69	3	t1	t1	PROPN
ijassa-1367	69	4	t0	t0	PROPN
ijassa-1367	69	5	l(t	l(t	PROPN
ijassa-1367	69	6	,	,	PUNCT
ijassa-1367	69	7	x(t	x(t	PROPN
ijassa-1367	69	8	)	)	PUNCT
ijassa-1367	69	9	,	,	PUNCT
ijassa-1367	69	10	u(t))dt	u(t))dt	PROPN
ijassa-1367	69	11	→	→	SYM
ijassa-1367	69	12	min	min	PROPN
ijassa-1367	69	13	,	,	PUNCT
ijassa-1367	69	14	dx(t	dx(t	X
ijassa-1367	69	15	)	)	PUNCT
ijassa-1367	69	16	dt	dt	NOUN
ijassa-1367	69	17	=	=	SYM
ijassa-1367	69	18	f(t	f(t	NOUN
ijassa-1367	69	19	,	,	PUNCT
ijassa-1367	69	20	x(t	x(t	PROPN
ijassa-1367	69	21	)	)	PUNCT
ijassa-1367	69	22	,	,	PUNCT
ijassa-1367	69	23	u(t	u(t	NOUN
ijassa-1367	69	24	)	)	PUNCT
ijassa-1367	69	25	)	)	PUNCT
ijassa-1367	69	26	,	,	PUNCT
ijassa-1367	69	27	(	(	PUNCT
ijassa-1367	69	28	3.1	3.1	NUM
ijassa-1367	69	29	)	)	PUNCT
ijassa-1367	69	30	copyright	copyright	NOUN
ijassa-1367	69	31	©	©	PROPN
ijassa-1367	69	32	2023	2023	NUM
ijassa-1367	69	33	assa	assa	NOUN
ijassa-1367	69	34	.	.	PUNCT
ijassa-1367	70	1	adv	adv	PROPN
ijassa-1367	70	2	syst	syst	PROPN
ijassa-1367	70	3	sci	sci	PROPN
ijassa-1367	70	4	appl	appl	PROPN
ijassa-1367	70	5	(	(	PUNCT
ijassa-1367	70	6	2023	2023	NUM
ijassa-1367	70	7	)	)	PUNCT
ijassa-1367	70	8	38	38	NUM
ijassa-1367	70	9	o.	o.	PROPN
ijassa-1367	70	10	e.	e.	PROPN
ijassa-1367	70	11	orel	orel	PROPN
ijassa-1367	70	12	,	,	PUNCT
ijassa-1367	70	13	e.	e.	PROPN
ijassa-1367	70	14	n.	n.	PROPN
ijassa-1367	70	15	orel	orel	PROPN
ijassa-1367	70	16	x(t0	x(t0	PROPN
ijassa-1367	70	17	)	)	PUNCT
ijassa-1367	71	1	=	=	PUNCT
ijassa-1367	71	2	x0	x0	PROPN
ijassa-1367	71	3	,	,	PUNCT
ijassa-1367	71	4	x(t1	x(t1	X
ijassa-1367	71	5	)	)	PUNCT
ijassa-1367	72	1	=	=	SYM
ijassa-1367	72	2	x1	x1	PROPN
ijassa-1367	72	3	,	,	PUNCT
ijassa-1367	72	4	t0	t0	PROPN
ijassa-1367	72	5	<	<	X
ijassa-1367	72	6	t1	t1	PROPN
ijassa-1367	72	7	,	,	PUNCT
ijassa-1367	72	8	x(t	x(t	PROPN
ijassa-1367	72	9	)	)	PUNCT
ijassa-1367	72	10	∈	∈	PROPN
ijassa-1367	72	11	x	x	SYM
ijassa-1367	72	12	,	,	PUNCT
ijassa-1367	72	13	u(t	u(t	NOUN
ijassa-1367	72	14	)	)	PUNCT
ijassa-1367	72	15	∈	∈	PROPN
ijassa-1367	72	16	u.	u.	VERB
ijassa-1367	72	17	to	to	PART
ijassa-1367	72	18	solve	solve	VERB
ijassa-1367	72	19	it	it	PRON
ijassa-1367	72	20	numerically	numerically	ADV
ijassa-1367	72	21	,	,	PUNCT
ijassa-1367	72	22	as	as	ADP
ijassa-1367	72	23	in	in	ADP
ijassa-1367	72	24	calculus	calculus	NOUN
ijassa-1367	72	25	of	of	ADP
ijassa-1367	72	26	variations	variation	NOUN
ijassa-1367	72	27	,	,	PUNCT
ijassa-1367	72	28	we	we	PRON
ijassa-1367	72	29	divide	divide	VERB
ijassa-1367	72	30	the	the	DET
ijassa-1367	72	31	time	time	NOUN
ijassa-1367	72	32	segment	segment	NOUN
ijassa-1367	72	33	[	[	X
ijassa-1367	72	34	t0	t0	NOUN
ijassa-1367	72	35	,	,	PUNCT
ijassa-1367	72	36	t1	t1	PROPN
ijassa-1367	72	37	]	]	PUNCT
ijassa-1367	72	38	into	into	ADP
ijassa-1367	72	39	m	m	PROPN
ijassa-1367	72	40	equal	equal	ADJ
ijassa-1367	72	41	parts	part	NOUN
ijassa-1367	72	42	by	by	ADP
ijassa-1367	72	43	the	the	DET
ijassa-1367	72	44	points	point	NOUN
ijassa-1367	72	45	t0	t0	NOUN
ijassa-1367	73	1	=	=	PUNCT
ijassa-1367	73	2	τ0	τ0	NOUN
ijassa-1367	73	3	,	,	PUNCT
ijassa-1367	73	4	τ1	τ1	NOUN
ijassa-1367	73	5	,	,	PUNCT
ijassa-1367	73	6	τ2	τ2	NOUN
ijassa-1367	73	7	,	,	PUNCT
ijassa-1367	73	8	.	.	PUNCT
ijassa-1367	73	9	.	.	PUNCT
ijassa-1367	73	10	.	.	PUNCT
ijassa-1367	74	1	,	,	PUNCT
ijassa-1367	74	2	τi	τi	VERB
ijassa-1367	74	3	,	,	PUNCT
ijassa-1367	74	4	.	.	PUNCT
ijassa-1367	74	5	.	.	PUNCT
ijassa-1367	74	6	.	.	PUNCT
ijassa-1367	75	1	,	,	PUNCT
ijassa-1367	75	2	τm	τm	PRON
ijassa-1367	75	3	=	=	SYM
ijassa-1367	75	4	t1	t1	PROPN
ijassa-1367	75	5	,	,	PUNCT
ijassa-1367	75	6	τi	τi	ADP
ijassa-1367	75	7	−	−	PROPN
ijassa-1367	76	1	τi−1	τi−1	NOUN
ijassa-1367	76	2	=	=	SYM
ijassa-1367	76	3	∆τ	∆τ	PROPN
ijassa-1367	76	4	=	=	NOUN
ijassa-1367	76	5	t1	t1	NOUN
ijassa-1367	76	6	−	−	PROPN
ijassa-1367	76	7	t0	t0	PROPN
ijassa-1367	76	8	m	m	VERB
ijassa-1367	76	9	.	.	PUNCT
ijassa-1367	77	1	when	when	SCONJ
ijassa-1367	77	2	solving	solve	VERB
ijassa-1367	77	3	variational	variational	ADJ
ijassa-1367	77	4	problems	problem	NOUN
ijassa-1367	77	5	,	,	PUNCT
ijassa-1367	77	6	we	we	PRON
ijassa-1367	77	7	have	have	AUX
ijassa-1367	77	8	considered	consider	VERB
ijassa-1367	77	9	piecewise	piecewise	ADJ
ijassa-1367	77	10	constant	constant	ADJ
ijassa-1367	77	11	velocities	velocity	NOUN
ijassa-1367	77	12	.	.	PUNCT
ijassa-1367	78	1	now	now	ADV
ijassa-1367	78	2	we	we	PRON
ijassa-1367	78	3	will	will	AUX
ijassa-1367	78	4	consider	consider	VERB
ijassa-1367	78	5	controls	control	NOUN
ijassa-1367	78	6	that	that	PRON
ijassa-1367	78	7	are	be	AUX
ijassa-1367	78	8	constant	constant	ADJ
ijassa-1367	78	9	on	on	ADP
ijassa-1367	78	10	the	the	DET
ijassa-1367	78	11	intervals	interval	NOUN
ijassa-1367	78	12	[	[	X
ijassa-1367	78	13	τi−1	τi−1	NOUN
ijassa-1367	78	14	,	,	PUNCT
ijassa-1367	78	15	τi	τi	NOUN
ijassa-1367	78	16	)	)	PUNCT
ijassa-1367	78	17	.	.	PUNCT
ijassa-1367	79	1	for	for	ADP
ijassa-1367	79	2	convenience	convenience	NOUN
ijassa-1367	79	3	,	,	PUNCT
ijassa-1367	79	4	we	we	PRON
ijassa-1367	79	5	restrict	restrict	VERB
ijassa-1367	79	6	ourselves	ourselves	PRON
ijassa-1367	79	7	to	to	ADP
ijassa-1367	79	8	the	the	DET
ijassa-1367	79	9	simple	simple	ADJ
ijassa-1367	79	10	case	case	NOUN
ijassa-1367	79	11	when	when	SCONJ
ijassa-1367	79	12	the	the	DET
ijassa-1367	79	13	control	control	NOUN
ijassa-1367	79	14	actions	action	NOUN
ijassa-1367	79	15	belong	belong	VERB
ijassa-1367	79	16	to	to	ADP
ijassa-1367	79	17	the	the	DET
ijassa-1367	79	18	given	give	VERB
ijassa-1367	79	19	finite	finite	NOUN
ijassa-1367	79	20	set	set	VERB
ijassa-1367	79	21	v	v	ADP
ijassa-1367	79	22	⊂	⊂	PROPN
ijassa-1367	79	23	u	u	NOUN
ijassa-1367	79	24	,	,	PUNCT
ijassa-1367	79	25	v	v	NOUN
ijassa-1367	79	26	=	=	SYM
ijassa-1367	79	27	{	{	PUNCT
ijassa-1367	79	28	vj	vj	INTJ
ijassa-1367	79	29	}	}	PUNCT
ijassa-1367	79	30	,	,	PUNCT
ijassa-1367	79	31	j	j	PROPN
ijassa-1367	79	32	=	=	SYM
ijassa-1367	79	33	1	1	NUM
ijassa-1367	79	34	,	,	PUNCT
ijassa-1367	79	35	2	2	NUM
ijassa-1367	79	36	,	,	PUNCT
ijassa-1367	79	37	.	.	PUNCT
ijassa-1367	79	38	.	.	PUNCT
ijassa-1367	79	39	.	.	PUNCT
ijassa-1367	80	1	l.	l.	PROPN
ijassa-1367	80	2	in	in	ADP
ijassa-1367	80	3	general	general	ADJ
ijassa-1367	80	4	,	,	PUNCT
ijassa-1367	80	5	the	the	DET
ijassa-1367	80	6	number	number	NOUN
ijassa-1367	80	7	l	l	NOUN
ijassa-1367	80	8	and	and	CCONJ
ijassa-1367	80	9	the	the	DET
ijassa-1367	80	10	set	set	NOUN
ijassa-1367	80	11	of	of	ADP
ijassa-1367	80	12	controls	control	NOUN
ijassa-1367	80	13	v	v	NOUN
ijassa-1367	80	14	might	might	AUX
ijassa-1367	80	15	vary	vary	VERB
ijassa-1367	80	16	from	from	ADP
ijassa-1367	80	17	point	point	NOUN
ijassa-1367	80	18	to	to	PART
ijassa-1367	80	19	point	point	VERB
ijassa-1367	80	20	.	.	PUNCT
ijassa-1367	81	1	to	to	PART
ijassa-1367	81	2	specify	specify	VERB
ijassa-1367	81	3	the	the	DET
ijassa-1367	81	4	trajectory	trajectory	NOUN
ijassa-1367	81	5	γ	γ	NOUN
ijassa-1367	81	6	,	,	PUNCT
ijassa-1367	81	7	emanating	emanate	VERB
ijassa-1367	81	8	from	from	ADP
ijassa-1367	81	9	(	(	PUNCT
ijassa-1367	81	10	t0	t0	PROPN
ijassa-1367	81	11	,	,	PUNCT
ijassa-1367	81	12	x0	x0	PROPN
ijassa-1367	81	13	)	)	PUNCT
ijassa-1367	81	14	,	,	PUNCT
ijassa-1367	81	15	it	it	PRON
ijassa-1367	81	16	suffices	suffice	VERB
ijassa-1367	81	17	to	to	PART
ijassa-1367	81	18	choose	choose	VERB
ijassa-1367	81	19	a	a	DET
ijassa-1367	81	20	finite	finite	ADJ
ijassa-1367	81	21	sequence	sequence	NOUN
ijassa-1367	81	22	of	of	ADP
ijassa-1367	81	23	controls	control	NOUN
ijassa-1367	81	24	ui	ui	PROPN
ijassa-1367	81	25	∈	∈	PROPN
ijassa-1367	81	26	v	v	NOUN
ijassa-1367	81	27	on	on	ADP
ijassa-1367	81	28	the	the	DET
ijassa-1367	81	29	intervals	interval	NOUN
ijassa-1367	81	30	[	[	X
ijassa-1367	81	31	τi−1	τi−1	NOUN
ijassa-1367	81	32	,	,	PUNCT
ijassa-1367	81	33	τi	τi	NOUN
ijassa-1367	81	34	)	)	PUNCT
ijassa-1367	81	35	.	.	PUNCT
ijassa-1367	82	1	we	we	PRON
ijassa-1367	82	2	write	write	VERB
ijassa-1367	82	3	γ	γ	X
ijassa-1367	82	4	=	=	SYM
ijassa-1367	82	5	(	(	PUNCT
ijassa-1367	82	6	ξ0;u1	ξ0;u1	NOUN
ijassa-1367	82	7	,	,	PUNCT
ijassa-1367	82	8	ξ1	ξ1	NOUN
ijassa-1367	82	9	;	;	PUNCT
ijassa-1367	82	10	.	.	PUNCT
ijassa-1367	82	11	.	.	PUNCT
ijassa-1367	82	12	.	.	PUNCT
ijassa-1367	83	1	;	;	PUNCT
ijassa-1367	83	2	uµ−1	uµ−1	PROPN
ijassa-1367	83	3	,	,	PUNCT
ijassa-1367	83	4	ξµ−1;uµ	ξµ−1;uµ	NUM
ijassa-1367	83	5	,	,	PUNCT
ijassa-1367	83	6	ξµ	ξµ	NOUN
ijassa-1367	83	7	)	)	PUNCT
ijassa-1367	83	8	,	,	PUNCT
ijassa-1367	83	9	ui	ui	PROPN
ijassa-1367	83	10	∈	∈	PROPN
ijassa-1367	83	11	v	v	NOUN
ijassa-1367	83	12	,	,	PUNCT
ijassa-1367	83	13	ξi	ξi	PROPN
ijassa-1367	83	14	∈	∈	PROPN
ijassa-1367	83	15	x	x	SYM
ijassa-1367	83	16	,	,	PUNCT
ijassa-1367	83	17	1	1	NUM
ijassa-1367	83	18	≤	≤	NUM
ijassa-1367	83	19	µ	µ	PRON
ijassa-1367	83	20	≤	≤	NUM
ijassa-1367	83	21	m	m	ADP
ijassa-1367	83	22	,	,	PUNCT
ijassa-1367	83	23	(	(	PUNCT
ijassa-1367	83	24	3.2	3.2	NUM
ijassa-1367	83	25	)	)	PUNCT
ijassa-1367	83	26	where	where	SCONJ
ijassa-1367	83	27	ξ0	ξ0	NOUN
ijassa-1367	83	28	=	=	PUNCT
ijassa-1367	83	29	x0	x0	PROPN
ijassa-1367	83	30	and	and	CCONJ
ijassa-1367	83	31	ξi	ξi	PROPN
ijassa-1367	83	32	is	be	AUX
ijassa-1367	83	33	a	a	DET
ijassa-1367	83	34	state	state	NOUN
ijassa-1367	83	35	,	,	PUNCT
ijassa-1367	83	36	at	at	ADP
ijassa-1367	83	37	which	which	PRON
ijassa-1367	83	38	the	the	DET
ijassa-1367	83	39	system	system	NOUN
ijassa-1367	83	40	appears	appear	VERB
ijassa-1367	83	41	at	at	ADP
ijassa-1367	83	42	time	time	NOUN
ijassa-1367	83	43	τi	τi	ADJ
ijassa-1367	83	44	.	.	PUNCT
ijassa-1367	84	1	we	we	PRON
ijassa-1367	84	2	will	will	AUX
ijassa-1367	84	3	also	also	ADV
ijassa-1367	84	4	refer	refer	VERB
ijassa-1367	84	5	to	to	ADP
ijassa-1367	84	6	such	such	ADJ
ijassa-1367	84	7	trajectories	trajectory	NOUN
ijassa-1367	84	8	as	as	ADP
ijassa-1367	84	9	polygonal	polygonal	ADJ
ijassa-1367	84	10	lines	line	NOUN
ijassa-1367	84	11	and	and	CCONJ
ijassa-1367	84	12	to	to	ADP
ijassa-1367	84	13	the	the	DET
ijassa-1367	84	14	regions	region	NOUN
ijassa-1367	84	15	with	with	ADP
ijassa-1367	84	16	constant	constant	ADJ
ijassa-1367	84	17	controls	control	NOUN
ijassa-1367	84	18	as	as	ADP
ijassa-1367	84	19	segments	segment	NOUN
ijassa-1367	84	20	.	.	PUNCT
ijassa-1367	85	1	let	let	VERB
ijassa-1367	85	2	γ	γ	NOUN
ijassa-1367	85	3	be	be	AUX
ijassa-1367	85	4	the	the	DET
ijassa-1367	85	5	set	set	NOUN
ijassa-1367	85	6	of	of	ADP
ijassa-1367	85	7	polygonal	polygonal	ADJ
ijassa-1367	85	8	lines	line	NOUN
ijassa-1367	85	9	.	.	PUNCT
ijassa-1367	86	1	the	the	DET
ijassa-1367	86	2	value	value	NOUN
ijassa-1367	86	3	of	of	ADP
ijassa-1367	86	4	the	the	DET
ijassa-1367	86	5	functional	functional	ADJ
ijassa-1367	86	6	j	j	PROPN
ijassa-1367	86	7	assigned	assign	VERB
ijassa-1367	86	8	to	to	ADP
ijassa-1367	86	9	the	the	DET
ijassa-1367	86	10	polygonal	polygonal	ADJ
ijassa-1367	86	11	line	line	NOUN
ijassa-1367	86	12	γ	γ	NOUN
ijassa-1367	86	13	will	will	AUX
ijassa-1367	86	14	be	be	AUX
ijassa-1367	86	15	called	call	VERB
ijassa-1367	86	16	cost	cost	NOUN
ijassa-1367	86	17	and	and	CCONJ
ijassa-1367	86	18	denoted	denote	VERB
ijassa-1367	86	19	by	by	ADP
ijassa-1367	86	20	c(γ	c(γ	PROPN
ijassa-1367	86	21	)	)	PUNCT
ijassa-1367	86	22	.	.	PUNCT
ijassa-1367	87	1	all	all	DET
ijassa-1367	87	2	the	the	DET
ijassa-1367	87	3	polygonal	polygonal	ADJ
ijassa-1367	87	4	lines	line	NOUN
ijassa-1367	87	5	,	,	PUNCT
ijassa-1367	87	6	which	which	PRON
ijassa-1367	87	7	are	be	AUX
ijassa-1367	87	8	constructed	construct	VERB
ijassa-1367	87	9	by	by	ADP
ijassa-1367	87	10	the	the	DET
ijassa-1367	87	11	algorithm	algorithm	NOUN
ijassa-1367	87	12	,	,	PUNCT
ijassa-1367	87	13	are	be	AUX
ijassa-1367	87	14	emanated	emanate	VERB
ijassa-1367	87	15	from	from	ADP
ijassa-1367	87	16	a	a	DET
ijassa-1367	87	17	common	common	ADJ
ijassa-1367	87	18	point	point	NOUN
ijassa-1367	87	19	(	(	PUNCT
ijassa-1367	87	20	t0	t0	PROPN
ijassa-1367	87	21	,	,	PUNCT
ijassa-1367	87	22	x0	x0	PROPN
ijassa-1367	87	23	)	)	PUNCT
ijassa-1367	87	24	.	.	PUNCT
ijassa-1367	88	1	here	here	ADV
ijassa-1367	88	2	,	,	PUNCT
ijassa-1367	88	3	just	just	ADV
ijassa-1367	88	4	as	as	ADP
ijassa-1367	88	5	in	in	ADP
ijassa-1367	88	6	the	the	DET
ijassa-1367	88	7	calculus	calculus	NOUN
ijassa-1367	88	8	of	of	ADP
ijassa-1367	88	9	variations	variation	NOUN
ijassa-1367	88	10	,	,	PUNCT
ijassa-1367	88	11	by	by	ADP
ijassa-1367	88	12	considering	consider	VERB
ijassa-1367	88	13	polygonal	polygonal	ADJ
ijassa-1367	88	14	lines	line	NOUN
ijassa-1367	88	15	,	,	PUNCT
ijassa-1367	88	16	we	we	PRON
ijassa-1367	88	17	give	give	VERB
ijassa-1367	88	18	up	up	ADP
ijassa-1367	88	19	the	the	DET
ijassa-1367	88	20	idea	idea	NOUN
ijassa-1367	88	21	to	to	PART
ijassa-1367	88	22	obtain	obtain	VERB
ijassa-1367	88	23	the	the	DET
ijassa-1367	88	24	exact	exact	ADJ
ijassa-1367	88	25	solution	solution	NOUN
ijassa-1367	88	26	,	,	PUNCT
ijassa-1367	88	27	but	but	CCONJ
ijassa-1367	88	28	the	the	DET
ijassa-1367	88	29	finer	fine	ADJ
ijassa-1367	88	30	the	the	DET
ijassa-1367	88	31	step	step	NOUN
ijassa-1367	88	32	∆τ	∆τ	NOUN
ijassa-1367	88	33	and	and	CCONJ
ijassa-1367	88	34	the	the	PRON
ijassa-1367	88	35	wider	wide	ADJ
ijassa-1367	88	36	the	the	DET
ijassa-1367	88	37	set	set	NOUN
ijassa-1367	88	38	v	v	NOUN
ijassa-1367	88	39	,	,	PUNCT
ijassa-1367	88	40	the	the	PRON
ijassa-1367	88	41	closer	close	ADV
ijassa-1367	88	42	we	we	PRON
ijassa-1367	88	43	get	get	VERB
ijassa-1367	88	44	(	(	PUNCT
ijassa-1367	88	45	by	by	ADP
ijassa-1367	88	46	functional	functional	ADJ
ijassa-1367	88	47	)	)	PUNCT
ijassa-1367	88	48	to	to	ADP
ijassa-1367	88	49	the	the	DET
ijassa-1367	88	50	global	global	ADJ
ijassa-1367	88	51	extremum	extremum	PROPN
ijassa-1367	88	52	.	.	PUNCT
ijassa-1367	89	1	a	a	DET
ijassa-1367	89	2	particular	particular	ADJ
ijassa-1367	89	3	segment	segment	NOUN
ijassa-1367	89	4	is	be	AUX
ijassa-1367	89	5	a	a	DET
ijassa-1367	89	6	function	function	NOUN
ijassa-1367	89	7	x(t	x(t	NOUN
ijassa-1367	89	8	)	)	PUNCT
ijassa-1367	89	9	defined	define	VERB
ijassa-1367	89	10	over	over	ADP
ijassa-1367	89	11	the	the	DET
ijassa-1367	89	12	time	time	NOUN
ijassa-1367	89	13	interval	interval	NOUN
ijassa-1367	89	14	[	[	X
ijassa-1367	89	15	τi−1	τi−1	NOUN
ijassa-1367	89	16	,	,	PUNCT
ijassa-1367	89	17	τi	τi	ADP
ijassa-1367	89	18	]	]	PUNCT
ijassa-1367	89	19	,	,	PUNCT
ijassa-1367	89	20	1	1	NUM
ijassa-1367	89	21	≤	≤	NUM
ijassa-1367	89	22	i	i	PRON
ijassa-1367	89	23	≤	≤	NOUN
ijassa-1367	89	24	m	m	VERB
ijassa-1367	89	25	and	and	CCONJ
ijassa-1367	89	26	satisfying	satisfy	VERB
ijassa-1367	89	27	the	the	DET
ijassa-1367	89	28	differential	differential	ADJ
ijassa-1367	89	29	equation	equation	NOUN
ijassa-1367	89	30	dx(t	dx(t	NOUN
ijassa-1367	89	31	)	)	PUNCT
ijassa-1367	89	32	dt	dt	NOUN
ijassa-1367	90	1	=	=	SYM
ijassa-1367	90	2	f(t	f(t	NOUN
ijassa-1367	90	3	,	,	PUNCT
ijassa-1367	90	4	x(t	x(t	PROPN
ijassa-1367	90	5	)	)	PUNCT
ijassa-1367	90	6	,	,	PUNCT
ijassa-1367	90	7	vk	vk	PROPN
ijassa-1367	90	8	)	)	PUNCT
ijassa-1367	90	9	,	,	PUNCT
ijassa-1367	90	10	vk	vk	ADP
ijassa-1367	90	11	∈	∈	PROPN
ijassa-1367	90	12	v	v	NOUN
ijassa-1367	90	13	,	,	PUNCT
ijassa-1367	90	14	1	1	NUM
ijassa-1367	90	15	≤	≤	NUM
ijassa-1367	90	16	k	k	NOUN
ijassa-1367	90	17	≤	≤	NUM
ijassa-1367	90	18	l	l	NOUN
ijassa-1367	90	19	(	(	PUNCT
ijassa-1367	90	20	3.3	3.3	NUM
ijassa-1367	90	21	)	)	PUNCT
ijassa-1367	90	22	with	with	ADP
ijassa-1367	90	23	constant	constant	ADJ
ijassa-1367	90	24	control	control	NOUN
ijassa-1367	90	25	vk	vk	NOUN
ijassa-1367	90	26	.	.	PUNCT
ijassa-1367	91	1	the	the	DET
ijassa-1367	91	2	interval	interval	NOUN
ijassa-1367	91	3	has	have	VERB
ijassa-1367	91	4	an	an	DET
ijassa-1367	91	5	initial	initial	ADJ
ijassa-1367	91	6	point	point	NOUN
ijassa-1367	91	7	(	(	PUNCT
ijassa-1367	91	8	τi−1	τi−1	NOUN
ijassa-1367	91	9	,	,	PUNCT
ijassa-1367	91	10	x	x	X
ijassa-1367	91	11	(	(	PUNCT
ijassa-1367	91	12	τi−1	τi−1	NOUN
ijassa-1367	91	13	)	)	PUNCT
ijassa-1367	91	14	)	)	PUNCT
ijassa-1367	91	15	,	,	PUNCT
ijassa-1367	91	16	a	a	DET
ijassa-1367	91	17	terminal	terminal	ADJ
ijassa-1367	91	18	point	point	NOUN
ijassa-1367	91	19	(	(	PUNCT
ijassa-1367	91	20	τi	τi	ADP
ijassa-1367	91	21	,	,	PUNCT
ijassa-1367	91	22	x	x	X
ijassa-1367	91	23	(	(	PUNCT
ijassa-1367	91	24	τi	τi	NOUN
ijassa-1367	91	25	)	)	PUNCT
ijassa-1367	91	26	)	)	PUNCT
ijassa-1367	91	27	,	,	PUNCT
ijassa-1367	91	28	and	and	CCONJ
ijassa-1367	91	29	a	a	DET
ijassa-1367	91	30	cost	cost	NOUN
ijassa-1367	91	31	j	j	NOUN
ijassa-1367	91	32	(	(	PUNCT
ijassa-1367	91	33	[	[	X
ijassa-1367	91	34	τi−1	τi−1	NOUN
ijassa-1367	91	35	,	,	PUNCT
ijassa-1367	91	36	τi	τi	ADP
ijassa-1367	91	37	]	]	PUNCT
ijassa-1367	91	38	,	,	PUNCT
ijassa-1367	91	39	x	x	X
ijassa-1367	91	40	(	(	PUNCT
ijassa-1367	91	41	.	.	PUNCT
ijassa-1367	91	42	)	)	PUNCT
ijassa-1367	91	43	,	,	PUNCT
ijassa-1367	91	44	vj	vj	INTJ
ijassa-1367	91	45	)	)	PUNCT
ijassa-1367	91	46	=	=	SYM
ijassa-1367	91	47	∫	∫	PROPN
ijassa-1367	91	48	τi	τi	PROPN
ijassa-1367	91	49	τi−1	τi−1	PROPN
ijassa-1367	91	50	l(t	l(t	PROPN
ijassa-1367	91	51	,	,	PUNCT
ijassa-1367	91	52	x(t	x(t	PROPN
ijassa-1367	91	53	)	)	PUNCT
ijassa-1367	91	54	,	,	PUNCT
ijassa-1367	91	55	vj)dt	vj)dt	PROPN
ijassa-1367	91	56	.	.	PROPN
ijassa-1367	92	1	according	accord	VERB
ijassa-1367	92	2	to	to	ADP
ijassa-1367	92	3	the	the	DET
ijassa-1367	92	4	cauchy	cauchy	ADJ
ijassa-1367	92	5	uniqueness	uniqueness	NOUN
ijassa-1367	92	6	theorem	theorem	VERB
ijassa-1367	92	7	,	,	PUNCT
ijassa-1367	92	8	we	we	PRON
ijassa-1367	92	9	can	can	AUX
ijassa-1367	92	10	conclude	conclude	VERB
ijassa-1367	92	11	that	that	SCONJ
ijassa-1367	92	12	all	all	DET
ijassa-1367	92	13	these	these	DET
ijassa-1367	92	14	objects	object	NOUN
ijassa-1367	92	15	are	be	AUX
ijassa-1367	92	16	uniquely	uniquely	ADV
ijassa-1367	92	17	defined	define	VERB
ijassa-1367	92	18	by	by	ADP
ijassa-1367	92	19	the	the	DET
ijassa-1367	92	20	number	number	NOUN
ijassa-1367	92	21	i	i	PRON
ijassa-1367	92	22	of	of	ADP
ijassa-1367	92	23	the	the	DET
ijassa-1367	92	24	time	time	NOUN
ijassa-1367	92	25	segment	segment	NOUN
ijassa-1367	92	26	,	,	PUNCT
ijassa-1367	92	27	the	the	DET
ijassa-1367	92	28	number	number	NOUN
ijassa-1367	92	29	k	k	PROPN
ijassa-1367	92	30	of	of	ADP
ijassa-1367	92	31	the	the	DET
ijassa-1367	92	32	control	control	NOUN
ijassa-1367	92	33	,	,	PUNCT
ijassa-1367	92	34	and	and	CCONJ
ijassa-1367	92	35	the	the	DET
ijassa-1367	92	36	initial	initial	ADJ
ijassa-1367	92	37	point	point	NOUN
ijassa-1367	92	38	a	a	DET
ijassa-1367	92	39	=	=	X
ijassa-1367	92	40	x	x	X
ijassa-1367	92	41	(	(	PUNCT
ijassa-1367	92	42	τi−1	τi−1	NOUN
ijassa-1367	92	43	)	)	PUNCT
ijassa-1367	92	44	.	.	PUNCT
ijassa-1367	93	1	so	so	ADV
ijassa-1367	93	2	for	for	ADP
ijassa-1367	93	3	the	the	DET
ijassa-1367	93	4	segment	segment	NOUN
ijassa-1367	93	5	(	(	PUNCT
ijassa-1367	93	6	3.3	3.3	NUM
ijassa-1367	93	7	)	)	PUNCT
ijassa-1367	93	8	we	we	PRON
ijassa-1367	93	9	set	set	VERB
ijassa-1367	93	10	b	b	PROPN
ijassa-1367	93	11	(	(	PUNCT
ijassa-1367	93	12	i	i	PROPN
ijassa-1367	93	13	,	,	PUNCT
ijassa-1367	93	14	k	k	PROPN
ijassa-1367	93	15	,	,	PUNCT
ijassa-1367	93	16	a	a	PRON
ijassa-1367	93	17	)	)	PUNCT
ijassa-1367	93	18	=	=	SYM
ijassa-1367	93	19	x	x	X
ijassa-1367	93	20	(	(	PUNCT
ijassa-1367	93	21	τi	τi	NOUN
ijassa-1367	93	22	)	)	PUNCT
ijassa-1367	93	23	,	,	PUNCT
ijassa-1367	94	1	c	c	X
ijassa-1367	94	2	(	(	PUNCT
ijassa-1367	94	3	i	i	NOUN
ijassa-1367	94	4	,	,	PUNCT
ijassa-1367	94	5	k	k	PROPN
ijassa-1367	94	6	,	,	PUNCT
ijassa-1367	94	7	a	a	PRON
ijassa-1367	94	8	)	)	PUNCT
ijassa-1367	94	9	=	=	SYM
ijassa-1367	94	10	∫	∫	PROPN
ijassa-1367	94	11	τi	τi	PROPN
ijassa-1367	94	12	τi−1	τi−1	PROPN
ijassa-1367	94	13	l(t	l(t	PROPN
ijassa-1367	94	14	,	,	PUNCT
ijassa-1367	94	15	x(t	x(t	PROPN
ijassa-1367	94	16	)	)	PUNCT
ijassa-1367	94	17	,	,	PUNCT
ijassa-1367	94	18	vk)dt	vk)dt	SYM
ijassa-1367	94	19	.	.	PROPN
ijassa-1367	94	20	(	(	PUNCT
ijassa-1367	94	21	3.4	3.4	NUM
ijassa-1367	94	22	)	)	PUNCT
ijassa-1367	94	23	the	the	DET
ijassa-1367	94	24	complexity	complexity	NOUN
ijassa-1367	94	25	of	of	ADP
ijassa-1367	94	26	the	the	DET
ijassa-1367	94	27	problem	problem	NOUN
ijassa-1367	94	28	is	be	AUX
ijassa-1367	94	29	the	the	DET
ijassa-1367	94	30	following	following	NOUN
ijassa-1367	94	31	.	.	PUNCT
ijassa-1367	95	1	for	for	ADP
ijassa-1367	95	2	µ	µ	NOUN
ijassa-1367	95	3	=	=	SYM
ijassa-1367	95	4	m	m	VERB
ijassa-1367	95	5	there	there	PRON
ijassa-1367	95	6	are	be	VERB
ijassa-1367	95	7	lm	lm	INTJ
ijassa-1367	95	8	sequences	sequence	NOUN
ijassa-1367	95	9	of	of	ADP
ijassa-1367	95	10	the	the	DET
ijassa-1367	95	11	form	form	NOUN
ijassa-1367	95	12	(	(	PUNCT
ijassa-1367	95	13	3.2	3.2	NUM
ijassa-1367	95	14	)	)	PUNCT
ijassa-1367	95	15	.	.	PUNCT
ijassa-1367	96	1	it	it	PRON
ijassa-1367	96	2	is	be	AUX
ijassa-1367	96	3	important	important	ADJ
ijassa-1367	96	4	that	that	SCONJ
ijassa-1367	96	5	each	each	DET
ijassa-1367	96	6	polygonal	polygonal	ADJ
ijassa-1367	96	7	line	line	NOUN
ijassa-1367	96	8	passes	pass	VERB
ijassa-1367	96	9	through	through	ADP
ijassa-1367	96	10	its	its	PRON
ijassa-1367	96	11	own	own	ADJ
ijassa-1367	96	12	nodes	node	NOUN
ijassa-1367	96	13	,	,	PUNCT
ijassa-1367	96	14	that	that	ADV
ijassa-1367	96	15	is	is	ADV
ijassa-1367	96	16	,	,	PUNCT
ijassa-1367	96	17	generally	generally	ADV
ijassa-1367	96	18	speaking	speak	VERB
ijassa-1367	96	19	,	,	PUNCT
ijassa-1367	96	20	the	the	DET
ijassa-1367	96	21	polygonal	polygonal	ADJ
ijassa-1367	96	22	lines	line	NOUN
ijassa-1367	96	23	have	have	VERB
ijassa-1367	96	24	no	no	DET
ijassa-1367	96	25	break	break	NOUN
ijassa-1367	96	26	points	point	NOUN
ijassa-1367	96	27	in	in	ADP
ijassa-1367	96	28	common	common	ADJ
ijassa-1367	96	29	,	,	PUNCT
ijassa-1367	96	30	except	except	SCONJ
ijassa-1367	96	31	for	for	ADP
ijassa-1367	96	32	the	the	DET
ijassa-1367	96	33	initial	initial	ADJ
ijassa-1367	96	34	one	one	NUM
ijassa-1367	96	35	.	.	PUNCT
ijassa-1367	97	1	note	note	VERB
ijassa-1367	97	2	that	that	SCONJ
ijassa-1367	97	3	the	the	DET
ijassa-1367	97	4	number	number	NOUN
ijassa-1367	97	5	of	of	ADP
ijassa-1367	97	6	intermediate	intermediate	ADJ
ijassa-1367	97	7	nodes	node	NOUN
ijassa-1367	97	8	grows	grows	AUX
ijassa-1367	97	9	exponentially	exponentially	ADV
ijassa-1367	97	10	depending	depend	VERB
ijassa-1367	97	11	on	on	ADP
ijassa-1367	97	12	m	m	NOUN
ijassa-1367	97	13	in	in	ADP
ijassa-1367	97	14	contrast	contrast	NOUN
ijassa-1367	97	15	to	to	ADP
ijassa-1367	97	16	the	the	DET
ijassa-1367	97	17	linear	linear	ADJ
ijassa-1367	97	18	dependence	dependence	NOUN
ijassa-1367	97	19	in	in	ADP
ijassa-1367	97	20	variational	variational	ADJ
ijassa-1367	97	21	calculus	calculus	NOUN
ijassa-1367	97	22	,	,	PUNCT
ijassa-1367	97	23	where	where	SCONJ
ijassa-1367	97	24	the	the	DET
ijassa-1367	97	25	number	number	NOUN
ijassa-1367	97	26	of	of	ADP
ijassa-1367	97	27	nodes	node	NOUN
ijassa-1367	97	28	is	be	AUX
ijassa-1367	97	29	mn	mn	PROPN
ijassa-1367	97	30	.	.	PROPN
ijassa-1367	97	31	on	on	ADP
ijassa-1367	97	32	the	the	DET
ijassa-1367	97	33	graph	graph	NOUN
ijassa-1367	97	34	with	with	ADP
ijassa-1367	97	35	,	,	PUNCT
ijassa-1367	97	36	for	for	ADP
ijassa-1367	97	37	example	example	NOUN
ijassa-1367	97	38	,	,	PUNCT
ijassa-1367	97	39	3100	3100	NUM
ijassa-1367	97	40	≈	≈	PROPN
ijassa-1367	97	41	5	5	NUM
ijassa-1367	97	42	·	·	SYM
ijassa-1367	97	43	1047	1047	NUM
ijassa-1367	97	44	vertices	vertex	NOUN
ijassa-1367	97	45	,	,	PUNCT
ijassa-1367	97	46	it	it	PRON
ijassa-1367	97	47	is	be	AUX
ijassa-1367	97	48	almost	almost	ADV
ijassa-1367	97	49	impossible	impossible	ADJ
ijassa-1367	97	50	to	to	PART
ijassa-1367	97	51	find	find	VERB
ijassa-1367	97	52	the	the	DET
ijassa-1367	97	53	optimal	optimal	ADJ
ijassa-1367	97	54	path	path	NOUN
ijassa-1367	97	55	.	.	PUNCT
ijassa-1367	98	1	if	if	SCONJ
ijassa-1367	98	2	we	we	PRON
ijassa-1367	98	3	try	try	VERB
ijassa-1367	98	4	,	,	PUNCT
ijassa-1367	98	5	just	just	ADV
ijassa-1367	98	6	as	as	ADP
ijassa-1367	98	7	in	in	ADP
ijassa-1367	98	8	calculus	calculus	NOUN
ijassa-1367	98	9	of	of	ADP
ijassa-1367	98	10	variations	variation	NOUN
ijassa-1367	98	11	,	,	PUNCT
ijassa-1367	98	12	to	to	PART
ijassa-1367	98	13	move	move	VERB
ijassa-1367	98	14	through	through	ADP
ijassa-1367	98	15	the	the	DET
ijassa-1367	98	16	nodes	node	NOUN
ijassa-1367	98	17	(	(	PUNCT
ijassa-1367	98	18	τi	τi	ADP
ijassa-1367	98	19	,	,	PUNCT
ijassa-1367	98	20	xj	xj	NOUN
ijassa-1367	98	21	)	)	PUNCT
ijassa-1367	98	22	of	of	ADP
ijassa-1367	98	23	the	the	DET
ijassa-1367	98	24	given	give	VERB
ijassa-1367	98	25	regular	regular	ADJ
ijassa-1367	98	26	lattice	lattice	NOUN
ijassa-1367	98	27	,	,	PUNCT
ijassa-1367	98	28	we	we	PRON
ijassa-1367	98	29	will	will	AUX
ijassa-1367	98	30	face	face	VERB
ijassa-1367	98	31	some	some	DET
ijassa-1367	98	32	difficulties	difficulty	NOUN
ijassa-1367	98	33	in	in	ADP
ijassa-1367	98	34	choosing	choose	VERB
ijassa-1367	98	35	controls	control	VERB
ijassa-1367	98	36	u	u	PROPN
ijassa-1367	98	37	∈	∈	PROPN
ijassa-1367	98	38	v	v	NOUN
ijassa-1367	98	39	,	,	PUNCT
ijassa-1367	98	40	passing	pass	VERB
ijassa-1367	98	41	from	from	ADP
ijassa-1367	98	42	points	point	NOUN
ijassa-1367	98	43	(	(	PUNCT
ijassa-1367	98	44	τi−1	τi−1	PROPN
ijassa-1367	98	45	,	,	PUNCT
ijassa-1367	98	46	xj	xj	NOUN
ijassa-1367	98	47	)	)	PUNCT
ijassa-1367	98	48	to	to	ADP
ijassa-1367	98	49	neighboring	neighboring	NOUN
ijassa-1367	98	50	points	point	NOUN
ijassa-1367	98	51	(	(	PUNCT
ijassa-1367	98	52	τi	τi	ADP
ijassa-1367	98	53	,	,	PUNCT
ijassa-1367	98	54	xk	xk	ADJ
ijassa-1367	98	55	)	)	PUNCT
ijassa-1367	98	56	,	,	PUNCT
ijassa-1367	98	57	and	and	CCONJ
ijassa-1367	98	58	the	the	DET
ijassa-1367	98	59	moiseev	moiseev	ADJ
ijassa-1367	98	60	“	"	PUNCT
ijassa-1367	98	61	elementary	elementary	ADJ
ijassa-1367	98	62	operation	operation	NOUN
ijassa-1367	98	63	”	"	PUNCT
ijassa-1367	99	1	[	[	X
ijassa-1367	99	2	7	7	NUM
ijassa-1367	99	3	]	]	PUNCT
ijassa-1367	99	4	will	will	AUX
ijassa-1367	99	5	sometimes	sometimes	ADV
ijassa-1367	99	6	not	not	PART
ijassa-1367	99	7	succeed	succeed	VERB
ijassa-1367	99	8	.	.	PUNCT
ijassa-1367	100	1	copyright	copyright	NOUN
ijassa-1367	100	2	©	©	PROPN
ijassa-1367	100	3	2023	2023	NUM
ijassa-1367	100	4	assa	assa	NOUN
ijassa-1367	100	5	.	.	PUNCT
ijassa-1367	101	1	adv	adv	PROPN
ijassa-1367	101	2	syst	syst	PROPN
ijassa-1367	101	3	sci	sci	PROPN
ijassa-1367	101	4	appl	appl	PROPN
ijassa-1367	101	5	(	(	PUNCT
ijassa-1367	101	6	2023	2023	NUM
ijassa-1367	101	7	)	)	PUNCT
ijassa-1367	101	8	piecewise	piecewise	NOUN
ijassa-1367	101	9	constant	constant	ADJ
ijassa-1367	101	10	functions	function	NOUN
ijassa-1367	101	11	in	in	ADP
ijassa-1367	101	12	dynamic	dynamic	ADJ
ijassa-1367	101	13	optimization	optimization	NOUN
ijassa-1367	101	14	problems	problem	NOUN
ijassa-1367	101	15	39	39	NUM
ijassa-1367	101	16	3.2	3.2	NUM
ijassa-1367	101	17	.	.	PUNCT
ijassa-1367	102	1	splitting	split	VERB
ijassa-1367	102	2	into	into	ADP
ijassa-1367	102	3	cells	cell	NOUN
ijassa-1367	102	4	we	we	PRON
ijassa-1367	102	5	suggest	suggest	VERB
ijassa-1367	102	6	the	the	DET
ijassa-1367	102	7	following	follow	VERB
ijassa-1367	102	8	algorithm	algorithm	NOUN
ijassa-1367	102	9	to	to	PART
ijassa-1367	102	10	solve	solve	VERB
ijassa-1367	102	11	the	the	DET
ijassa-1367	102	12	problem	problem	NOUN
ijassa-1367	102	13	.	.	PUNCT
ijassa-1367	103	1	we	we	PRON
ijassa-1367	103	2	should	should	AUX
ijassa-1367	103	3	split	split	VERB
ijassa-1367	103	4	the	the	DET
ijassa-1367	103	5	set	set	NOUN
ijassa-1367	103	6	x	x	PUNCT
ijassa-1367	103	7	into	into	ADP
ijassa-1367	103	8	a	a	DET
ijassa-1367	103	9	finite	finite	ADJ
ijassa-1367	103	10	number	number	NOUN
ijassa-1367	103	11	n	n	NUM
ijassa-1367	103	12	of	of	ADP
ijassa-1367	103	13	subsets	subset	NOUN
ijassa-1367	103	14	x	x	PUNCT
ijassa-1367	104	1	=	=	PRON
ijassa-1367	104	2	n⋃	n⋃	PRON
ijassa-1367	104	3	j=1	j=1	PROPN
ijassa-1367	104	4	xj	xj	PROPN
ijassa-1367	104	5	,	,	PUNCT
ijassa-1367	104	6	xj	xj	PROPN
ijassa-1367	104	7	⋂	⋂	PROPN
ijassa-1367	104	8	xk	xk	PROPN
ijassa-1367	104	9	=	=	PUNCT
ijassa-1367	104	10	∅	∅	NOUN
ijassa-1367	104	11	,	,	PUNCT
ijassa-1367	104	12	which	which	PRON
ijassa-1367	104	13	we	we	PRON
ijassa-1367	104	14	refer	refer	VERB
ijassa-1367	104	15	to	to	ADP
ijassa-1367	104	16	as	as	ADP
ijassa-1367	104	17	classes	class	NOUN
ijassa-1367	104	18	,	,	PUNCT
ijassa-1367	104	19	or	or	CCONJ
ijassa-1367	104	20	cells	cell	NOUN
ijassa-1367	104	21	.	.	PUNCT
ijassa-1367	105	1	we	we	PRON
ijassa-1367	105	2	recommend	recommend	VERB
ijassa-1367	105	3	that	that	SCONJ
ijassa-1367	105	4	the	the	DET
ijassa-1367	105	5	diameters	diameter	NOUN
ijassa-1367	105	6	of	of	ADP
ijassa-1367	105	7	the	the	DET
ijassa-1367	105	8	sets	set	NOUN
ijassa-1367	105	9	xj	xj	PROPN
ijassa-1367	105	10	should	should	AUX
ijassa-1367	105	11	be	be	AUX
ijassa-1367	105	12	as	as	ADV
ijassa-1367	105	13	small	small	ADJ
ijassa-1367	105	14	as	as	ADP
ijassa-1367	105	15	possible	possible	ADJ
ijassa-1367	105	16	.	.	PUNCT
ijassa-1367	106	1	during	during	ADP
ijassa-1367	106	2	processing	processing	NOUN
ijassa-1367	106	3	of	of	ADP
ijassa-1367	106	4	the	the	DET
ijassa-1367	106	5	algorithm	algorithm	NOUN
ijassa-1367	106	6	,	,	PUNCT
ijassa-1367	106	7	if	if	SCONJ
ijassa-1367	106	8	there	there	PRON
ijassa-1367	106	9	are	be	VERB
ijassa-1367	106	10	two	two	NUM
ijassa-1367	106	11	points	point	NOUN
ijassa-1367	106	12	in	in	ADP
ijassa-1367	106	13	the	the	DET
ijassa-1367	106	14	same	same	ADJ
ijassa-1367	106	15	cell	cell	NOUN
ijassa-1367	106	16	at	at	ADP
ijassa-1367	106	17	time	time	NOUN
ijassa-1367	106	18	τi	τi	ADP
ijassa-1367	106	19	,	,	PUNCT
ijassa-1367	106	20	we	we	PRON
ijassa-1367	106	21	must	must	AUX
ijassa-1367	106	22	remove	remove	VERB
ijassa-1367	106	23	less	less	ADV
ijassa-1367	106	24	promising	promising	ADJ
ijassa-1367	106	25	one	one	NUM
ijassa-1367	106	26	,	,	PUNCT
ijassa-1367	106	27	so	so	SCONJ
ijassa-1367	106	28	that	that	SCONJ
ijassa-1367	106	29	not	not	PART
ijassa-1367	106	30	more	more	ADJ
ijassa-1367	106	31	than	than	SCONJ
ijassa-1367	106	32	mn	mn	PROPN
ijassa-1367	106	33	nodes	node	NOUN
ijassa-1367	106	34	are	be	AUX
ijassa-1367	106	35	stored	store	VERB
ijassa-1367	106	36	in	in	ADP
ijassa-1367	106	37	the	the	DET
ijassa-1367	106	38	memory	memory	NOUN
ijassa-1367	106	39	,	,	PUNCT
ijassa-1367	106	40	just	just	ADV
ijassa-1367	106	41	as	as	ADP
ijassa-1367	106	42	in	in	ADP
ijassa-1367	106	43	calculus	calculus	NOUN
ijassa-1367	106	44	of	of	ADP
ijassa-1367	106	45	variations	variation	NOUN
ijassa-1367	106	46	.	.	PUNCT
ijassa-1367	107	1	if	if	SCONJ
ijassa-1367	107	2	x	x	PROPN
ijassa-1367	107	3	∈	∈	PROPN
ijassa-1367	107	4	xj	xj	PROPN
ijassa-1367	107	5	,	,	PUNCT
ijassa-1367	107	6	we	we	PRON
ijassa-1367	107	7	will	will	AUX
ijassa-1367	107	8	write	write	VERB
ijassa-1367	107	9	x̄	x̄	NOUN
ijassa-1367	107	10	=	=	PUNCT
ijassa-1367	108	1	j.	j.	PROPN
ijassa-1367	108	2	the	the	DET
ijassa-1367	108	3	points	point	NOUN
ijassa-1367	108	4	x	x	X
ijassa-1367	108	5	,	,	PUNCT
ijassa-1367	108	6	y	y	PROPN
ijassa-1367	108	7	∈	∈	PROPN
ijassa-1367	108	8	xj	xj	PROPN
ijassa-1367	108	9	of	of	ADP
ijassa-1367	108	10	one	one	NUM
ijassa-1367	108	11	cell	cell	NOUN
ijassa-1367	108	12	xj	xj	PROPN
ijassa-1367	108	13	will	will	AUX
ijassa-1367	108	14	be	be	AUX
ijassa-1367	108	15	regarded	regard	VERB
ijassa-1367	108	16	as	as	ADP
ijassa-1367	108	17	equivalent	equivalent	ADJ
ijassa-1367	108	18	:	:	PUNCT
ijassa-1367	108	19	x	x	SYM
ijassa-1367	108	20	∼	∼	NOUN
ijassa-1367	108	21	y.	y.	NOUN
ijassa-1367	108	22	as	as	SCONJ
ijassa-1367	108	23	was	be	AUX
ijassa-1367	108	24	already	already	ADV
ijassa-1367	108	25	mentioned	mention	VERB
ijassa-1367	108	26	,	,	PUNCT
ijassa-1367	108	27	we	we	PRON
ijassa-1367	108	28	can	can	AUX
ijassa-1367	108	29	achieve	achieve	VERB
ijassa-1367	108	30	that	that	SCONJ
ijassa-1367	108	31	each	each	DET
ijassa-1367	108	32	cell	cell	NOUN
ijassa-1367	108	33	except	except	SCONJ
ijassa-1367	108	34	for	for	ADP
ijassa-1367	108	35	one	one	NUM
ijassa-1367	108	36	consists	consist	NOUN
ijassa-1367	108	37	of	of	ADP
ijassa-1367	108	38	only	only	ADV
ijassa-1367	108	39	one	one	NUM
ijassa-1367	108	40	point	point	NOUN
ijassa-1367	108	41	,	,	PUNCT
ijassa-1367	108	42	and	and	CCONJ
ijassa-1367	108	43	all	all	DET
ijassa-1367	108	44	other	other	ADJ
ijassa-1367	108	45	points	point	NOUN
ijassa-1367	108	46	are	be	AUX
ijassa-1367	108	47	contained	contain	VERB
ijassa-1367	108	48	in	in	ADP
ijassa-1367	108	49	a	a	DET
ijassa-1367	108	50	common	common	ADJ
ijassa-1367	108	51	cell	cell	NOUN
ijassa-1367	108	52	.	.	PUNCT
ijassa-1367	109	1	then	then	ADV
ijassa-1367	109	2	,	,	PUNCT
ijassa-1367	109	3	just	just	ADV
ijassa-1367	109	4	as	as	ADP
ijassa-1367	109	5	in	in	ADP
ijassa-1367	109	6	variational	variational	ADJ
ijassa-1367	109	7	calculus	calculus	NOUN
ijassa-1367	109	8	,	,	PUNCT
ijassa-1367	109	9	there	there	PRON
ijassa-1367	109	10	will	will	AUX
ijassa-1367	109	11	appear	appear	VERB
ijassa-1367	109	12	a	a	DET
ijassa-1367	109	13	regular	regular	ADJ
ijassa-1367	109	14	lattice	lattice	NOUN
ijassa-1367	109	15	in	in	ADP
ijassa-1367	109	16	plane	plane	NOUN
ijassa-1367	109	17	.	.	PUNCT
ijassa-1367	110	1	let	let	VERB
ijassa-1367	110	2	(	(	PUNCT
ijassa-1367	110	3	ξ0	ξ0	ADJ
ijassa-1367	110	4	,	,	PUNCT
ijassa-1367	110	5	ξ1	ξ1	NOUN
ijassa-1367	110	6	,	,	PUNCT
ijassa-1367	110	7	.	.	PUNCT
ijassa-1367	110	8	.	.	PUNCT
ijassa-1367	111	1	.	.	PUNCT
ijassa-1367	112	1	,	,	PUNCT
ijassa-1367	112	2	ξµ	ξµ	X
ijassa-1367	112	3	)	)	PUNCT
ijassa-1367	112	4	(	(	PUNCT
ijassa-1367	112	5	3.5	3.5	NUM
ijassa-1367	112	6	)	)	PUNCT
ijassa-1367	112	7	be	be	VERB
ijassa-1367	112	8	y	y	NOUN
ijassa-1367	112	9	-	-	PUNCT
ijassa-1367	112	10	coordinates	coordinate	NOUN
ijassa-1367	112	11	of	of	ADP
ijassa-1367	112	12	break	break	NOUN
ijassa-1367	112	13	points	point	NOUN
ijassa-1367	112	14	of	of	ADP
ijassa-1367	112	15	a	a	DET
ijassa-1367	112	16	polygonal	polygonal	ADJ
ijassa-1367	112	17	line	line	NOUN
ijassa-1367	112	18	(	(	PUNCT
ijassa-1367	112	19	3.2	3.2	NUM
ijassa-1367	112	20	)	)	PUNCT
ijassa-1367	112	21	.	.	PUNCT
ijassa-1367	113	1	setting	set	VERB
ijassa-1367	113	2	ξ̄i	ξ̄i	PROPN
ijassa-1367	113	3	=	=	SYM
ijassa-1367	113	4	νi	νi	NOUN
ijassa-1367	113	5	,	,	PUNCT
ijassa-1367	113	6	we	we	PRON
ijassa-1367	113	7	get	get	VERB
ijassa-1367	113	8	a	a	DET
ijassa-1367	113	9	sequence	sequence	NOUN
ijassa-1367	113	10	of	of	ADP
ijassa-1367	113	11	integers	integer	NOUN
ijassa-1367	113	12	(	(	PUNCT
ijassa-1367	113	13	ν0	ν0	PROPN
ijassa-1367	113	14	,	,	PUNCT
ijassa-1367	113	15	ν1	ν1	NOUN
ijassa-1367	113	16	,	,	PUNCT
ijassa-1367	113	17	.	.	PUNCT
ijassa-1367	113	18	.	.	PUNCT
ijassa-1367	114	1	.	.	PUNCT
ijassa-1367	115	1	,	,	PUNCT
ijassa-1367	115	2	νµ	νµ	PROPN
ijassa-1367	115	3	)	)	PUNCT
ijassa-1367	115	4	,	,	PUNCT
ijassa-1367	115	5	(	(	PUNCT
ijassa-1367	115	6	3.6	3.6	NUM
ijassa-1367	115	7	)	)	PUNCT
ijassa-1367	116	1	representing	represent	VERB
ijassa-1367	116	2	the	the	DET
ijassa-1367	116	3	numbers	number	NOUN
ijassa-1367	116	4	of	of	ADP
ijassa-1367	116	5	cells	cell	NOUN
ijassa-1367	116	6	,	,	PUNCT
ijassa-1367	116	7	through	through	ADP
ijassa-1367	116	8	which	which	PRON
ijassa-1367	116	9	the	the	DET
ijassa-1367	116	10	polygonal	polygonal	ADJ
ijassa-1367	116	11	line	line	NOUN
ijassa-1367	116	12	passes	pass	VERB
ijassa-1367	116	13	.	.	PUNCT
ijassa-1367	117	1	the	the	DET
ijassa-1367	117	2	program	program	NOUN
ijassa-1367	117	3	is	be	AUX
ijassa-1367	117	4	supposed	suppose	VERB
ijassa-1367	117	5	to	to	PART
ijassa-1367	117	6	include	include	VERB
ijassa-1367	117	7	procedures	procedure	NOUN
ijassa-1367	117	8	to	to	PART
ijassa-1367	117	9	find	find	VERB
ijassa-1367	117	10	(	(	PUNCT
ijassa-1367	117	11	exact	exact	ADJ
ijassa-1367	117	12	or	or	CCONJ
ijassa-1367	117	13	approximate	approximate	ADJ
ijassa-1367	117	14	)	)	PUNCT
ijassa-1367	117	15	values	value	NOUN
ijassa-1367	117	16	of	of	ADP
ijassa-1367	117	17	the	the	DET
ijassa-1367	117	18	functions	function	NOUN
ijassa-1367	117	19	b	b	X
ijassa-1367	117	20	(	(	PUNCT
ijassa-1367	117	21	i	i	PROPN
ijassa-1367	117	22	,	,	PUNCT
ijassa-1367	117	23	j	j	PROPN
ijassa-1367	117	24	,	,	PUNCT
ijassa-1367	117	25	a	a	PRON
ijassa-1367	117	26	)	)	PUNCT
ijassa-1367	117	27	and	and	CCONJ
ijassa-1367	117	28	c	c	X
ijassa-1367	117	29	(	(	PUNCT
ijassa-1367	117	30	i	i	PROPN
ijassa-1367	117	31	,	,	PUNCT
ijassa-1367	117	32	j	j	PROPN
ijassa-1367	117	33	,	,	PUNCT
ijassa-1367	117	34	a	a	PRON
ijassa-1367	117	35	)	)	PUNCT
ijassa-1367	117	36	for	for	ADP
ijassa-1367	117	37	arbitrary	arbitrary	ADJ
ijassa-1367	117	38	integers	integer	NOUN
ijassa-1367	118	1	i	i	NOUN
ijassa-1367	118	2	=	=	NOUN
ijassa-1367	118	3	0	0	NUM
ijassa-1367	118	4	,	,	PUNCT
ijassa-1367	118	5	1	1	NUM
ijassa-1367	118	6	,	,	PUNCT
ijassa-1367	118	7	.	.	PUNCT
ijassa-1367	118	8	.	.	PUNCT
ijassa-1367	118	9	.	.	PUNCT
ijassa-1367	119	1	,	,	PUNCT
ijassa-1367	119	2	m	m	PROPN
ijassa-1367	119	3	,	,	PUNCT
ijassa-1367	119	4	j	j	PROPN
ijassa-1367	119	5	=	=	SYM
ijassa-1367	119	6	1	1	NUM
ijassa-1367	119	7	,	,	PUNCT
ijassa-1367	119	8	.	.	PUNCT
ijassa-1367	119	9	.	.	PUNCT
ijassa-1367	120	1	.	.	PUNCT
ijassa-1367	121	1	,	,	PUNCT
ijassa-1367	121	2	l	l	NOUN
ijassa-1367	121	3	and	and	CCONJ
ijassa-1367	121	4	a	a	DET
ijassa-1367	121	5	real	real	ADJ
ijassa-1367	121	6	number	number	NOUN
ijassa-1367	121	7	a	a	DET
ijassa-1367	121	8	∈	∈	NOUN
ijassa-1367	121	9	x	x	SYM
ijassa-1367	121	10	(	(	PUNCT
ijassa-1367	121	11	3.4	3.4	NUM
ijassa-1367	121	12	)	)	PUNCT
ijassa-1367	121	13	.	.	PUNCT
ijassa-1367	122	1	3.3	3.3	NUM
ijassa-1367	122	2	.	.	PUNCT
ijassa-1367	123	1	optimization	optimization	NOUN
ijassa-1367	123	2	algorithm	algorithm	NOUN
ijassa-1367	123	3	while	while	SCONJ
ijassa-1367	123	4	processing	processing	NOUN
ijassa-1367	123	5	,	,	PUNCT
ijassa-1367	123	6	the	the	DET
ijassa-1367	123	7	program	program	NOUN
ijassa-1367	123	8	forms	form	VERB
ijassa-1367	123	9	the	the	DET
ijassa-1367	123	10	arrays	array	NOUN
ijassa-1367	123	11	s[i	s[i	NOUN
ijassa-1367	123	12	,	,	PUNCT
ijassa-1367	123	13	j	j	NOUN
ijassa-1367	123	14	]	]	X
ijassa-1367	123	15	,	,	PUNCT
ijassa-1367	123	16	φ[i	φ[i	PROPN
ijassa-1367	123	17	,	,	PUNCT
ijassa-1367	123	18	j	j	PROPN
ijassa-1367	123	19	]	]	X
ijassa-1367	123	20	,	,	PUNCT
ijassa-1367	123	21	w[i	w[i	PROPN
ijassa-1367	123	22	,	,	PUNCT
ijassa-1367	123	23	j	j	PROPN
ijassa-1367	123	24	]	]	X
ijassa-1367	123	25	,	,	PUNCT
ijassa-1367	123	26	a[i	a[i	PROPN
ijassa-1367	123	27	,	,	PUNCT
ijassa-1367	123	28	j	j	PROPN
ijassa-1367	123	29	]	]	X
ijassa-1367	123	30	,	,	PUNCT
ijassa-1367	123	31	i	i	PRON
ijassa-1367	123	32	=	=	NOUN
ijassa-1367	123	33	1	1	NUM
ijassa-1367	123	34	,	,	PUNCT
ijassa-1367	123	35	.	.	PUNCT
ijassa-1367	123	36	.	.	PUNCT
ijassa-1367	123	37	.	.	PUNCT
ijassa-1367	124	1	,	,	PUNCT
ijassa-1367	124	2	m	m	PROPN
ijassa-1367	124	3	,	,	PUNCT
ijassa-1367	124	4	j	j	PROPN
ijassa-1367	124	5	=	=	SYM
ijassa-1367	124	6	1	1	NUM
ijassa-1367	124	7	,	,	PUNCT
ijassa-1367	124	8	.	.	PUNCT
ijassa-1367	124	9	.	.	PUNCT
ijassa-1367	125	1	.	.	PUNCT
ijassa-1367	126	1	,	,	PUNCT
ijassa-1367	126	2	n	n	CCONJ
ijassa-1367	126	3	which	which	PRON
ijassa-1367	126	4	could	could	AUX
ijassa-1367	126	5	be	be	AUX
ijassa-1367	126	6	interpreted	interpret	VERB
ijassa-1367	126	7	as	as	ADP
ijassa-1367	126	8	follows	follow	VERB
ijassa-1367	126	9	:	:	PUNCT
ijassa-1367	126	10	σ	σ	NUM
ijassa-1367	126	11	=	=	SYM
ijassa-1367	126	12	s[i	s[i	NOUN
ijassa-1367	126	13	,	,	PUNCT
ijassa-1367	126	14	j	j	PROPN
ijassa-1367	126	15	]	]	X
ijassa-1367	126	16	is	be	AUX
ijassa-1367	126	17	a	a	DET
ijassa-1367	126	18	number	number	NOUN
ijassa-1367	126	19	of	of	ADP
ijassa-1367	126	20	the	the	DET
ijassa-1367	126	21	preceding	precede	VERB
ijassa-1367	126	22	cell	cell	NOUN
ijassa-1367	126	23	xσ	xσ	ADP
ijassa-1367	126	24	;	;	PUNCT
ijassa-1367	126	25	x	x	X
ijassa-1367	126	26	=	=	SYM
ijassa-1367	126	27	φ[i	φ[i	PROPN
ijassa-1367	126	28	,	,	PUNCT
ijassa-1367	126	29	j	j	X
ijassa-1367	126	30	]	]	X
ijassa-1367	126	31	∈	∈	PROPN
ijassa-1367	126	32	xj	xj	PROPN
ijassa-1367	126	33	–	–	PUNCT
ijassa-1367	126	34	is	be	AUX
ijassa-1367	126	35	a	a	DET
ijassa-1367	126	36	“	"	PUNCT
ijassa-1367	126	37	best	good	ADJ
ijassa-1367	126	38	”	"	PUNCT
ijassa-1367	126	39	point	point	NOUN
ijassa-1367	126	40	of	of	ADP
ijassa-1367	126	41	the	the	DET
ijassa-1367	126	42	cell	cell	NOUN
ijassa-1367	126	43	xj	xj	PROPN
ijassa-1367	126	44	,	,	PUNCT
ijassa-1367	126	45	into	into	ADP
ijassa-1367	126	46	which	which	PRON
ijassa-1367	126	47	the	the	DET
ijassa-1367	126	48	system	system	NOUN
ijassa-1367	126	49	is	be	AUX
ijassa-1367	126	50	got	get	VERB
ijassa-1367	126	51	at	at	ADP
ijassa-1367	126	52	the	the	DET
ijassa-1367	126	53	moment	moment	NOUN
ijassa-1367	126	54	τi	τi	ADP
ijassa-1367	126	55	;	;	PUNCT
ijassa-1367	126	56	u	u	NOUN
ijassa-1367	126	57	=	=	PROPN
ijassa-1367	126	58	w[i	w[i	PROPN
ijassa-1367	126	59	,	,	PUNCT
ijassa-1367	126	60	j	j	X
ijassa-1367	126	61	]	]	X
ijassa-1367	126	62	∈	∈	PROPN
ijassa-1367	126	63	v	v	NOUN
ijassa-1367	126	64	is	be	AUX
ijassa-1367	126	65	a	a	DET
ijassa-1367	126	66	control	control	NOUN
ijassa-1367	126	67	bringing	bring	VERB
ijassa-1367	126	68	the	the	DET
ijassa-1367	126	69	system	system	NOUN
ijassa-1367	126	70	to	to	ADP
ijassa-1367	126	71	the	the	DET
ijassa-1367	126	72	point	point	NOUN
ijassa-1367	126	73	(	(	PUNCT
ijassa-1367	126	74	τi	τi	ADP
ijassa-1367	126	75	,	,	PUNCT
ijassa-1367	126	76	φ[i	φ[i	PROPN
ijassa-1367	126	77	,	,	PUNCT
ijassa-1367	126	78	j	j	NOUN
ijassa-1367	126	79	]	]	X
ijassa-1367	126	80	)	)	PUNCT
ijassa-1367	126	81	;	;	PUNCT
ijassa-1367	126	82	a[i	a[i	PROPN
ijassa-1367	126	83	,	,	PUNCT
ijassa-1367	126	84	j	j	PROPN
ijassa-1367	126	85	]	]	X
ijassa-1367	126	86	is	be	AUX
ijassa-1367	126	87	a	a	DET
ijassa-1367	126	88	hamilton	hamilton	PROPN
ijassa-1367	126	89	function	function	NOUN
ijassa-1367	126	90	of	of	ADP
ijassa-1367	126	91	action	action	NOUN
ijassa-1367	126	92	(	(	PUNCT
ijassa-1367	126	93	the	the	DET
ijassa-1367	126	94	analogue	analogue	NOUN
ijassa-1367	126	95	of	of	ADP
ijassa-1367	126	96	a	a	DET
ijassa-1367	126	97	bellman	bellman	NOUN
ijassa-1367	126	98	function	function	NOUN
ijassa-1367	126	99	with	with	ADP
ijassa-1367	126	100	time	time	NOUN
ijassa-1367	126	101	reversal	reversal	NOUN
ijassa-1367	126	102	)	)	PUNCT
ijassa-1367	126	103	.	.	PUNCT
ijassa-1367	127	1	the	the	DET
ijassa-1367	127	2	function	function	NOUN
ijassa-1367	127	3	a(i	a(i	PROPN
ijassa-1367	127	4	,	,	PUNCT
ijassa-1367	127	5	j	j	NOUN
ijassa-1367	127	6	)	)	PUNCT
ijassa-1367	127	7	represents	represent	VERB
ijassa-1367	127	8	the	the	DET
ijassa-1367	127	9	estimation	estimation	NOUN
ijassa-1367	127	10	of	of	ADP
ijassa-1367	127	11	the	the	DET
ijassa-1367	127	12	cost	cost	NOUN
ijassa-1367	127	13	of	of	ADP
ijassa-1367	127	14	an	an	DET
ijassa-1367	127	15	optimal	optimal	ADJ
ijassa-1367	127	16	polygonal	polygonal	ADJ
ijassa-1367	127	17	line	line	NOUN
ijassa-1367	127	18	starting	start	VERB
ijassa-1367	127	19	at	at	ADP
ijassa-1367	127	20	(	(	PUNCT
ijassa-1367	127	21	t0	t0	PROPN
ijassa-1367	127	22	,	,	PUNCT
ijassa-1367	127	23	x0	x0	PROPN
ijassa-1367	127	24	)	)	PUNCT
ijassa-1367	127	25	and	and	CCONJ
ijassa-1367	127	26	terminating	terminate	VERB
ijassa-1367	127	27	at	at	ADP
ijassa-1367	127	28	xj	xj	PROPN
ijassa-1367	127	29	at	at	ADP
ijassa-1367	127	30	instant	instant	ADJ
ijassa-1367	127	31	τi	τi	NOUN
ijassa-1367	127	32	.	.	PUNCT
ijassa-1367	128	1	generally	generally	ADV
ijassa-1367	128	2	,	,	PUNCT
ijassa-1367	128	3	the	the	DET
ijassa-1367	128	4	program	program	NOUN
ijassa-1367	128	5	consists	consist	VERB
ijassa-1367	128	6	of	of	ADP
ijassa-1367	128	7	four	four	NUM
ijassa-1367	128	8	subsequent	subsequent	ADJ
ijassa-1367	128	9	procedures	procedure	NOUN
ijassa-1367	128	10	.	.	PUNCT
ijassa-1367	129	1	the	the	DET
ijassa-1367	129	2	comments	comment	NOUN
ijassa-1367	129	3	are	be	AUX
ijassa-1367	129	4	enclosed	enclose	VERB
ijassa-1367	129	5	in	in	ADP
ijassa-1367	129	6	braces	brace	NOUN
ijassa-1367	129	7	.	.	PUNCT
ijassa-1367	130	1	program	program	NOUN
ijassa-1367	130	2	“	"	PUNCT
ijassa-1367	130	3	solution	solution	NOUN
ijassa-1367	130	4	of	of	ADP
ijassa-1367	130	5	a	a	DET
ijassa-1367	130	6	fixed	fix	VERB
ijassa-1367	130	7	time	time	NOUN
ijassa-1367	130	8	optimal	optimal	ADJ
ijassa-1367	130	9	control	control	NOUN
ijassa-1367	130	10	problem	problem	NOUN
ijassa-1367	130	11	in	in	ADP
ijassa-1367	130	12	the	the	DET
ijassa-1367	130	13	class	class	NOUN
ijassa-1367	130	14	of	of	ADP
ijassa-1367	130	15	polygonal	polygonal	ADJ
ijassa-1367	130	16	lines	line	NOUN
ijassa-1367	130	17	”	"	PUNCT
ijassa-1367	130	18	{	{	PUNCT
ijassa-1367	130	19	set	set	VERB
ijassa-1367	130	20	initial	initial	ADJ
ijassa-1367	130	21	values	value	NOUN
ijassa-1367	130	22	of	of	ADP
ijassa-1367	130	23	action	action	NOUN
ijassa-1367	130	24	:}	:}	PUNCT
ijassa-1367	131	1	a	a	PRON
ijassa-1367	132	1	[	[	X
ijassa-1367	132	2	0	0	NUM
ijassa-1367	132	3	,	,	PUNCT
ijassa-1367	132	4	x̄0	x̄0	PROPN
ijassa-1367	132	5	]	]	X
ijassa-1367	132	6	:	:	PUNCT
ijassa-1367	132	7	=	=	SYM
ijassa-1367	132	8	0	0	NUM
ijassa-1367	132	9	;	;	PUNCT
ijassa-1367	132	10	a	a	DET
ijassa-1367	132	11	[	[	X
ijassa-1367	132	12	i	i	PROPN
ijassa-1367	132	13	,	,	PUNCT
ijassa-1367	132	14	j	j	PROPN
ijassa-1367	132	15	]	]	X
ijassa-1367	132	16	:	:	PUNCT
ijassa-1367	132	17	=	=	SYM
ijassa-1367	132	18	∞	∞	PROPN
ijassa-1367	132	19	for	for	ADP
ijassa-1367	132	20	all	all	DET
ijassa-1367	132	21	i	i	PROPN
ijassa-1367	132	22	,	,	PUNCT
ijassa-1367	132	23	j	j	PROPN
ijassa-1367	132	24	>	>	X
ijassa-1367	132	25	0	0	NUM
ijassa-1367	132	26	;	;	PUNCT
ijassa-1367	132	27	fill	fill	VERB
ijassa-1367	132	28	in	in	ADP
ijassa-1367	132	29	the	the	DET
ijassa-1367	132	30	left	left	ADJ
ijassa-1367	132	31	vertical	vertical	ADJ
ijassa-1367	132	32	column	column	NOUN
ijassa-1367	132	33	t	t	PROPN
ijassa-1367	132	34	=	=	SYM
ijassa-1367	132	35	τ1	τ1	PROPN
ijassa-1367	132	36	;	;	PUNCT
ijassa-1367	132	37	fill	fill	NOUN
ijassa-1367	132	38	in	in	ADP
ijassa-1367	132	39	the	the	DET
ijassa-1367	132	40	other	other	ADJ
ijassa-1367	132	41	columns	column	NOUN
ijassa-1367	132	42	t	t	NOUN
ijassa-1367	132	43	=	=	PUNCT
ijassa-1367	132	44	τi	τi	PROPN
ijassa-1367	132	45	,	,	PUNCT
ijassa-1367	132	46	i	i	PRON
ijassa-1367	132	47	>	>	X
ijassa-1367	132	48	1	1	NUM
ijassa-1367	132	49	,	,	PUNCT
ijassa-1367	132	50	from	from	ADP
ijassa-1367	132	51	left	leave	VERB
ijassa-1367	132	52	to	to	ADP
ijassa-1367	132	53	right	right	NOUN
ijassa-1367	132	54	;	;	PUNCT
ijassa-1367	132	55	construct	construct	VERB
ijassa-1367	132	56	the	the	DET
ijassa-1367	132	57	polygonal	polygonal	ADJ
ijassa-1367	132	58	line	line	NOUN
ijassa-1367	132	59	by	by	ADP
ijassa-1367	132	60	moving	move	VERB
ijassa-1367	132	61	backward	backward	ADV
ijassa-1367	132	62	;	;	PUNCT
ijassa-1367	132	63	end	end	NOUN
ijassa-1367	132	64	of	of	ADP
ijassa-1367	132	65	program	program	NOUN
ijassa-1367	132	66	now	now	ADV
ijassa-1367	132	67	we	we	PRON
ijassa-1367	132	68	describe	describe	VERB
ijassa-1367	132	69	procedures	procedure	NOUN
ijassa-1367	132	70	constituting	constitute	VERB
ijassa-1367	132	71	the	the	DET
ijassa-1367	132	72	program	program	NOUN
ijassa-1367	132	73	.	.	PUNCT
ijassa-1367	133	1	copyright	copyright	NOUN
ijassa-1367	133	2	©	©	PROPN
ijassa-1367	133	3	2023	2023	NUM
ijassa-1367	133	4	assa	assa	NOUN
ijassa-1367	133	5	.	.	PUNCT
ijassa-1367	134	1	adv	adv	PROPN
ijassa-1367	134	2	syst	syst	PROPN
ijassa-1367	134	3	sci	sci	PROPN
ijassa-1367	134	4	appl	appl	PROPN
ijassa-1367	134	5	(	(	PUNCT
ijassa-1367	134	6	2023	2023	NUM
ijassa-1367	134	7	)	)	PUNCT
ijassa-1367	134	8	40	40	NUM
ijassa-1367	135	1	o.	o.	PROPN
ijassa-1367	135	2	e.	e.	PROPN
ijassa-1367	135	3	orel	orel	PROPN
ijassa-1367	135	4	,	,	PUNCT
ijassa-1367	135	5	e.	e.	PROPN
ijassa-1367	135	6	n.	n.	PROPN
ijassa-1367	135	7	orel	orel	PROPN
ijassa-1367	135	8	procedure	procedure	NOUN
ijassa-1367	135	9	“	"	PUNCT
ijassa-1367	135	10	fill	fill	VERB
ijassa-1367	135	11	in	in	ADP
ijassa-1367	135	12	the	the	DET
ijassa-1367	135	13	left	left	ADJ
ijassa-1367	135	14	vertical	vertical	ADJ
ijassa-1367	135	15	column	column	NOUN
ijassa-1367	135	16	”	"	PUNCT
ijassa-1367	135	17	for	for	ADP
ijassa-1367	135	18	k	k	PROPN
ijassa-1367	135	19	:	:	PUNCT
ijassa-1367	135	20	=	=	SYM
ijassa-1367	135	21	1	1	NUM
ijassa-1367	135	22	to	to	PART
ijassa-1367	135	23	l	l	PROPN
ijassa-1367	135	24	do	do	AUX
ijassa-1367	135	25	begin	begin	VERB
ijassa-1367	135	26	{	{	PUNCT
ijassa-1367	135	27	sorting	sort	VERB
ijassa-1367	135	28	all	all	DET
ijassa-1367	135	29	the	the	DET
ijassa-1367	135	30	controls	control	NOUN
ijassa-1367	135	31	of	of	ADP
ijassa-1367	135	32	v	v	NOUN
ijassa-1367	135	33	}	}	PUNCT
ijassa-1367	135	34	y	y	NOUN
ijassa-1367	135	35	:	:	PUNCT
ijassa-1367	135	36	=	=	SYM
ijassa-1367	135	37	b	b	X
ijassa-1367	135	38	(	(	PUNCT
ijassa-1367	135	39	1	1	NUM
ijassa-1367	135	40	,	,	PUNCT
ijassa-1367	135	41	k	k	NOUN
ijassa-1367	135	42	,	,	PUNCT
ijassa-1367	135	43	x0	x0	PROPN
ijassa-1367	135	44	)	)	PUNCT
ijassa-1367	135	45	;	;	PUNCT
ijassa-1367	135	46	ν	ν	X
ijassa-1367	135	47	:	:	PUNCT
ijassa-1367	135	48	=	=	SYM
ijassa-1367	135	49	ȳ	ȳ	PROPN
ijassa-1367	135	50	;	;	PUNCT
ijassa-1367	135	51	r	r	NOUN
ijassa-1367	135	52	:	:	PUNCT
ijassa-1367	136	1	=	=	SYM
ijassa-1367	136	2	c	c	X
ijassa-1367	136	3	(	(	PUNCT
ijassa-1367	136	4	1	1	NUM
ijassa-1367	136	5	,	,	PUNCT
ijassa-1367	136	6	k	k	NOUN
ijassa-1367	136	7	,	,	PUNCT
ijassa-1367	136	8	x0	x0	PROPN
ijassa-1367	136	9	)	)	PUNCT
ijassa-1367	136	10	;	;	PUNCT
ijassa-1367	136	11	{	{	PUNCT
ijassa-1367	136	12	next	next	ADJ
ijassa-1367	136	13	node	node	PROPN
ijassa-1367	136	14	(	(	PUNCT
ijassa-1367	136	15	τ1	τ1	PROPN
ijassa-1367	136	16	,	,	PUNCT
ijassa-1367	136	17	y	y	NOUN
ijassa-1367	136	18	)	)	PUNCT
ijassa-1367	136	19	and	and	CCONJ
ijassa-1367	136	20	action	action	NOUN
ijassa-1367	136	21	r	r	NOUN
ijassa-1367	136	22	=	=	PUNCT
ijassa-1367	136	23	a(1	a(1	PROPN
ijassa-1367	136	24	,	,	PUNCT
ijassa-1367	136	25	ȳ	ȳ	NOUN
ijassa-1367	136	26	)	)	PUNCT
ijassa-1367	136	27	}	}	PUNCT
ijassa-1367	136	28	if	if	SCONJ
ijassa-1367	136	29	r	r	NOUN
ijassa-1367	136	30	<	<	X
ijassa-1367	136	31	a	a	PRON
ijassa-1367	136	32	[	[	X
ijassa-1367	136	33	1	1	NUM
ijassa-1367	136	34	,	,	PUNCT
ijassa-1367	136	35	ν	ν	X
ijassa-1367	136	36	]	]	PUNCT
ijassa-1367	136	37	then	then	ADV
ijassa-1367	136	38	begin	begin	VERB
ijassa-1367	136	39	{	{	PUNCT
ijassa-1367	136	40	value	value	VERB
ijassa-1367	136	41	a	a	PRON
ijassa-1367	136	42	[	[	X
ijassa-1367	136	43	1	1	NUM
ijassa-1367	136	44	,	,	PUNCT
ijassa-1367	136	45	ν	ν	X
ijassa-1367	136	46	]	]	PUNCT
ijassa-1367	136	47	is	be	AUX
ijassa-1367	136	48	decreased	decrease	VERB
ijassa-1367	136	49	}	}	PUNCT
ijassa-1367	136	50	s	s	PART
ijassa-1367	136	51	[	[	X
ijassa-1367	136	52	1	1	NUM
ijassa-1367	136	53	,	,	PUNCT
ijassa-1367	136	54	ν	ν	X
ijassa-1367	136	55	]	]	X
ijassa-1367	136	56	:	:	PUNCT
ijassa-1367	136	57	=	=	SYM
ijassa-1367	136	58	x̄0	x̄0	X
ijassa-1367	136	59	;	;	PUNCT
ijassa-1367	136	60	{	{	PUNCT
ijassa-1367	136	61	initial	initial	ADJ
ijassa-1367	136	62	class	class	NOUN
ijassa-1367	136	63	}	}	PUNCT
ijassa-1367	136	64	a	a	PRON
ijassa-1367	137	1	[	[	X
ijassa-1367	137	2	1	1	NUM
ijassa-1367	137	3	,	,	PUNCT
ijassa-1367	137	4	ν	ν	X
ijassa-1367	137	5	]	]	X
ijassa-1367	137	6	:	:	PUNCT
ijassa-1367	137	7	=	=	SYM
ijassa-1367	137	8	r	r	NOUN
ijassa-1367	137	9	;	;	PUNCT
ijassa-1367	137	10	{	{	PUNCT
ijassa-1367	137	11	action	action	NOUN
ijassa-1367	137	12	}	}	PUNCT
ijassa-1367	137	13	φ[1	φ[1	PROPN
ijassa-1367	137	14	,	,	PUNCT
ijassa-1367	137	15	ν	ν	X
ijassa-1367	137	16	]	]	X
ijassa-1367	137	17	:	:	PUNCT
ijassa-1367	137	18	=	=	SYM
ijassa-1367	137	19	y	y	NOUN
ijassa-1367	137	20	;	;	PUNCT
ijassa-1367	137	21	w[1	w[1	NOUN
ijassa-1367	137	22	,	,	PUNCT
ijassa-1367	137	23	ν	ν	X
ijassa-1367	137	24	]	]	X
ijassa-1367	137	25	:	:	PUNCT
ijassa-1367	137	26	=	=	SYM
ijassa-1367	137	27	k	k	X
ijassa-1367	137	28	;	;	PUNCT
ijassa-1367	137	29	{	{	PUNCT
ijassa-1367	137	30	control	control	NOUN
ijassa-1367	137	31	x̄0	x̄0	PUNCT
ijassa-1367	137	32	→	→	PUNCT
ijassa-1367	137	33	ν	ν	NOUN
ijassa-1367	137	34	}	}	PUNCT
ijassa-1367	137	35	end	end	NOUN
ijassa-1367	137	36	;	;	PUNCT
ijassa-1367	137	37	end	end	NOUN
ijassa-1367	137	38	;	;	PUNCT
ijassa-1367	137	39	end	end	NOUN
ijassa-1367	137	40	of	of	ADP
ijassa-1367	137	41	procedure	procedure	NOUN
ijassa-1367	137	42	procedure	procedure	NOUN
ijassa-1367	137	43	“	"	PUNCT
ijassa-1367	137	44	fill	fill	NOUN
ijassa-1367	137	45	in	in	ADP
ijassa-1367	137	46	the	the	DET
ijassa-1367	137	47	other	other	ADJ
ijassa-1367	137	48	columns	column	NOUN
ijassa-1367	137	49	”	"	PUNCT
ijassa-1367	137	50	for	for	ADP
ijassa-1367	137	51	i	i	PRON
ijassa-1367	137	52	:	:	PUNCT
ijassa-1367	137	53	=	=	SYM
ijassa-1367	137	54	2	2	NUM
ijassa-1367	137	55	to	to	PART
ijassa-1367	137	56	m	m	PROPN
ijassa-1367	137	57	do	do	AUX
ijassa-1367	137	58	{	{	PUNCT
ijassa-1367	137	59	processing	process	VERB
ijassa-1367	137	60	vertical	vertical	ADJ
ijassa-1367	137	61	columns	column	NOUN
ijassa-1367	137	62	i	i	PRON
ijassa-1367	137	63	>	>	X
ijassa-1367	137	64	1	1	NUM
ijassa-1367	137	65	from	from	ADP
ijassa-1367	137	66	left	leave	VERB
ijassa-1367	137	67	to	to	ADP
ijassa-1367	137	68	right	right	NOUN
ijassa-1367	137	69	}	}	PUNCT
ijassa-1367	137	70	for	for	ADP
ijassa-1367	137	71	j	j	PROPN
ijassa-1367	137	72	:	:	PUNCT
ijassa-1367	137	73	=	=	SYM
ijassa-1367	137	74	1	1	NUM
ijassa-1367	137	75	to	to	PART
ijassa-1367	137	76	n	n	PRON
ijassa-1367	137	77	do	do	AUX
ijassa-1367	137	78	begin	begin	VERB
ijassa-1367	137	79	{	{	PUNCT
ijassa-1367	137	80	passing	pass	VERB
ijassa-1367	137	81	through	through	ADP
ijassa-1367	137	82	cells	cell	NOUN
ijassa-1367	137	83	for	for	ADP
ijassa-1367	137	84	t	t	PROPN
ijassa-1367	137	85	=	=	SYM
ijassa-1367	137	86	τi−1	τi−1	PROPN
ijassa-1367	137	87	}	}	PUNCT
ijassa-1367	137	88	x	x	SYM
ijassa-1367	137	89	:	:	PUNCT
ijassa-1367	137	90	=	=	SYM
ijassa-1367	137	91	φ[i−	φ[i−	X
ijassa-1367	137	92	1	1	NUM
ijassa-1367	137	93	,	,	PUNCT
ijassa-1367	137	94	j	j	PROPN
ijassa-1367	137	95	]	]	X
ijassa-1367	137	96	;	;	PUNCT
ijassa-1367	137	97	p	p	X
ijassa-1367	137	98	:	:	PUNCT
ijassa-1367	137	99	=	=	PUNCT
ijassa-1367	137	100	a	a	DET
ijassa-1367	137	101	[	[	X
ijassa-1367	137	102	i−	i−	PROPN
ijassa-1367	137	103	1	1	NUM
ijassa-1367	137	104	,	,	PUNCT
ijassa-1367	137	105	j	j	NOUN
ijassa-1367	137	106	]	]	X
ijassa-1367	137	107	;	;	PUNCT
ijassa-1367	137	108	for	for	ADP
ijassa-1367	137	109	k	k	PROPN
ijassa-1367	137	110	:	:	PUNCT
ijassa-1367	137	111	=	=	SYM
ijassa-1367	138	1	1	1	NUM
ijassa-1367	138	2	to	to	PART
ijassa-1367	138	3	l	l	PROPN
ijassa-1367	138	4	do	do	AUX
ijassa-1367	138	5	begin	begin	VERB
ijassa-1367	138	6	{	{	PUNCT
ijassa-1367	138	7	sorting	sort	VERB
ijassa-1367	138	8	all	all	DET
ijassa-1367	138	9	the	the	DET
ijassa-1367	138	10	controls	control	NOUN
ijassa-1367	138	11	of	of	ADP
ijassa-1367	138	12	v	v	NOUN
ijassa-1367	138	13	}	}	PUNCT
ijassa-1367	138	14	y	y	NOUN
ijassa-1367	138	15	:	:	PUNCT
ijassa-1367	138	16	=	=	SYM
ijassa-1367	138	17	b	b	X
ijassa-1367	138	18	(	(	PUNCT
ijassa-1367	138	19	i	i	PROPN
ijassa-1367	138	20	,	,	PUNCT
ijassa-1367	138	21	k	k	PROPN
ijassa-1367	138	22	,	,	PUNCT
ijassa-1367	138	23	x	x	X
ijassa-1367	138	24	)	)	PUNCT
ijassa-1367	138	25	;	;	PUNCT
ijassa-1367	138	26	ν	ν	X
ijassa-1367	138	27	:	:	PUNCT
ijassa-1367	138	28	=	=	SYM
ijassa-1367	138	29	ȳ	ȳ	PROPN
ijassa-1367	138	30	;	;	PUNCT
ijassa-1367	138	31	r	r	NOUN
ijassa-1367	138	32	:	:	PUNCT
ijassa-1367	138	33	=	=	SYM
ijassa-1367	138	34	p+	p+	PROPN
ijassa-1367	138	35	c	c	X
ijassa-1367	138	36	(	(	PUNCT
ijassa-1367	138	37	i	i	PROPN
ijassa-1367	138	38	,	,	PUNCT
ijassa-1367	138	39	k	k	PROPN
ijassa-1367	138	40	,	,	PUNCT
ijassa-1367	138	41	x	x	X
ijassa-1367	138	42	)	)	PUNCT
ijassa-1367	138	43	;	;	PUNCT
ijassa-1367	138	44	{	{	PUNCT
ijassa-1367	138	45	next	next	ADJ
ijassa-1367	138	46	node	node	PROPN
ijassa-1367	138	47	(	(	PUNCT
ijassa-1367	138	48	τi	τi	PROPN
ijassa-1367	138	49	,	,	PUNCT
ijassa-1367	138	50	y	y	NOUN
ijassa-1367	138	51	)	)	PUNCT
ijassa-1367	138	52	and	and	CCONJ
ijassa-1367	138	53	action	action	NOUN
ijassa-1367	138	54	r	r	NOUN
ijassa-1367	138	55	=	=	SYM
ijassa-1367	138	56	a(i	a(i	PROPN
ijassa-1367	138	57	,	,	PUNCT
ijassa-1367	138	58	ȳ	ȳ	NOUN
ijassa-1367	138	59	)	)	PUNCT
ijassa-1367	138	60	}	}	PUNCT
ijassa-1367	138	61	if	if	SCONJ
ijassa-1367	138	62	r	r	NOUN
ijassa-1367	138	63	<	<	X
ijassa-1367	138	64	a	a	PRON
ijassa-1367	138	65	[	[	X
ijassa-1367	138	66	i	i	X
ijassa-1367	138	67	,	,	PUNCT
ijassa-1367	138	68	ν	ν	X
ijassa-1367	138	69	]	]	PUNCT
ijassa-1367	138	70	then	then	ADV
ijassa-1367	138	71	begin	begin	VERB
ijassa-1367	138	72	{	{	PUNCT
ijassa-1367	138	73	value	value	VERB
ijassa-1367	138	74	a	a	PRON
ijassa-1367	138	75	[	[	X
ijassa-1367	138	76	i	i	X
ijassa-1367	138	77	,	,	PUNCT
ijassa-1367	138	78	ν	ν	X
ijassa-1367	138	79	]	]	PUNCT
ijassa-1367	138	80	is	be	AUX
ijassa-1367	138	81	decreased	decrease	VERB
ijassa-1367	138	82	}	}	PUNCT
ijassa-1367	138	83	s	s	PART
ijassa-1367	139	1	[	[	X
ijassa-1367	139	2	i	i	PRON
ijassa-1367	139	3	,	,	PUNCT
ijassa-1367	139	4	ν	ν	X
ijassa-1367	139	5	]	]	X
ijassa-1367	139	6	:	:	PUNCT
ijassa-1367	139	7	=	=	SYM
ijassa-1367	139	8	j	j	PROPN
ijassa-1367	139	9	;	;	PUNCT
ijassa-1367	139	10	{	{	PUNCT
ijassa-1367	139	11	preceding	precede	VERB
ijassa-1367	139	12	class	class	NOUN
ijassa-1367	139	13	}	}	PUNCT
ijassa-1367	139	14	a	a	PRON
ijassa-1367	140	1	[	[	X
ijassa-1367	140	2	i	i	X
ijassa-1367	140	3	,	,	PUNCT
ijassa-1367	140	4	ν	ν	X
ijassa-1367	140	5	]	]	PUNCT
ijassa-1367	140	6	:	:	PUNCT
ijassa-1367	140	7	=	=	SYM
ijassa-1367	140	8	r	r	NOUN
ijassa-1367	140	9	;	;	PUNCT
ijassa-1367	140	10	{	{	PUNCT
ijassa-1367	140	11	action	action	NOUN
ijassa-1367	140	12	}	}	PUNCT
ijassa-1367	140	13	φ[i	φ[i	PROPN
ijassa-1367	140	14	,	,	PUNCT
ijassa-1367	140	15	ν	ν	X
ijassa-1367	140	16	]	]	X
ijassa-1367	140	17	:	:	PUNCT
ijassa-1367	140	18	=	=	SYM
ijassa-1367	140	19	y	y	PROPN
ijassa-1367	140	20	;	;	PUNCT
ijassa-1367	140	21	w[i	w[i	NOUN
ijassa-1367	140	22	,	,	PUNCT
ijassa-1367	140	23	ν	ν	X
ijassa-1367	140	24	]	]	X
ijassa-1367	140	25	:	:	PUNCT
ijassa-1367	140	26	=	=	SYM
ijassa-1367	140	27	k	k	X
ijassa-1367	140	28	;	;	PUNCT
ijassa-1367	140	29	{	{	PUNCT
ijassa-1367	140	30	control	control	NOUN
ijassa-1367	140	31	j	j	PROPN
ijassa-1367	140	32	→	→	SYM
ijassa-1367	140	33	ν	ν	NOUN
ijassa-1367	140	34	}	}	PUNCT
ijassa-1367	140	35	end	end	NOUN
ijassa-1367	140	36	;	;	PUNCT
ijassa-1367	140	37	end	end	NOUN
ijassa-1367	140	38	;	;	PUNCT
ijassa-1367	140	39	end	end	NOUN
ijassa-1367	140	40	;	;	PUNCT
ijassa-1367	140	41	end	end	NOUN
ijassa-1367	140	42	of	of	ADP
ijassa-1367	140	43	procedure	procedure	NOUN
ijassa-1367	140	44	procedure	procedure	NOUN
ijassa-1367	140	45	“	"	PUNCT
ijassa-1367	140	46	construct	construct	VERB
ijassa-1367	140	47	γ	γ	NOUN
ijassa-1367	140	48	,	,	PUNCT
ijassa-1367	140	49	starting	start	VERB
ijassa-1367	140	50	at	at	ADP
ijassa-1367	140	51	(	(	PUNCT
ijassa-1367	140	52	t0	t0	PROPN
ijassa-1367	140	53	,	,	PUNCT
ijassa-1367	140	54	x0	x0	PROPN
ijassa-1367	140	55	)	)	PUNCT
ijassa-1367	140	56	and	and	CCONJ
ijassa-1367	140	57	bringing	bring	VERB
ijassa-1367	140	58	the	the	DET
ijassa-1367	140	59	system	system	NOUN
ijassa-1367	140	60	to	to	ADP
ijassa-1367	140	61	x1	x1	PROPN
ijassa-1367	140	62	at	at	ADP
ijassa-1367	140	63	t1	t1	NOUN
ijassa-1367	140	64	=	=	SYM
ijassa-1367	141	1	t0	t0	PROPN
ijassa-1367	141	2	+	+	NOUN
ijassa-1367	141	3	m	m	PROPN
ijassa-1367	141	4	·	·	SYM
ijassa-1367	141	5	∆τ	∆τ	PROPN
ijassa-1367	141	6	”	"	PUNCT
ijassa-1367	141	7	j	j	NOUN
ijassa-1367	141	8	:	:	PUNCT
ijassa-1367	141	9	=	=	SYM
ijassa-1367	141	10	x̄1	x̄1	NOUN
ijassa-1367	141	11	;	;	PUNCT
ijassa-1367	141	12	y	y	PROPN
ijassa-1367	141	13	:	:	PUNCT
ijassa-1367	141	14	=	=	SYM
ijassa-1367	141	15	φ[i	φ[i	PROPN
ijassa-1367	141	16	,	,	PUNCT
ijassa-1367	141	17	j	j	PROPN
ijassa-1367	141	18	]	]	X
ijassa-1367	141	19	;	;	PUNCT
ijassa-1367	141	20	if	if	SCONJ
ijassa-1367	141	21	x1	x1	PROPN
ijassa-1367	141	22	̸=	̸=	PROPN
ijassa-1367	141	23	y	y	PROPN
ijassa-1367	141	24	then	then	ADV
ijassa-1367	141	25	stop	stop	VERB
ijassa-1367	141	26	;	;	PUNCT
ijassa-1367	141	27	{	{	PUNCT
ijassa-1367	141	28	polygonal	polygonal	ADJ
ijassa-1367	141	29	line	line	NOUN
ijassa-1367	141	30	does	do	AUX
ijassa-1367	141	31	not	not	PART
ijassa-1367	141	32	exist	exist	VERB
ijassa-1367	141	33	}	}	PUNCT
ijassa-1367	141	34	u	u	NOUN
ijassa-1367	141	35	:	:	PUNCT
ijassa-1367	141	36	=	=	SYM
ijassa-1367	141	37	w[m	w[m	NOUN
ijassa-1367	141	38	,	,	PUNCT
ijassa-1367	141	39	j	j	NOUN
ijassa-1367	141	40	]	]	X
ijassa-1367	141	41	;	;	PUNCT
ijassa-1367	141	42	j	j	NOUN
ijassa-1367	141	43	:	:	PUNCT
ijassa-1367	142	1	=	=	SYM
ijassa-1367	142	2	s	s	X
ijassa-1367	143	1	[	[	X
ijassa-1367	143	2	y	y	PROPN
ijassa-1367	143	3	,	,	PUNCT
ijassa-1367	143	4	u	u	NOUN
ijassa-1367	143	5	]	]	X
ijassa-1367	143	6	;	;	PUNCT
ijassa-1367	143	7	γ	γ	X
ijassa-1367	143	8	:	:	PUNCT
ijassa-1367	143	9	=	=	SYM
ijassa-1367	143	10	(	(	PUNCT
ijassa-1367	143	11	y	y	PROPN
ijassa-1367	143	12	,	,	PUNCT
ijassa-1367	143	13	u	u	NOUN
ijassa-1367	143	14	)	)	PUNCT
ijassa-1367	143	15	;	;	PUNCT
ijassa-1367	143	16	{	{	PUNCT
ijassa-1367	143	17	construction	construction	NOUN
ijassa-1367	143	18	starts	start	VERB
ijassa-1367	143	19	from	from	ADP
ijassa-1367	143	20	the	the	DET
ijassa-1367	143	21	end	end	NOUN
ijassa-1367	143	22	;	;	PUNCT
ijassa-1367	143	23	now	now	ADV
ijassa-1367	143	24	a	a	DET
ijassa-1367	143	25	polygonal	polygonal	ADJ
ijassa-1367	143	26	line	line	NOUN
ijassa-1367	143	27	consists	consist	VERB
ijassa-1367	143	28	of	of	ADP
ijassa-1367	143	29	the	the	DET
ijassa-1367	143	30	pair	pair	NOUN
ijassa-1367	143	31	(	(	PUNCT
ijassa-1367	143	32	y	y	NOUN
ijassa-1367	143	33	,	,	PUNCT
ijassa-1367	143	34	u	u	NOUN
ijassa-1367	143	35	)	)	PUNCT
ijassa-1367	143	36	}	}	PUNCT
ijassa-1367	143	37	for	for	ADP
ijassa-1367	143	38	i	i	PRON
ijassa-1367	143	39	:	:	PUNCT
ijassa-1367	143	40	=	=	PUNCT
ijassa-1367	143	41	m−	m−	PROPN
ijassa-1367	143	42	1	1	NUM
ijassa-1367	143	43	by	by	ADP
ijassa-1367	143	44	−1	−1	NOUN
ijassa-1367	143	45	to	to	ADP
ijassa-1367	143	46	1	1	NUM
ijassa-1367	143	47	do	do	AUX
ijassa-1367	143	48	begin	begin	VERB
ijassa-1367	143	49	{	{	PUNCT
ijassa-1367	143	50	backward	backward	ADJ
ijassa-1367	143	51	motion	motion	NOUN
ijassa-1367	143	52	}	}	PUNCT
ijassa-1367	143	53	y	y	NOUN
ijassa-1367	144	1	:	:	PUNCT
ijassa-1367	144	2	=	=	SYM
ijassa-1367	144	3	φ[i	φ[i	PROPN
ijassa-1367	144	4	,	,	PUNCT
ijassa-1367	144	5	j	j	PROPN
ijassa-1367	144	6	]	]	X
ijassa-1367	144	7	;	;	PUNCT
ijassa-1367	144	8	u	u	NOUN
ijassa-1367	144	9	:	:	PUNCT
ijassa-1367	144	10	=	=	SYM
ijassa-1367	144	11	w[i	w[i	PROPN
ijassa-1367	144	12	,	,	PUNCT
ijassa-1367	144	13	j	j	PROPN
ijassa-1367	144	14	]	]	X
ijassa-1367	144	15	;	;	PUNCT
ijassa-1367	144	16	j	j	NOUN
ijassa-1367	144	17	:	:	PUNCT
ijassa-1367	144	18	=	=	SYM
ijassa-1367	144	19	s	s	X
ijassa-1367	145	1	[	[	X
ijassa-1367	145	2	x	x	NOUN
ijassa-1367	145	3	,	,	PUNCT
ijassa-1367	145	4	u	u	NOUN
ijassa-1367	145	5	]	]	X
ijassa-1367	145	6	;	;	PUNCT
ijassa-1367	145	7	γ	γ	X
ijassa-1367	145	8	:	:	PUNCT
ijassa-1367	145	9	=	=	SYM
ijassa-1367	145	10	(	(	PUNCT
ijassa-1367	145	11	y	y	PROPN
ijassa-1367	145	12	,	,	PUNCT
ijassa-1367	145	13	u	u	NOUN
ijassa-1367	145	14	)	)	PUNCT
ijassa-1367	145	15	∨	∨	PROPN
ijassa-1367	145	16	γ	γ	X
ijassa-1367	145	17	;	;	PUNCT
ijassa-1367	145	18	{	{	PUNCT
ijassa-1367	145	19	concatenation	concatenation	NOUN
ijassa-1367	145	20	:	:	PUNCT
ijassa-1367	145	21	the	the	DET
ijassa-1367	145	22	pair	pair	NOUN
ijassa-1367	145	23	(	(	PUNCT
ijassa-1367	145	24	y	y	NOUN
ijassa-1367	145	25	,	,	PUNCT
ijassa-1367	145	26	u	u	NOUN
ijassa-1367	145	27	)	)	PUNCT
ijassa-1367	145	28	is	be	AUX
ijassa-1367	145	29	attached	attach	VERB
ijassa-1367	145	30	to	to	ADP
ijassa-1367	145	31	the	the	DET
ijassa-1367	145	32	obtained	obtain	VERB
ijassa-1367	145	33	trajectory	trajectory	NOUN
ijassa-1367	145	34	γ	γ	NOUN
ijassa-1367	145	35	on	on	ADP
ijassa-1367	145	36	the	the	DET
ijassa-1367	145	37	left	left	ADJ
ijassa-1367	145	38	}	}	PUNCT
ijassa-1367	145	39	end	end	NOUN
ijassa-1367	145	40	;	;	PUNCT
ijassa-1367	145	41	γ	γ	X
ijassa-1367	145	42	:	:	PUNCT
ijassa-1367	145	43	=	=	SYM
ijassa-1367	145	44	x0	x0	PROPN
ijassa-1367	145	45	∨	∨	NUM
ijassa-1367	145	46	γ	γ	X
ijassa-1367	145	47	;	;	PUNCT
ijassa-1367	145	48	end	end	NOUN
ijassa-1367	145	49	of	of	ADP
ijassa-1367	145	50	procedure	procedure	NOUN
ijassa-1367	145	51	as	as	ADP
ijassa-1367	145	52	a	a	DET
ijassa-1367	145	53	result	result	NOUN
ijassa-1367	145	54	,	,	PUNCT
ijassa-1367	145	55	we	we	PRON
ijassa-1367	145	56	get	get	VERB
ijassa-1367	145	57	the	the	DET
ijassa-1367	145	58	sequence	sequence	NOUN
ijassa-1367	145	59	of	of	ADP
ijassa-1367	145	60	coordinates	coordinate	NOUN
ijassa-1367	145	61	and	and	CCONJ
ijassa-1367	145	62	controls	control	VERB
ijassa-1367	145	63	γ	γ	X
ijassa-1367	145	64	=	=	SYM
ijassa-1367	145	65	(	(	PUNCT
ijassa-1367	145	66	ξ0;u1	ξ0;u1	NOUN
ijassa-1367	145	67	,	,	PUNCT
ijassa-1367	145	68	ξ1	ξ1	NOUN
ijassa-1367	145	69	;	;	PUNCT
ijassa-1367	145	70	.	.	PUNCT
ijassa-1367	145	71	.	.	PUNCT
ijassa-1367	145	72	.	.	PUNCT
ijassa-1367	146	1	;	;	PUNCT
ijassa-1367	146	2	um−1	um−1	PROPN
ijassa-1367	146	3	,	,	PUNCT
ijassa-1367	146	4	ξm−1;um	ξm−1;um	PROPN
ijassa-1367	146	5	,	,	PUNCT
ijassa-1367	146	6	ξm	ξm	NUM
ijassa-1367	146	7	)	)	PUNCT
ijassa-1367	146	8	,	,	PUNCT
ijassa-1367	146	9	(	(	PUNCT
ijassa-1367	146	10	3.7	3.7	NUM
ijassa-1367	146	11	)	)	PUNCT
ijassa-1367	146	12	where	where	SCONJ
ijassa-1367	146	13	ξ0	ξ0	NOUN
ijassa-1367	146	14	=	=	SYM
ijassa-1367	146	15	x0	x0	PROPN
ijassa-1367	146	16	,	,	PUNCT
ijassa-1367	146	17	ξm	ξm	PROPN
ijassa-1367	146	18	=	=	SYM
ijassa-1367	146	19	x1	x1	PROPN
ijassa-1367	146	20	.	.	PUNCT
ijassa-1367	146	21	3.4	3.4	NUM
ijassa-1367	146	22	.	.	PUNCT
ijassa-1367	146	23	justification	justification	NOUN
ijassa-1367	146	24	of	of	ADP
ijassa-1367	146	25	the	the	DET
ijassa-1367	146	26	algorithm	algorithm	NOUN
ijassa-1367	146	27	we	we	PRON
ijassa-1367	146	28	will	will	AUX
ijassa-1367	146	29	show	show	VERB
ijassa-1367	146	30	that	that	SCONJ
ijassa-1367	146	31	for	for	ADP
ijassa-1367	146	32	a	a	DET
ijassa-1367	146	33	sufficiently	sufficiently	ADV
ijassa-1367	146	34	fine	fine	ADJ
ijassa-1367	146	35	partition	partition	NOUN
ijassa-1367	146	36	x	x	PUNCT
ijassa-1367	146	37	into	into	ADP
ijassa-1367	146	38	cells	cell	NOUN
ijassa-1367	146	39	,	,	PUNCT
ijassa-1367	146	40	the	the	DET
ijassa-1367	146	41	algorithm	algorithm	NOUN
ijassa-1367	146	42	constructs	construct	VERB
ijassa-1367	146	43	optimal	optimal	ADJ
ijassa-1367	146	44	polygonal	polygonal	ADJ
ijassa-1367	146	45	lines	line	NOUN
ijassa-1367	146	46	.	.	PUNCT
ijassa-1367	147	1	fix	fix	VERB
ijassa-1367	147	2	an	an	DET
ijassa-1367	147	3	arbitrary	arbitrary	ADJ
ijassa-1367	147	4	natural	natural	ADJ
ijassa-1367	147	5	number	number	NOUN
ijassa-1367	147	6	µ	µ	NOUN
ijassa-1367	147	7	≤	≤	NOUN
ijassa-1367	147	8	m	m	NOUN
ijassa-1367	147	9	and	and	CCONJ
ijassa-1367	147	10	consider	consider	VERB
ijassa-1367	147	11	a	a	DET
ijassa-1367	147	12	set	set	NOUN
ijassa-1367	147	13	of	of	ADP
ijassa-1367	147	14	polygonal	polygonal	ADJ
ijassa-1367	147	15	lines	line	NOUN
ijassa-1367	147	16	(	(	PUNCT
ijassa-1367	147	17	6	6	NUM
ijassa-1367	147	18	)	)	PUNCT
ijassa-1367	147	19	,	,	PUNCT
ijassa-1367	147	20	consisting	consist	VERB
ijassa-1367	147	21	of	of	ADP
ijassa-1367	147	22	µ	µ	DET
ijassa-1367	147	23	segments	segment	NOUN
ijassa-1367	147	24	.	.	PUNCT
ijassa-1367	148	1	there	there	PRON
ijassa-1367	148	2	are	be	VERB
ijassa-1367	148	3	finitely	finitely	ADV
ijassa-1367	148	4	many	many	ADJ
ijassa-1367	148	5	such	such	ADJ
ijassa-1367	148	6	polygonal	polygonal	ADJ
ijassa-1367	148	7	lines	line	NOUN
ijassa-1367	148	8	,	,	PUNCT
ijassa-1367	148	9	so	so	SCONJ
ijassa-1367	148	10	the	the	DET
ijassa-1367	148	11	set	set	NOUN
ijassa-1367	148	12	yµ	yµ	NOUN
ijassa-1367	148	13	=	=	SYM
ijassa-1367	148	14	{	{	PUNCT
ijassa-1367	148	15	xµ	xµ	ADJ
ijassa-1367	148	16	}	}	PUNCT
ijassa-1367	148	17	of	of	ADP
ijassa-1367	148	18	their	their	PRON
ijassa-1367	148	19	copyright	copyright	NOUN
ijassa-1367	148	20	©	©	PROPN
ijassa-1367	148	21	2023	2023	NUM
ijassa-1367	148	22	assa	assa	NOUN
ijassa-1367	148	23	.	.	PUNCT
ijassa-1367	149	1	adv	adv	PROPN
ijassa-1367	149	2	syst	syst	PROPN
ijassa-1367	149	3	sci	sci	PROPN
ijassa-1367	149	4	appl	appl	PROPN
ijassa-1367	149	5	(	(	PUNCT
ijassa-1367	149	6	2023	2023	NUM
ijassa-1367	149	7	)	)	PUNCT
ijassa-1367	149	8	piecewise	piecewise	NOUN
ijassa-1367	149	9	constant	constant	ADJ
ijassa-1367	149	10	functions	function	NOUN
ijassa-1367	149	11	in	in	ADP
ijassa-1367	149	12	dynamic	dynamic	ADJ
ijassa-1367	149	13	optimization	optimization	NOUN
ijassa-1367	149	14	problems	problem	NOUN
ijassa-1367	149	15	41	41	NUM
ijassa-1367	149	16	right	right	ADV
ijassa-1367	149	17	-	-	PUNCT
ijassa-1367	149	18	most	most	ADJ
ijassa-1367	149	19	nodes	node	NOUN
ijassa-1367	149	20	(	(	PUNCT
ijassa-1367	149	21	points	point	NOUN
ijassa-1367	149	22	)	)	PUNCT
ijassa-1367	149	23	is	be	AUX
ijassa-1367	149	24	also	also	ADV
ijassa-1367	149	25	finite	finite	ADJ
ijassa-1367	149	26	.	.	PUNCT
ijassa-1367	150	1	let	let	VERB
ijassa-1367	150	2	ρµ	ρµ	PRON
ijassa-1367	150	3	be	be	AUX
ijassa-1367	150	4	the	the	DET
ijassa-1367	150	5	minimum	minimum	ADJ
ijassa-1367	150	6	distance	distance	NOUN
ijassa-1367	150	7	between	between	ADP
ijassa-1367	150	8	pairs	pair	NOUN
ijassa-1367	150	9	of	of	ADP
ijassa-1367	150	10	points	point	NOUN
ijassa-1367	150	11	of	of	ADP
ijassa-1367	150	12	the	the	DET
ijassa-1367	150	13	set	set	NOUN
ijassa-1367	150	14	yµ	yµ	NOUN
ijassa-1367	150	15	,	,	PUNCT
ijassa-1367	150	16	and	and	CCONJ
ijassa-1367	150	17	let	let	VERB
ijassa-1367	150	18	r	r	NOUN
ijassa-1367	150	19	=	=	SYM
ijassa-1367	150	20	min	min	NOUN
ijassa-1367	151	1	[	[	X
ijassa-1367	151	2	rµ|1	rµ|1	X
ijassa-1367	151	3	≤	≤	X
ijassa-1367	151	4	µ	µ	X
ijassa-1367	151	5	≤	≤	NUM
ijassa-1367	151	6	m	m	NOUN
ijassa-1367	151	7	]	]	X
ijassa-1367	151	8	.	.	PUNCT
ijassa-1367	152	1	it	it	PRON
ijassa-1367	152	2	is	be	AUX
ijassa-1367	152	3	clear	clear	ADJ
ijassa-1367	152	4	that	that	SCONJ
ijassa-1367	152	5	r	r	NOUN
ijassa-1367	152	6	>	>	X
ijassa-1367	152	7	0	0	X
ijassa-1367	152	8	.	.	PUNCT
ijassa-1367	152	9	theorem	theorem	VERB
ijassa-1367	152	10	3.1	3.1	NUM
ijassa-1367	152	11	:	:	PUNCT
ijassa-1367	152	12	if	if	SCONJ
ijassa-1367	152	13	the	the	DET
ijassa-1367	152	14	diameters	diameter	NOUN
ijassa-1367	152	15	of	of	ADP
ijassa-1367	152	16	all	all	DET
ijassa-1367	152	17	the	the	DET
ijassa-1367	152	18	sets	set	NOUN
ijassa-1367	152	19	xj	xj	NOUN
ijassa-1367	152	20	are	be	AUX
ijassa-1367	152	21	less	less	ADJ
ijassa-1367	152	22	than	than	ADP
ijassa-1367	152	23	r	r	NOUN
ijassa-1367	152	24	,	,	PUNCT
ijassa-1367	152	25	then	then	ADV
ijassa-1367	152	26	the	the	DET
ijassa-1367	152	27	program	program	NOUN
ijassa-1367	152	28	constructs	construct	VERB
ijassa-1367	152	29	the	the	DET
ijassa-1367	152	30	optimal	optimal	ADJ
ijassa-1367	152	31	polygonal	polygonal	ADJ
ijassa-1367	152	32	line	line	NOUN
ijassa-1367	152	33	from	from	ADP
ijassa-1367	152	34	(	(	PUNCT
ijassa-1367	152	35	t0	t0	PROPN
ijassa-1367	152	36	,	,	PUNCT
ijassa-1367	152	37	x0	x0	PROPN
ijassa-1367	152	38	)	)	PUNCT
ijassa-1367	152	39	to	to	PART
ijassa-1367	152	40	(	(	PUNCT
ijassa-1367	152	41	t1	t1	INTJ
ijassa-1367	152	42	,	,	PUNCT
ijassa-1367	152	43	x1	x1	PROPN
ijassa-1367	152	44	)	)	PUNCT
ijassa-1367	152	45	,	,	PUNCT
ijassa-1367	152	46	and	and	CCONJ
ijassa-1367	152	47	the	the	DET
ijassa-1367	152	48	cost	cost	NOUN
ijassa-1367	152	49	of	of	ADP
ijassa-1367	152	50	this	this	DET
ijassa-1367	152	51	polygonal	polygonal	ADJ
ijassa-1367	152	52	line	line	NOUN
ijassa-1367	152	53	is	be	AUX
ijassa-1367	152	54	equal	equal	ADJ
ijassa-1367	152	55	to	to	ADP
ijassa-1367	152	56	a	a	DET
ijassa-1367	152	57	[	[	X
ijassa-1367	152	58	m	m	PROPN
ijassa-1367	152	59	,	,	PUNCT
ijassa-1367	152	60	j	j	X
ijassa-1367	152	61	]	]	X
ijassa-1367	152	62	,	,	PUNCT
ijassa-1367	152	63	m	m	VERB
ijassa-1367	152	64	=	=	NOUN
ijassa-1367	153	1	t1	t1	NOUN
ijassa-1367	153	2	−	−	PROPN
ijassa-1367	153	3	t0	t0	PROPN
ijassa-1367	153	4	∆τ	∆τ	PROPN
ijassa-1367	153	5	,	,	PUNCT
ijassa-1367	153	6	j	j	PROPN
ijassa-1367	153	7	=	=	SYM
ijassa-1367	153	8	x̄1	x̄1	PROPN
ijassa-1367	153	9	.	.	PUNCT
ijassa-1367	154	1	proof	proof	NOUN
ijassa-1367	154	2	consider	consider	VERB
ijassa-1367	154	3	arbitrary	arbitrary	ADJ
ijassa-1367	154	4	natural	natural	ADJ
ijassa-1367	154	5	numbers	number	NOUN
ijassa-1367	154	6	µ	µ	NOUN
ijassa-1367	154	7	≤	≤	NUM
ijassa-1367	154	8	m	m	PROPN
ijassa-1367	154	9	and	and	CCONJ
ijassa-1367	154	10	j	j	PROPN
ijassa-1367	154	11	≤	≤	PROPN
ijassa-1367	154	12	n.	n.	NOUN
ijassa-1367	154	13	since	since	SCONJ
ijassa-1367	154	14	the	the	DET
ijassa-1367	154	15	distances	distance	NOUN
ijassa-1367	154	16	between	between	ADP
ijassa-1367	154	17	the	the	DET
ijassa-1367	154	18	points	point	NOUN
ijassa-1367	154	19	of	of	ADP
ijassa-1367	154	20	the	the	DET
ijassa-1367	154	21	set	set	NOUN
ijassa-1367	154	22	yµ	yµ	NOUN
ijassa-1367	154	23	are	be	AUX
ijassa-1367	154	24	greater	great	ADJ
ijassa-1367	154	25	than	than	ADP
ijassa-1367	154	26	the	the	DET
ijassa-1367	154	27	diameter	diameter	NOUN
ijassa-1367	154	28	of	of	ADP
ijassa-1367	154	29	the	the	DET
ijassa-1367	154	30	set	set	PROPN
ijassa-1367	154	31	xj	xj	PROPN
ijassa-1367	154	32	,	,	PUNCT
ijassa-1367	154	33	then	then	ADV
ijassa-1367	154	34	the	the	DET
ijassa-1367	154	35	set	set	NOUN
ijassa-1367	154	36	yµ	yµ	NOUN
ijassa-1367	154	37	∩xj	∩xj	NOUN
ijassa-1367	154	38	consists	consist	VERB
ijassa-1367	154	39	of	of	ADP
ijassa-1367	154	40	at	at	ADP
ijassa-1367	154	41	most	most	ADV
ijassa-1367	154	42	one	one	NUM
ijassa-1367	154	43	element	element	NOUN
ijassa-1367	154	44	.	.	PUNCT
ijassa-1367	155	1	denote	denote	VERB
ijassa-1367	155	2	this	this	DET
ijassa-1367	155	3	element	element	NOUN
ijassa-1367	155	4	by	by	ADP
ijassa-1367	155	5	zµj	zµj	NOUN
ijassa-1367	155	6	if	if	SCONJ
ijassa-1367	155	7	it	it	PRON
ijassa-1367	155	8	exists	exist	VERB
ijassa-1367	155	9	.	.	PUNCT
ijassa-1367	156	1	therefore	therefore	ADV
ijassa-1367	156	2	,	,	PUNCT
ijassa-1367	156	3	the	the	DET
ijassa-1367	156	4	polygonal	polygonal	ADJ
ijassa-1367	156	5	line	line	NOUN
ijassa-1367	156	6	γ	γ	NOUN
ijassa-1367	156	7	,	,	PUNCT
ijassa-1367	156	8	terminating	terminate	VERB
ijassa-1367	156	9	at	at	ADP
ijassa-1367	156	10	or	or	CCONJ
ijassa-1367	156	11	passing	pass	VERB
ijassa-1367	156	12	through	through	ADP
ijassa-1367	156	13	the	the	DET
ijassa-1367	156	14	cell	cell	NOUN
ijassa-1367	156	15	xj	xj	PROPN
ijassa-1367	156	16	at	at	ADP
ijassa-1367	156	17	instant	instant	ADJ
ijassa-1367	156	18	τµ	τµ	NOUN
ijassa-1367	156	19	,	,	PUNCT
ijassa-1367	156	20	has	have	VERB
ijassa-1367	156	21	a	a	DET
ijassa-1367	156	22	node	node	ADJ
ijassa-1367	156	23	zµj	zµj	NOUN
ijassa-1367	156	24	at	at	ADP
ijassa-1367	156	25	this	this	DET
ijassa-1367	156	26	set	set	NOUN
ijassa-1367	156	27	.	.	PUNCT
ijassa-1367	157	1	if	if	SCONJ
ijassa-1367	157	2	yµ	yµ	NOUN
ijassa-1367	157	3	∩xj	∩xj	NOUN
ijassa-1367	157	4	=	=	NOUN
ijassa-1367	157	5	∅	∅	NOUN
ijassa-1367	157	6	,	,	PUNCT
ijassa-1367	157	7	then	then	ADV
ijassa-1367	157	8	there	there	PRON
ijassa-1367	157	9	are	be	VERB
ijassa-1367	157	10	no	no	DET
ijassa-1367	157	11	polygonal	polygonal	ADJ
ijassa-1367	157	12	line	line	NOUN
ijassa-1367	157	13	passing	pass	VERB
ijassa-1367	157	14	through	through	ADP
ijassa-1367	157	15	the	the	DET
ijassa-1367	157	16	cell	cell	NOUN
ijassa-1367	157	17	xj	xj	PROPN
ijassa-1367	157	18	at	at	ADP
ijassa-1367	157	19	instant	instant	ADJ
ijassa-1367	157	20	τµ.	τµ.	NOUN
ijassa-1367	157	21	then	then	ADV
ijassa-1367	157	22	for	for	ADP
ijassa-1367	157	23	this	this	DET
ijassa-1367	157	24	cell	cell	NOUN
ijassa-1367	157	25	we	we	PRON
ijassa-1367	157	26	will	will	AUX
ijassa-1367	157	27	have	have	VERB
ijassa-1367	157	28	a	a	DET
ijassa-1367	157	29	[	[	X
ijassa-1367	157	30	µ	µ	X
ijassa-1367	157	31	,	,	PUNCT
ijassa-1367	157	32	j	j	NOUN
ijassa-1367	157	33	]	]	X
ijassa-1367	157	34	=	=	PUNCT
ijassa-1367	157	35	∞.	∞.	PROPN
ijassa-1367	157	36	now	now	ADV
ijassa-1367	157	37	we	we	PRON
ijassa-1367	157	38	prove	prove	VERB
ijassa-1367	157	39	the	the	DET
ijassa-1367	157	40	statement	statement	NOUN
ijassa-1367	157	41	by	by	ADP
ijassa-1367	157	42	induction	induction	NOUN
ijassa-1367	157	43	on	on	ADP
ijassa-1367	157	44	the	the	DET
ijassa-1367	157	45	time	time	NOUN
ijassa-1367	157	46	step	step	NOUN
ijassa-1367	157	47	m.	m.	NOUN
ijassa-1367	157	48	for	for	ADP
ijassa-1367	157	49	m	m	PROPN
ijassa-1367	157	50	=	=	SYM
ijassa-1367	157	51	0	0	NUM
ijassa-1367	158	1	it	it	PRON
ijassa-1367	158	2	is	be	AUX
ijassa-1367	158	3	trivial	trivial	ADJ
ijassa-1367	158	4	because	because	SCONJ
ijassa-1367	158	5	the	the	DET
ijassa-1367	158	6	polygonal	polygonal	ADJ
ijassa-1367	158	7	line	line	NOUN
ijassa-1367	158	8	consisting	consist	VERB
ijassa-1367	158	9	on	on	ADP
ijassa-1367	158	10	0	0	NUM
ijassa-1367	158	11	steps	step	NOUN
ijassa-1367	158	12	degenerates	degenerate	NOUN
ijassa-1367	158	13	into	into	ADP
ijassa-1367	158	14	the	the	DET
ijassa-1367	158	15	point	point	NOUN
ijassa-1367	158	16	(	(	PUNCT
ijassa-1367	158	17	t0	t0	PROPN
ijassa-1367	158	18	,	,	PUNCT
ijassa-1367	158	19	x0	x0	PROPN
ijassa-1367	158	20	)	)	PUNCT
ijassa-1367	158	21	and	and	CCONJ
ijassa-1367	158	22	,	,	PUNCT
ijassa-1367	158	23	by	by	ADP
ijassa-1367	158	24	construction	construction	NOUN
ijassa-1367	158	25	,	,	PUNCT
ijassa-1367	158	26	a	a	DET
ijassa-1367	158	27	[	[	X
ijassa-1367	158	28	0	0	NUM
ijassa-1367	158	29	,	,	PUNCT
ijassa-1367	158	30	x̄0	x̄0	PROPN
ijassa-1367	158	31	]	]	X
ijassa-1367	158	32	:	:	PUNCT
ijassa-1367	159	1	=	=	SYM
ijassa-1367	159	2	0	0	X
ijassa-1367	159	3	.	.	PUNCT
ijassa-1367	159	4	assume	assume	VERB
ijassa-1367	159	5	the	the	DET
ijassa-1367	159	6	statement	statement	NOUN
ijassa-1367	159	7	is	be	AUX
ijassa-1367	159	8	true	true	ADJ
ijassa-1367	159	9	for	for	ADP
ijassa-1367	159	10	µ	µ	NOUN
ijassa-1367	159	11	=	=	SYM
ijassa-1367	159	12	m−	m−	PROPN
ijassa-1367	159	13	1	1	NUM
ijassa-1367	159	14	steps	step	NOUN
ijassa-1367	159	15	and	and	CCONJ
ijassa-1367	159	16	prove	prove	VERB
ijassa-1367	159	17	it	it	PRON
ijassa-1367	159	18	for	for	ADP
ijassa-1367	159	19	the	the	DET
ijassa-1367	159	20	next	next	ADJ
ijassa-1367	159	21	step	step	NOUN
ijassa-1367	159	22	m.	m.	NOUN
ijassa-1367	159	23	let	let	VERB
ijassa-1367	159	24	(	(	PUNCT
ijassa-1367	159	25	3.7	3.7	NUM
ijassa-1367	159	26	)	)	PUNCT
ijassa-1367	159	27	be	be	AUX
ijassa-1367	159	28	an	an	DET
ijassa-1367	159	29	optimal	optimal	ADJ
ijassa-1367	159	30	polygonal	polygonal	ADJ
ijassa-1367	159	31	line	line	NOUN
ijassa-1367	159	32	.	.	PUNCT
ijassa-1367	160	1	then	then	ADV
ijassa-1367	160	2	γ1	γ1	PROPN
ijassa-1367	160	3	=	=	SYM
ijassa-1367	160	4	(	(	PUNCT
ijassa-1367	160	5	x0;u1	x0;u1	PROPN
ijassa-1367	160	6	,	,	PUNCT
ijassa-1367	160	7	ξ1	ξ1	NOUN
ijassa-1367	160	8	;	;	PUNCT
ijassa-1367	160	9	.	.	PUNCT
ijassa-1367	160	10	.	.	PUNCT
ijassa-1367	160	11	.	.	PUNCT
ijassa-1367	161	1	;	;	PUNCT
ijassa-1367	161	2	um−1	um−1	PROPN
ijassa-1367	161	3	,	,	PUNCT
ijassa-1367	161	4	ξm−1	ξm−1	NOUN
ijassa-1367	161	5	)	)	PUNCT
ijassa-1367	161	6	is	be	AUX
ijassa-1367	161	7	also	also	ADV
ijassa-1367	161	8	an	an	DET
ijassa-1367	161	9	optimal	optimal	ADJ
ijassa-1367	161	10	polygonal	polygonal	ADJ
ijassa-1367	161	11	line	line	NOUN
ijassa-1367	161	12	,	,	PUNCT
ijassa-1367	161	13	going	go	VERB
ijassa-1367	161	14	to	to	PART
ijassa-1367	161	15	(	(	PUNCT
ijassa-1367	161	16	τm−1	τm−1	PROPN
ijassa-1367	161	17	,	,	PUNCT
ijassa-1367	161	18	ξm−1	ξm−1	NOUN
ijassa-1367	161	19	)	)	PUNCT
ijassa-1367	161	20	.	.	PUNCT
ijassa-1367	162	1	by	by	ADP
ijassa-1367	162	2	inductive	inductive	ADJ
ijassa-1367	162	3	hypothesis	hypothesis	NOUN
ijassa-1367	162	4	,	,	PUNCT
ijassa-1367	162	5	this	this	DET
ijassa-1367	162	6	line	line	NOUN
ijassa-1367	162	7	or	or	CCONJ
ijassa-1367	162	8	the	the	DET
ijassa-1367	162	9	polygonal	polygonal	ADJ
ijassa-1367	162	10	line	line	NOUN
ijassa-1367	162	11	of	of	ADP
ijassa-1367	162	12	equal	equal	ADJ
ijassa-1367	162	13	cost	cost	NOUN
ijassa-1367	162	14	would	would	AUX
ijassa-1367	162	15	have	have	AUX
ijassa-1367	162	16	already	already	ADV
ijassa-1367	162	17	been	be	AUX
ijassa-1367	162	18	constructed	construct	VERB
ijassa-1367	162	19	by	by	ADP
ijassa-1367	162	20	the	the	DET
ijassa-1367	162	21	algorithm	algorithm	NOUN
ijassa-1367	162	22	if	if	SCONJ
ijassa-1367	162	23	the	the	DET
ijassa-1367	162	24	point	point	NOUN
ijassa-1367	162	25	(	(	PUNCT
ijassa-1367	162	26	τm−1	τm−1	PROPN
ijassa-1367	162	27	,	,	PUNCT
ijassa-1367	162	28	ξm−1	ξm−1	NOUN
ijassa-1367	162	29	)	)	PUNCT
ijassa-1367	162	30	were	be	AUX
ijassa-1367	162	31	finite	finite	ADJ
ijassa-1367	162	32	.	.	PUNCT
ijassa-1367	163	1	we	we	PRON
ijassa-1367	163	2	have	have	VERB
ijassa-1367	163	3	c(γ1	c(γ1	NOUN
ijassa-1367	163	4	)	)	PUNCT
ijassa-1367	163	5	=	=	PUNCT
ijassa-1367	164	1	a	a	PRON
ijassa-1367	165	1	[	[	X
ijassa-1367	165	2	m−	m−	PROPN
ijassa-1367	165	3	1	1	NUM
ijassa-1367	165	4	,	,	PUNCT
ijassa-1367	165	5	j	j	NOUN
ijassa-1367	165	6	]	]	X
ijassa-1367	165	7	,	,	PUNCT
ijassa-1367	165	8	where	where	SCONJ
ijassa-1367	165	9	j	j	PROPN
ijassa-1367	165	10	=	=	PROPN
ijassa-1367	165	11	ξ̄m−1	ξ̄m−1	PROPN
ijassa-1367	165	12	.	.	PUNCT
ijassa-1367	166	1	let	let	VERB
ijassa-1367	166	2	x	x	PUNCT
ijassa-1367	166	3	=	=	PUNCT
ijassa-1367	166	4	zm−1,j	zm−1,j	PROPN
ijassa-1367	166	5	.	.	PUNCT
ijassa-1367	167	1	analyse	analyse	NOUN
ijassa-1367	167	2	what	what	PRON
ijassa-1367	167	3	happens	happen	VERB
ijassa-1367	167	4	when	when	SCONJ
ijassa-1367	167	5	we	we	PRON
ijassa-1367	167	6	fill	fill	VERB
ijassa-1367	167	7	in	in	ADP
ijassa-1367	167	8	the	the	DET
ijassa-1367	167	9	vertical	vertical	ADJ
ijassa-1367	167	10	column	column	NOUN
ijassa-1367	167	11	m	m	VERB
ijassa-1367	167	12	as	as	SCONJ
ijassa-1367	167	13	the	the	DET
ijassa-1367	167	14	program	program	NOUN
ijassa-1367	167	15	processes	process	VERB
ijassa-1367	167	16	segments	segment	NOUN
ijassa-1367	167	17	emanating	emanate	VERB
ijassa-1367	167	18	from	from	ADP
ijassa-1367	167	19	(	(	PUNCT
ijassa-1367	167	20	τm−1	τm−1	PROPN
ijassa-1367	167	21	,	,	PUNCT
ijassa-1367	167	22	ξm−1	ξm−1	NOUN
ijassa-1367	167	23	)	)	PUNCT
ijassa-1367	167	24	.	.	PUNCT
ijassa-1367	168	1	under	under	ADP
ijassa-1367	168	2	control	control	NOUN
ijassa-1367	168	3	um	um	INTJ
ijassa-1367	168	4	=	=	PUNCT
ijassa-1367	168	5	vk	vk	ADP
ijassa-1367	168	6	∈	∈	PROPN
ijassa-1367	168	7	v	v	ADP
ijassa-1367	168	8	the	the	DET
ijassa-1367	168	9	system	system	NOUN
ijassa-1367	168	10	gets	get	VERB
ijassa-1367	168	11	to	to	ADP
ijassa-1367	168	12	(	(	PUNCT
ijassa-1367	168	13	τm	τm	PROPN
ijassa-1367	168	14	,	,	PUNCT
ijassa-1367	168	15	ξm	ξm	PROPN
ijassa-1367	168	16	)	)	PUNCT
ijassa-1367	168	17	.	.	PUNCT
ijassa-1367	169	1	the	the	DET
ijassa-1367	169	2	cost	cost	NOUN
ijassa-1367	169	3	of	of	ADP
ijassa-1367	169	4	this	this	DET
ijassa-1367	169	5	step	step	NOUN
ijassa-1367	169	6	is	be	AUX
ijassa-1367	169	7	equal	equal	ADJ
ijassa-1367	169	8	to	to	ADP
ijassa-1367	169	9	c	c	PROPN
ijassa-1367	169	10	(	(	PUNCT
ijassa-1367	169	11	m	m	PROPN
ijassa-1367	169	12	,	,	PUNCT
ijassa-1367	169	13	k	k	NOUN
ijassa-1367	169	14	,	,	PUNCT
ijassa-1367	169	15	x	x	NOUN
ijassa-1367	169	16	)	)	PUNCT
ijassa-1367	169	17	.	.	PUNCT
ijassa-1367	170	1	therefore	therefore	ADV
ijassa-1367	170	2	,	,	PUNCT
ijassa-1367	170	3	by	by	ADP
ijassa-1367	170	4	inductive	inductive	ADJ
ijassa-1367	170	5	hypothesis	hypothesis	NOUN
ijassa-1367	170	6	,	,	PUNCT
ijassa-1367	170	7	we	we	PRON
ijassa-1367	170	8	have	have	VERB
ijassa-1367	170	9	r	r	NOUN
ijassa-1367	170	10	=	=	PUNCT
ijassa-1367	170	11	c(γ1	c(γ1	NOUN
ijassa-1367	170	12	)	)	PUNCT
ijassa-1367	171	1	+	+	CCONJ
ijassa-1367	171	2	c	c	X
ijassa-1367	171	3	(	(	PUNCT
ijassa-1367	171	4	i	i	NOUN
ijassa-1367	171	5	,	,	PUNCT
ijassa-1367	171	6	k	k	PROPN
ijassa-1367	171	7	,	,	PUNCT
ijassa-1367	171	8	x	x	NOUN
ijassa-1367	171	9	)	)	PUNCT
ijassa-1367	171	10	=	=	SYM
ijassa-1367	171	11	c(γ	c(γ	PROPN
ijassa-1367	171	12	)	)	PUNCT
ijassa-1367	171	13	.	.	PUNCT
ijassa-1367	172	1	the	the	DET
ijassa-1367	172	2	last	last	ADJ
ijassa-1367	172	3	equality	equality	NOUN
ijassa-1367	172	4	is	be	AUX
ijassa-1367	172	5	valid	valid	ADJ
ijassa-1367	172	6	by	by	ADP
ijassa-1367	172	7	virtue	virtue	NOUN
ijassa-1367	172	8	of	of	ADP
ijassa-1367	172	9	the	the	DET
ijassa-1367	172	10	additivity	additivity	NOUN
ijassa-1367	172	11	of	of	ADP
ijassa-1367	172	12	a	a	DET
ijassa-1367	172	13	cost	cost	NOUN
ijassa-1367	172	14	functional	functional	ADJ
ijassa-1367	172	15	.	.	PUNCT
ijassa-1367	173	1	as	as	ADP
ijassa-1367	173	2	a	a	DET
ijassa-1367	173	3	result	result	NOUN
ijassa-1367	173	4	,	,	PUNCT
ijassa-1367	173	5	we	we	PRON
ijassa-1367	173	6	will	will	AUX
ijassa-1367	173	7	definitely	definitely	ADV
ijassa-1367	173	8	get	get	VERB
ijassa-1367	173	9	a	a	DET
ijassa-1367	173	10	[	[	PUNCT
ijassa-1367	173	11	m	m	NOUN
ijassa-1367	173	12	,	,	PUNCT
ijassa-1367	173	13	ξ̄m	ξ̄m	PROPN
ijassa-1367	173	14	]	]	PUNCT
ijassa-1367	173	15	≤	≤	NUM
ijassa-1367	173	16	c(γ	c(γ	PROPN
ijassa-1367	173	17	)	)	PUNCT
ijassa-1367	173	18	.	.	PUNCT
ijassa-1367	174	1	from	from	ADP
ijassa-1367	174	2	the	the	DET
ijassa-1367	174	3	other	other	ADJ
ijassa-1367	174	4	hand	hand	NOUN
ijassa-1367	174	5	,	,	PUNCT
ijassa-1367	174	6	the	the	DET
ijassa-1367	174	7	strict	strict	ADJ
ijassa-1367	174	8	inequality	inequality	NOUN
ijassa-1367	174	9	a	a	DET
ijassa-1367	174	10	[	[	PUNCT
ijassa-1367	174	11	m	m	PROPN
ijassa-1367	174	12	,	,	PUNCT
ijassa-1367	174	13	ξ̄m	ξ̄m	PROPN
ijassa-1367	174	14	]	]	PUNCT
ijassa-1367	174	15	<	<	X
ijassa-1367	174	16	c(γ	c(γ	X
ijassa-1367	174	17	)	)	PUNCT
ijassa-1367	174	18	is	be	AUX
ijassa-1367	174	19	impossible	impossible	ADJ
ijassa-1367	174	20	since	since	SCONJ
ijassa-1367	174	21	otherwise	otherwise	ADV
ijassa-1367	174	22	the	the	DET
ijassa-1367	174	23	trajectory	trajectory	NOUN
ijassa-1367	174	24	γ	γ	NOUN
ijassa-1367	174	25	would	would	AUX
ijassa-1367	174	26	not	not	PART
ijassa-1367	174	27	be	be	AUX
ijassa-1367	174	28	optimal	optimal	ADJ
ijassa-1367	174	29	.	.	PUNCT
ijassa-1367	175	1	3.5	3.5	NUM
ijassa-1367	175	2	.	.	PUNCT
ijassa-1367	176	1	economic	economic	ADJ
ijassa-1367	176	2	example	example	NOUN
ijassa-1367	176	3	consider	consider	VERB
ijassa-1367	176	4	the	the	DET
ijassa-1367	176	5	following	follow	VERB
ijassa-1367	176	6	dynamic	dynamic	ADJ
ijassa-1367	176	7	optimization	optimization	NOUN
ijassa-1367	176	8	problem	problem	NOUN
ijassa-1367	176	9	arisen	arise	VERB
ijassa-1367	176	10	in	in	ADP
ijassa-1367	176	11	economics	economic	NOUN
ijassa-1367	176	12	[	[	X
ijassa-1367	176	13	19	19	NUM
ijassa-1367	176	14	]	]	PUNCT
ijassa-1367	176	15	.	.	PUNCT
ijassa-1367	177	1	the	the	DET
ijassa-1367	177	2	conceptual	conceptual	ADJ
ijassa-1367	177	3	meaning	meaning	NOUN
ijassa-1367	177	4	of	of	ADP
ijassa-1367	177	5	the	the	DET
ijassa-1367	177	6	problem	problem	NOUN
ijassa-1367	177	7	is	be	AUX
ijassa-1367	177	8	as	as	SCONJ
ijassa-1367	177	9	follows	follow	VERB
ijassa-1367	177	10	.	.	PUNCT
ijassa-1367	178	1	a	a	DET
ijassa-1367	178	2	firm	firm	NOUN
ijassa-1367	178	3	has	have	AUX
ijassa-1367	178	4	received	receive	VERB
ijassa-1367	178	5	an	an	DET
ijassa-1367	178	6	order	order	NOUN
ijassa-1367	178	7	for	for	SCONJ
ijassa-1367	178	8	h	h	NOUN
ijassa-1367	178	9	units	unit	NOUN
ijassa-1367	178	10	of	of	ADP
ijassa-1367	178	11	product	product	NOUN
ijassa-1367	178	12	to	to	PART
ijassa-1367	178	13	be	be	AUX
ijassa-1367	178	14	delivered	deliver	VERB
ijassa-1367	178	15	by	by	ADP
ijassa-1367	178	16	time	time	NOUN
ijassa-1367	178	17	t	t	PROPN
ijassa-1367	178	18	.	.	PUNCT
ijassa-1367	179	1	it	it	PRON
ijassa-1367	179	2	seeks	seek	VERB
ijassa-1367	179	3	a	a	DET
ijassa-1367	179	4	production	production	NOUN
ijassa-1367	179	5	schedule	schedule	NOUN
ijassa-1367	179	6	for	for	ADP
ijassa-1367	179	7	filling	fill	VERB
ijassa-1367	179	8	this	this	DET
ijassa-1367	179	9	order	order	NOUN
ijassa-1367	179	10	at	at	ADP
ijassa-1367	179	11	the	the	DET
ijassa-1367	179	12	specified	specify	VERB
ijassa-1367	179	13	delivery	delivery	NOUN
ijassa-1367	179	14	date	date	NOUN
ijassa-1367	179	15	at	at	ADP
ijassa-1367	179	16	minimum	minimum	ADJ
ijassa-1367	179	17	cost	cost	NOUN
ijassa-1367	179	18	,	,	PUNCT
ijassa-1367	179	19	bearing	bear	VERB
ijassa-1367	179	20	in	in	ADP
ijassa-1367	179	21	mind	mind	NOUN
ijassa-1367	179	22	that	that	SCONJ
ijassa-1367	179	23	unit	unit	NOUN
ijassa-1367	179	24	production	production	NOUN
ijassa-1367	179	25	cost	cost	NOUN
ijassa-1367	179	26	rises	rise	VERB
ijassa-1367	179	27	linearly	linearly	ADV
ijassa-1367	179	28	with	with	ADP
ijassa-1367	179	29	the	the	DET
ijassa-1367	179	30	production	production	NOUN
ijassa-1367	179	31	rate	rate	NOUN
ijassa-1367	179	32	and	and	CCONJ
ijassa-1367	179	33	that	that	SCONJ
ijassa-1367	179	34	the	the	DET
ijassa-1367	179	35	unit	unit	NOUN
ijassa-1367	179	36	cost	cost	NOUN
ijassa-1367	179	37	of	of	ADP
ijassa-1367	179	38	holding	hold	VERB
ijassa-1367	179	39	inventory	inventory	NOUN
ijassa-1367	179	40	per	per	ADP
ijassa-1367	179	41	unit	unit	NOUN
ijassa-1367	179	42	time	time	NOUN
ijassa-1367	179	43	is	be	AUX
ijassa-1367	179	44	constant	constant	ADJ
ijassa-1367	179	45	.	.	PUNCT
ijassa-1367	180	1	let	let	VERB
ijassa-1367	180	2	x(t	x(t	PROPN
ijassa-1367	180	3	)	)	PUNCT
ijassa-1367	180	4	denote	denote	VERB
ijassa-1367	180	5	the	the	DET
ijassa-1367	180	6	inventory	inventory	NOUN
ijassa-1367	180	7	accumulated	accumulate	VERB
ijassa-1367	180	8	by	by	ADP
ijassa-1367	180	9	time	time	NOUN
ijassa-1367	181	1	t.	t.	PROPN
ijassa-1367	181	2	then	then	ADV
ijassa-1367	181	3	we	we	PRON
ijassa-1367	181	4	have	have	VERB
ijassa-1367	181	5	x(0	x(0	PROPN
ijassa-1367	181	6	)	)	PUNCT
ijassa-1367	182	1	=	=	SYM
ijassa-1367	182	2	0	0	PUNCT
ijassa-1367	182	3	and	and	CCONJ
ijassa-1367	182	4	must	must	AUX
ijassa-1367	182	5	achieve	achieve	VERB
ijassa-1367	182	6	x(t	x(t	PROPN
ijassa-1367	182	7	)	)	PUNCT
ijassa-1367	183	1	=	=	SYM
ijassa-1367	183	2	h	h	NOUN
ijassa-1367	183	3	.	.	PUNCT
ijassa-1367	184	1	the	the	DET
ijassa-1367	184	2	inventory	inventory	NOUN
ijassa-1367	184	3	level	level	NOUN
ijassa-1367	184	4	,	,	PUNCT
ijassa-1367	184	5	at	at	ADP
ijassa-1367	184	6	any	any	DET
ijassa-1367	184	7	moment	moment	NOUN
ijassa-1367	184	8	,	,	PUNCT
ijassa-1367	184	9	is	be	AUX
ijassa-1367	184	10	the	the	DET
ijassa-1367	184	11	cumulated	cumulated	ADJ
ijassa-1367	184	12	past	past	ADJ
ijassa-1367	184	13	production	production	NOUN
ijassa-1367	184	14	;	;	PUNCT
ijassa-1367	184	15	the	the	DET
ijassa-1367	184	16	rate	rate	NOUN
ijassa-1367	184	17	of	of	ADP
ijassa-1367	184	18	change	change	NOUN
ijassa-1367	184	19	of	of	ADP
ijassa-1367	184	20	inventory	inventory	NOUN
ijassa-1367	184	21	is	be	AUX
ijassa-1367	184	22	the	the	DET
ijassa-1367	184	23	production	production	NOUN
ijassa-1367	184	24	rate	rate	NOUN
ijassa-1367	184	25	x′(t	x′(t	PROPN
ijassa-1367	184	26	)	)	PUNCT
ijassa-1367	184	27	.	.	PUNCT
ijassa-1367	185	1	thus	thus	ADV
ijassa-1367	185	2	the	the	DET
ijassa-1367	185	3	firm	firm	NOUN
ijassa-1367	185	4	’s	’s	PART
ijassa-1367	185	5	total	total	ADJ
ijassa-1367	185	6	cost	cost	NOUN
ijassa-1367	185	7	at	at	ADP
ijassa-1367	185	8	any	any	DET
ijassa-1367	185	9	moment	moment	NOUN
ijassa-1367	185	10	t	t	NOUN
ijassa-1367	185	11	is	be	AUX
ijassa-1367	185	12	c1	c1	NOUN
ijassa-1367	185	13	(	(	PUNCT
ijassa-1367	185	14	x′(t	x′(t	PROPN
ijassa-1367	185	15	)	)	PUNCT
ijassa-1367	185	16	)	)	PUNCT
ijassa-1367	185	17	2	2	NUM
ijassa-1367	185	18	+	+	NUM
ijassa-1367	185	19	c2x(t	c2x(t	PROPN
ijassa-1367	185	20	)	)	PUNCT
ijassa-1367	185	21	,	,	PUNCT
ijassa-1367	185	22	where	where	SCONJ
ijassa-1367	185	23	the	the	DET
ijassa-1367	185	24	first	first	ADJ
ijassa-1367	185	25	term	term	NOUN
ijassa-1367	185	26	is	be	AUX
ijassa-1367	185	27	the	the	DET
ijassa-1367	185	28	total	total	ADJ
ijassa-1367	185	29	production	production	NOUN
ijassa-1367	185	30	cost	cost	NOUN
ijassa-1367	185	31	,	,	PUNCT
ijassa-1367	185	32	the	the	DET
ijassa-1367	185	33	product	product	NOUN
ijassa-1367	185	34	of	of	ADP
ijassa-1367	185	35	the	the	DET
ijassa-1367	185	36	unit	unit	NOUN
ijassa-1367	185	37	cost	cost	NOUN
ijassa-1367	185	38	of	of	ADP
ijassa-1367	185	39	production	production	NOUN
ijassa-1367	185	40	and	and	CCONJ
ijassa-1367	185	41	the	the	DET
ijassa-1367	185	42	level	level	NOUN
ijassa-1367	185	43	of	of	ADP
ijassa-1367	185	44	production	production	NOUN
ijassa-1367	185	45	;	;	PUNCT
ijassa-1367	185	46	the	the	DET
ijassa-1367	185	47	second	second	ADJ
ijassa-1367	185	48	term	term	NOUN
ijassa-1367	185	49	is	be	AUX
ijassa-1367	185	50	the	the	DET
ijassa-1367	185	51	total	total	ADJ
ijassa-1367	185	52	cost	cost	NOUN
ijassa-1367	185	53	of	of	ADP
ijassa-1367	185	54	holding	hold	VERB
ijassa-1367	185	55	inventory	inventory	NOUN
ijassa-1367	185	56	;	;	PUNCT
ijassa-1367	185	57	and	and	CCONJ
ijassa-1367	185	58	c1	c1	PROPN
ijassa-1367	185	59	and	and	CCONJ
ijassa-1367	185	60	c2	c2	PROPN
ijassa-1367	185	61	are	be	AUX
ijassa-1367	185	62	positive	positive	ADJ
ijassa-1367	185	63	constants	constant	NOUN
ijassa-1367	185	64	.	.	PUNCT
ijassa-1367	186	1	for	for	ADP
ijassa-1367	186	2	simplicity	simplicity	NOUN
ijassa-1367	186	3	,	,	PUNCT
ijassa-1367	186	4	in	in	ADP
ijassa-1367	186	5	what	what	PRON
ijassa-1367	186	6	follows	follow	VERB
ijassa-1367	186	7	we	we	PRON
ijassa-1367	186	8	set	set	VERB
ijassa-1367	186	9	c1	c1	PROPN
ijassa-1367	186	10	=	=	PROPN
ijassa-1367	186	11	c2	c2	PROPN
ijassa-1367	186	12	=	=	SYM
ijassa-1367	186	13	1	1	X
ijassa-1367	186	14	.	.	PUNCT
ijassa-1367	187	1	the	the	DET
ijassa-1367	187	2	firm	firm	NOUN
ijassa-1367	187	3	’s	’s	PART
ijassa-1367	187	4	copyright	copyright	NOUN
ijassa-1367	187	5	©	©	PROPN
ijassa-1367	187	6	2023	2023	NUM
ijassa-1367	187	7	assa	assa	NOUN
ijassa-1367	187	8	.	.	PUNCT
ijassa-1367	188	1	adv	adv	PROPN
ijassa-1367	188	2	syst	syst	PROPN
ijassa-1367	188	3	sci	sci	PROPN
ijassa-1367	188	4	appl	appl	PROPN
ijassa-1367	188	5	(	(	PUNCT
ijassa-1367	188	6	2023	2023	NUM
ijassa-1367	188	7	)	)	PUNCT
ijassa-1367	188	8	42	42	NUM
ijassa-1367	188	9	o.	o.	PROPN
ijassa-1367	188	10	e.	e.	PROPN
ijassa-1367	188	11	orel	orel	PROPN
ijassa-1367	188	12	,	,	PUNCT
ijassa-1367	188	13	e.	e.	PROPN
ijassa-1367	188	14	n.	n.	PROPN
ijassa-1367	188	15	orel	orel	PROPN
ijassa-1367	188	16	fig	fig	PROPN
ijassa-1367	188	17	.	.	PUNCT
ijassa-1367	189	1	3.2	3.2	NUM
ijassa-1367	189	2	.	.	PUNCT
ijassa-1367	190	1	optimal	optimal	ADJ
ijassa-1367	190	2	field	field	NOUN
ijassa-1367	190	3	of	of	ADP
ijassa-1367	190	4	extremals	extremal	NOUN
ijassa-1367	190	5	and	and	CCONJ
ijassa-1367	190	6	quasi	quasi	ADJ
ijassa-1367	190	7	-	-	ADJ
ijassa-1367	190	8	optimal	optimal	ADJ
ijassa-1367	190	9	field	field	NOUN
ijassa-1367	190	10	of	of	ADP
ijassa-1367	190	11	polygonal	polygonal	ADJ
ijassa-1367	190	12	lines	line	NOUN
ijassa-1367	190	13	in	in	ADP
ijassa-1367	190	14	the	the	DET
ijassa-1367	190	15	economic	economic	ADJ
ijassa-1367	190	16	problem	problem	NOUN
ijassa-1367	190	17	objective	objective	NOUN
ijassa-1367	190	18	is	be	AUX
ijassa-1367	190	19	to	to	PART
ijassa-1367	190	20	determine	determine	VERB
ijassa-1367	190	21	a	a	DET
ijassa-1367	190	22	production	production	NOUN
ijassa-1367	190	23	rate	rate	NOUN
ijassa-1367	190	24	u(t	u(t	NOUN
ijassa-1367	190	25	)	)	PUNCT
ijassa-1367	190	26	=	=	SYM
ijassa-1367	191	1	x′(t	x′(t	PROPN
ijassa-1367	191	2	)	)	PUNCT
ijassa-1367	191	3	and	and	CCONJ
ijassa-1367	191	4	inventory	inventory	NOUN
ijassa-1367	191	5	accumulation	accumulation	NOUN
ijassa-1367	191	6	x(t	x(t	PROPN
ijassa-1367	191	7	)	)	PUNCT
ijassa-1367	191	8	for	for	ADP
ijassa-1367	191	9	0	0	NUM
ijassa-1367	191	10	<	<	X
ijassa-1367	191	11	t	t	X
ijassa-1367	191	12	<	<	X
ijassa-1367	191	13	t	t	NOUN
ijassa-1367	192	1	such	such	ADJ
ijassa-1367	192	2	that	that	PRON
ijassa-1367	192	3	j	j	PROPN
ijassa-1367	192	4	=	=	SYM
ijassa-1367	192	5	∫	∫	PROPN
ijassa-1367	192	6	t	t	PROPN
ijassa-1367	192	7	0	0	NUM
ijassa-1367	192	8	[	[	PUNCT
ijassa-1367	192	9	u2(t	u2(t	NOUN
ijassa-1367	192	10	)	)	PUNCT
ijassa-1367	192	11	+	+	CCONJ
ijassa-1367	192	12	x(t	x(t	PROPN
ijassa-1367	192	13	)	)	PUNCT
ijassa-1367	192	14	]	]	PUNCT
ijassa-1367	192	15	dt	dt	X
ijassa-1367	192	16	→	→	SYM
ijassa-1367	192	17	min	min	PROPN
ijassa-1367	192	18	,	,	PUNCT
ijassa-1367	192	19	dx(t	dx(t	X
ijassa-1367	192	20	)	)	PUNCT
ijassa-1367	192	21	dt	dt	NOUN
ijassa-1367	192	22	=	=	SYM
ijassa-1367	192	23	u(t	u(t	PROPN
ijassa-1367	192	24	)	)	PUNCT
ijassa-1367	192	25	,	,	PUNCT
ijassa-1367	192	26	x(0	x(0	PROPN
ijassa-1367	192	27	)	)	PUNCT
ijassa-1367	192	28	=	=	SYM
ijassa-1367	192	29	0	0	NUM
ijassa-1367	192	30	,	,	PUNCT
ijassa-1367	192	31	x(t	x(t	PROPN
ijassa-1367	192	32	)	)	PUNCT
ijassa-1367	193	1	=	=	PUNCT
ijassa-1367	193	2	h	h	NOUN
ijassa-1367	193	3	≥	≥	NOUN
ijassa-1367	193	4	0	0	NUM
ijassa-1367	193	5	,	,	PUNCT
ijassa-1367	193	6	0	0	NUM
ijassa-1367	193	7	≤	≤	NUM
ijassa-1367	193	8	u	u	NOUN
ijassa-1367	193	9	≤	≤	X
ijassa-1367	193	10	v	v	NOUN
ijassa-1367	193	11	,	,	PUNCT
ijassa-1367	193	12	x(t	x(t	PROPN
ijassa-1367	193	13	)	)	PUNCT
ijassa-1367	193	14	≥	≥	NOUN
ijassa-1367	193	15	0	0	NUM
ijassa-1367	193	16	.	.	PUNCT
ijassa-1367	194	1	to	to	PART
ijassa-1367	194	2	solve	solve	VERB
ijassa-1367	194	3	this	this	DET
ijassa-1367	194	4	problem	problem	NOUN
ijassa-1367	194	5	,	,	PUNCT
ijassa-1367	194	6	in	in	ADP
ijassa-1367	194	7	[	[	X
ijassa-1367	194	8	19	19	NUM
ijassa-1367	194	9	]	]	X
ijassa-1367	194	10	we	we	PRON
ijassa-1367	194	11	have	have	AUX
ijassa-1367	194	12	constructed	construct	VERB
ijassa-1367	194	13	an	an	DET
ijassa-1367	194	14	optimal	optimal	ADJ
ijassa-1367	194	15	central	central	ADJ
ijassa-1367	194	16	field	field	NOUN
ijassa-1367	194	17	of	of	ADP
ijassa-1367	194	18	pontryagin	pontryagin	NOUN
ijassa-1367	194	19	extremals	extremal	NOUN
ijassa-1367	194	20	.	.	PUNCT
ijassa-1367	195	1	moreover	moreover	ADV
ijassa-1367	195	2	,	,	PUNCT
ijassa-1367	195	3	the	the	DET
ijassa-1367	195	4	problem	problem	NOUN
ijassa-1367	195	5	was	be	AUX
ijassa-1367	195	6	solved	solve	VERB
ijassa-1367	195	7	numerically	numerically	ADV
ijassa-1367	195	8	with	with	ADP
ijassa-1367	195	9	the	the	DET
ijassa-1367	195	10	help	help	NOUN
ijassa-1367	195	11	of	of	ADP
ijassa-1367	195	12	the	the	DET
ijassa-1367	195	13	partition	partition	NOUN
ijassa-1367	195	14	into	into	ADP
ijassa-1367	195	15	cells	cell	NOUN
ijassa-1367	195	16	considered	consider	VERB
ijassa-1367	195	17	above	above	ADV
ijassa-1367	195	18	.	.	PUNCT
ijassa-1367	196	1	the	the	DET
ijassa-1367	196	2	results	result	NOUN
ijassa-1367	196	3	of	of	ADP
ijassa-1367	196	4	both	both	DET
ijassa-1367	196	5	investigations	investigation	NOUN
ijassa-1367	196	6	is	be	AUX
ijassa-1367	196	7	represented	represent	VERB
ijassa-1367	196	8	in	in	ADP
ijassa-1367	196	9	figure	figure	NOUN
ijassa-1367	196	10	3.2	3.2	NUM
ijassa-1367	196	11	.	.	PUNCT
ijassa-1367	197	1	the	the	DET
ijassa-1367	197	2	demarcation	demarcation	NOUN
ijassa-1367	197	3	line	line	NOUN
ijassa-1367	197	4	to	to	ADP
ijassa-1367	197	5	the	the	DET
ijassa-1367	197	6	maximum	maximum	ADJ
ijassa-1367	197	7	production	production	NOUN
ijassa-1367	197	8	rate	rate	NOUN
ijassa-1367	197	9	v	v	NOUN
ijassa-1367	197	10	is	be	AUX
ijassa-1367	197	11	shown	show	VERB
ijassa-1367	197	12	on	on	ADP
ijassa-1367	197	13	the	the	DET
ijassa-1367	197	14	left	left	ADJ
ijassa-1367	197	15	part	part	NOUN
ijassa-1367	197	16	of	of	ADP
ijassa-1367	197	17	the	the	DET
ijassa-1367	197	18	figure	figure	NOUN
ijassa-1367	197	19	by	by	ADP
ijassa-1367	197	20	the	the	DET
ijassa-1367	197	21	dashed	dash	VERB
ijassa-1367	197	22	line	line	NOUN
ijassa-1367	197	23	.	.	PUNCT
ijassa-1367	198	1	4	4	X
ijassa-1367	198	2	.	.	NOUN
ijassa-1367	198	3	autonomous	autonomous	ADJ
ijassa-1367	198	4	problems	problem	NOUN
ijassa-1367	198	5	of	of	ADP
ijassa-1367	198	6	optimal	optimal	ADJ
ijassa-1367	198	7	control	control	NOUN
ijassa-1367	198	8	the	the	DET
ijassa-1367	198	9	method	method	NOUN
ijassa-1367	198	10	of	of	ADP
ijassa-1367	198	11	partition	partition	NOUN
ijassa-1367	198	12	into	into	ADP
ijassa-1367	198	13	classes	class	NOUN
ijassa-1367	198	14	for	for	ADP
ijassa-1367	198	15	autonomous	autonomous	ADJ
ijassa-1367	198	16	optimal	optimal	ADJ
ijassa-1367	198	17	control	control	NOUN
ijassa-1367	198	18	problems∫	problems∫	NOUN
ijassa-1367	198	19	t	t	PROPN
ijassa-1367	198	20	0	0	NUM
ijassa-1367	198	21	l(t	l(t	PROPN
ijassa-1367	198	22	,	,	PUNCT
ijassa-1367	198	23	x(t	x(t	PROPN
ijassa-1367	198	24	)	)	PUNCT
ijassa-1367	198	25	,	,	PUNCT
ijassa-1367	198	26	u(t))dt	u(t))dt	PROPN
ijassa-1367	198	27	→	→	SYM
ijassa-1367	198	28	min	min	PROPN
ijassa-1367	198	29	,	,	PUNCT
ijassa-1367	198	30	dx(t	dx(t	X
ijassa-1367	198	31	)	)	PUNCT
ijassa-1367	198	32	dt	dt	NOUN
ijassa-1367	198	33	=	=	SYM
ijassa-1367	198	34	f(x(t	f(x(t	PROPN
ijassa-1367	198	35	)	)	PUNCT
ijassa-1367	198	36	,	,	PUNCT
ijassa-1367	198	37	u(t	u(t	NOUN
ijassa-1367	198	38	)	)	PUNCT
ijassa-1367	198	39	)	)	PUNCT
ijassa-1367	198	40	,	,	PUNCT
ijassa-1367	198	41	x(0	x(0	PROPN
ijassa-1367	198	42	)	)	PUNCT
ijassa-1367	199	1	=	=	PUNCT
ijassa-1367	199	2	x0	x0	PROPN
ijassa-1367	199	3	,	,	PUNCT
ijassa-1367	199	4	x(t	x(t	PROPN
ijassa-1367	199	5	)	)	PUNCT
ijassa-1367	200	1	=	=	PUNCT
ijassa-1367	200	2	x1	x1	PROPN
ijassa-1367	200	3	,	,	PUNCT
ijassa-1367	200	4	x(t	x(t	PROPN
ijassa-1367	200	5	)	)	PUNCT
ijassa-1367	200	6	∈	∈	PROPN
ijassa-1367	200	7	x	x	SYM
ijassa-1367	200	8	,	,	PUNCT
ijassa-1367	200	9	u(t	u(t	NOUN
ijassa-1367	200	10	)	)	PUNCT
ijassa-1367	200	11	∈	∈	PROPN
ijassa-1367	200	12	u	u	NOUN
ijassa-1367	200	13	,	,	PUNCT
ijassa-1367	200	14	(	(	PUNCT
ijassa-1367	200	15	termination	termination	NOUN
ijassa-1367	200	16	time	time	NOUN
ijassa-1367	200	17	t	t	PROPN
ijassa-1367	200	18	>	>	X
ijassa-1367	200	19	0	0	NUM
ijassa-1367	200	20	of	of	ADP
ijassa-1367	200	21	the	the	DET
ijassa-1367	200	22	process	process	NOUN
ijassa-1367	200	23	is	be	AUX
ijassa-1367	200	24	not	not	PART
ijassa-1367	200	25	fixed	fix	VERB
ijassa-1367	200	26	)	)	PUNCT
ijassa-1367	200	27	has	have	AUX
ijassa-1367	200	28	been	be	AUX
ijassa-1367	200	29	considered	consider	VERB
ijassa-1367	200	30	in	in	ADP
ijassa-1367	200	31	[	[	X
ijassa-1367	200	32	9][11	9][11	X
ijassa-1367	200	33	]	]	PUNCT
ijassa-1367	200	34	in	in	ADP
ijassa-1367	200	35	details	detail	NOUN
ijassa-1367	200	36	.	.	PUNCT
ijassa-1367	201	1	generally	generally	ADV
ijassa-1367	201	2	speaking	speak	VERB
ijassa-1367	201	3	,	,	PUNCT
ijassa-1367	201	4	the	the	DET
ijassa-1367	201	5	state	state	NOUN
ijassa-1367	201	6	x(t	x(t	PROPN
ijassa-1367	201	7	)	)	PUNCT
ijassa-1367	201	8	and	and	CCONJ
ijassa-1367	201	9	the	the	DET
ijassa-1367	201	10	control	control	NOUN
ijassa-1367	201	11	u(t	u(t	NOUN
ijassa-1367	201	12	)	)	PUNCT
ijassa-1367	201	13	are	be	AUX
ijassa-1367	201	14	vectors	vector	NOUN
ijassa-1367	201	15	.	.	PUNCT
ijassa-1367	202	1	in	in	ADP
ijassa-1367	202	2	frames	frame	NOUN
ijassa-1367	202	3	of	of	ADP
ijassa-1367	202	4	a	a	DET
ijassa-1367	202	5	simple	simple	ADJ
ijassa-1367	202	6	version	version	NOUN
ijassa-1367	202	7	,	,	PUNCT
ijassa-1367	202	8	to	to	PART
ijassa-1367	202	9	solve	solve	VERB
ijassa-1367	202	10	the	the	DET
ijassa-1367	202	11	problem	problem	NOUN
ijassa-1367	202	12	numerically	numerically	ADV
ijassa-1367	202	13	,	,	PUNCT
ijassa-1367	202	14	we	we	PRON
ijassa-1367	202	15	should	should	AUX
ijassa-1367	202	16	take	take	VERB
ijassa-1367	202	17	a	a	DET
ijassa-1367	202	18	finite	finite	NOUN
ijassa-1367	202	19	set	set	VERB
ijassa-1367	202	20	v	v	ADP
ijassa-1367	202	21	⊂	⊂	PROPN
ijassa-1367	202	22	u	u	NOUN
ijassa-1367	202	23	and	and	CCONJ
ijassa-1367	202	24	a	a	DET
ijassa-1367	202	25	time	time	NOUN
ijassa-1367	202	26	step	step	NOUN
ijassa-1367	202	27	∆τ	∆τ	PROPN
ijassa-1367	202	28	.	.	PUNCT
ijassa-1367	203	1	thus	thus	ADV
ijassa-1367	203	2	,	,	PUNCT
ijassa-1367	203	3	the	the	DET
ijassa-1367	203	4	polygonal	polygonal	ADJ
ijassa-1367	203	5	lines	line	NOUN
ijassa-1367	203	6	are	be	AUX
ijassa-1367	203	7	defined	define	VERB
ijassa-1367	203	8	.	.	PUNCT
ijassa-1367	204	1	they	they	PRON
ijassa-1367	204	2	consist	consist	VERB
ijassa-1367	204	3	of	of	ADP
ijassa-1367	204	4	segments	segment	NOUN
ijassa-1367	204	5	,	,	PUNCT
ijassa-1367	204	6	i.e.	i.e.	X
ijassa-1367	204	7	,	,	PUNCT
ijassa-1367	204	8	solutions	solution	NOUN
ijassa-1367	204	9	of	of	ADP
ijassa-1367	204	10	the	the	DET
ijassa-1367	204	11	differential	differential	ADJ
ijassa-1367	204	12	equation	equation	NOUN
ijassa-1367	204	13	ẋ	ẋ	PUNCT
ijassa-1367	205	1	=	=	SYM
ijassa-1367	205	2	f(x	f(x	PROPN
ijassa-1367	205	3	,	,	PUNCT
ijassa-1367	205	4	u	u	NOUN
ijassa-1367	205	5	)	)	PUNCT
ijassa-1367	205	6	on	on	ADP
ijassa-1367	205	7	the	the	DET
ijassa-1367	205	8	interval	interval	NOUN
ijassa-1367	206	1	[	[	X
ijassa-1367	206	2	0,∆τ	0,∆τ	X
ijassa-1367	206	3	]	]	PUNCT
ijassa-1367	206	4	with	with	ADP
ijassa-1367	206	5	constant	constant	ADJ
ijassa-1367	206	6	control	control	NOUN
ijassa-1367	206	7	u	u	NOUN
ijassa-1367	206	8	∈	∈	PROPN
ijassa-1367	206	9	v	v	NOUN
ijassa-1367	206	10	.	.	PUNCT
ijassa-1367	207	1	now	now	ADV
ijassa-1367	207	2	we	we	PRON
ijassa-1367	207	3	need	need	VERB
ijassa-1367	207	4	to	to	PART
ijassa-1367	207	5	divide	divide	VERB
ijassa-1367	207	6	x	x	PUNCT
ijassa-1367	207	7	into	into	ADP
ijassa-1367	207	8	finite	finite	ADJ
ijassa-1367	207	9	number	number	NOUN
ijassa-1367	207	10	of	of	ADP
ijassa-1367	207	11	classes	class	NOUN
ijassa-1367	207	12	xi	xi	PRON
ijassa-1367	207	13	and	and	CCONJ
ijassa-1367	207	14	run	run	VERB
ijassa-1367	207	15	the	the	DET
ijassa-1367	207	16	program	program	NOUN
ijassa-1367	207	17	representing	represent	VERB
ijassa-1367	207	18	a	a	DET
ijassa-1367	207	19	generalization	generalization	NOUN
ijassa-1367	207	20	of	of	ADP
ijassa-1367	207	21	any	any	DET
ijassa-1367	207	22	algorithm	algorithm	NOUN
ijassa-1367	207	23	of	of	ADP
ijassa-1367	207	24	finding	find	VERB
ijassa-1367	207	25	the	the	DET
ijassa-1367	207	26	shortest	short	ADJ
ijassa-1367	207	27	path	path	NOUN
ijassa-1367	207	28	on	on	ADP
ijassa-1367	207	29	a	a	DET
ijassa-1367	207	30	graph	graph	NOUN
ijassa-1367	207	31	[	[	X
ijassa-1367	207	32	9	9	NUM
ijassa-1367	207	33	]	]	PUNCT
ijassa-1367	207	34	,	,	PUNCT
ijassa-1367	207	35	[	[	X
ijassa-1367	207	36	11	11	NUM
ijassa-1367	207	37	]	]	PUNCT
ijassa-1367	207	38	.	.	PUNCT
ijassa-1367	208	1	copyright	copyright	NOUN
ijassa-1367	208	2	©	©	PROPN
ijassa-1367	208	3	2023	2023	NUM
ijassa-1367	208	4	assa	assa	NOUN
ijassa-1367	208	5	.	.	PUNCT
ijassa-1367	209	1	adv	adv	PROPN
ijassa-1367	209	2	syst	syst	PROPN
ijassa-1367	209	3	sci	sci	PROPN
ijassa-1367	209	4	appl	appl	PROPN
ijassa-1367	209	5	(	(	PUNCT
ijassa-1367	209	6	2023	2023	NUM
ijassa-1367	209	7	)	)	PUNCT
ijassa-1367	209	8	piecewise	piecewise	NOUN
ijassa-1367	209	9	constant	constant	ADJ
ijassa-1367	209	10	functions	function	NOUN
ijassa-1367	209	11	in	in	ADP
ijassa-1367	209	12	dynamic	dynamic	ADJ
ijassa-1367	209	13	optimization	optimization	NOUN
ijassa-1367	209	14	problems	problem	NOUN
ijassa-1367	209	15	43	43	NUM
ijassa-1367	209	16	fig	fig	NOUN
ijassa-1367	209	17	.	.	PUNCT
ijassa-1367	210	1	4.3	4.3	NUM
ijassa-1367	210	2	.	.	PUNCT
ijassa-1367	210	3	central	central	ADJ
ijassa-1367	210	4	field	field	NOUN
ijassa-1367	210	5	of	of	ADP
ijassa-1367	210	6	extremals	extremal	NOUN
ijassa-1367	210	7	and	and	CCONJ
ijassa-1367	210	8	polygonal	polygonal	ADJ
ijassa-1367	210	9	lines	line	NOUN
ijassa-1367	210	10	in	in	ADP
ijassa-1367	210	11	the	the	DET
ijassa-1367	210	12	bushaw	bushaw	PROPN
ijassa-1367	210	13	problem	problem	NOUN
ijassa-1367	210	14	this	this	PRON
ijassa-1367	210	15	can	can	AUX
ijassa-1367	210	16	be	be	AUX
ijassa-1367	210	17	a	a	DET
ijassa-1367	210	18	breadth	breadth	NOUN
ijassa-1367	210	19	-	-	PUNCT
ijassa-1367	210	20	first	first	ADJ
ijassa-1367	210	21	search	search	NOUN
ijassa-1367	210	22	,	,	PUNCT
ijassa-1367	210	23	such	such	ADJ
ijassa-1367	210	24	as	as	ADP
ijassa-1367	210	25	the	the	DET
ijassa-1367	210	26	dijkstra	dijkstra	ADJ
ijassa-1367	210	27	algorithm	algorithm	NOUN
ijassa-1367	210	28	(	(	PUNCT
ijassa-1367	210	29	equal	equal	ADJ
ijassa-1367	210	30	price	price	NOUN
ijassa-1367	210	31	algorithm	algorithm	NOUN
ijassa-1367	210	32	)	)	PUNCT
ijassa-1367	210	33	or	or	CCONJ
ijassa-1367	210	34	the	the	DET
ijassa-1367	210	35	nillson	nillson	ADJ
ijassa-1367	210	36	algorithm	algorithm	NOUN
ijassa-1367	210	37	(	(	PUNCT
ijassa-1367	210	38	a∗	a∗	ADJ
ijassa-1367	210	39	search	search	NOUN
ijassa-1367	210	40	algorithm	algorithm	NOUN
ijassa-1367	210	41	)	)	PUNCT
ijassa-1367	210	42	.	.	PUNCT
ijassa-1367	211	1	however	however	ADV
ijassa-1367	211	2	,	,	PUNCT
ijassa-1367	211	3	it	it	PRON
ijassa-1367	211	4	can	can	AUX
ijassa-1367	211	5	be	be	AUX
ijassa-1367	211	6	a	a	DET
ijassa-1367	211	7	backtracking	backtrack	VERB
ijassa-1367	211	8	depthfirst	depthfirst	ADJ
ijassa-1367	211	9	search	search	NOUN
ijassa-1367	211	10	[	[	X
ijassa-1367	211	11	10	10	NUM
ijassa-1367	211	12	]	]	PUNCT
ijassa-1367	211	13	,	,	PUNCT
ijassa-1367	211	14	[	[	X
ijassa-1367	211	15	15	15	NUM
ijassa-1367	211	16	]	]	PUNCT
ijassa-1367	211	17	or	or	CCONJ
ijassa-1367	211	18	a	a	DET
ijassa-1367	211	19	combination	combination	NOUN
ijassa-1367	211	20	of	of	ADP
ijassa-1367	211	21	these	these	DET
ijassa-1367	211	22	algorithms	algorithm	NOUN
ijassa-1367	211	23	.	.	PUNCT
ijassa-1367	212	1	that	that	DET
ijassa-1367	212	2	machinery	machinery	NOUN
ijassa-1367	212	3	could	could	AUX
ijassa-1367	212	4	be	be	AUX
ijassa-1367	212	5	very	very	ADV
ijassa-1367	212	6	important	important	ADJ
ijassa-1367	212	7	to	to	PART
ijassa-1367	212	8	solve	solve	VERB
ijassa-1367	212	9	more	more	ADV
ijassa-1367	212	10	complicated	complicated	ADJ
ijassa-1367	212	11	optimization	optimization	NOUN
ijassa-1367	212	12	problems	problem	NOUN
ijassa-1367	212	13	with	with	ADP
ijassa-1367	212	14	any	any	DET
ijassa-1367	212	15	lack	lack	NOUN
ijassa-1367	212	16	of	of	ADP
ijassa-1367	212	17	information	information	NOUN
ijassa-1367	212	18	.	.	PUNCT
ijassa-1367	213	1	consider	consider	VERB
ijassa-1367	213	2	few	few	ADJ
ijassa-1367	213	3	examples	example	NOUN
ijassa-1367	213	4	on	on	ADP
ijassa-1367	213	5	the	the	DET
ijassa-1367	213	6	subject	subject	NOUN
ijassa-1367	213	7	.	.	PUNCT
ijassa-1367	214	1	4.1	4.1	NUM
ijassa-1367	214	2	.	.	PUNCT
ijassa-1367	214	3	fel’dbaum	fel’dbaum	PROPN
ijassa-1367	214	4	-	-	PUNCT
ijassa-1367	214	5	bushaw	bushaw	PROPN
ijassa-1367	214	6	problem	problem	NOUN
ijassa-1367	214	7	this	this	DET
ijassa-1367	214	8	time	time	NOUN
ijassa-1367	214	9	-	-	PUNCT
ijassa-1367	214	10	optimal	optimal	ADJ
ijassa-1367	214	11	control	control	NOUN
ijassa-1367	214	12	problem	problem	NOUN
ijassa-1367	214	13	(	(	PUNCT
ijassa-1367	214	14	it	it	PRON
ijassa-1367	214	15	is	be	AUX
ijassa-1367	214	16	also	also	ADV
ijassa-1367	214	17	called	call	VERB
ijassa-1367	214	18	an	an	DET
ijassa-1367	214	19	optimal	optimal	ADJ
ijassa-1367	214	20	stopping	stopping	NOUN
ijassa-1367	214	21	problem	problem	NOUN
ijassa-1367	214	22	)	)	PUNCT
ijassa-1367	214	23	could	could	AUX
ijassa-1367	214	24	be	be	AUX
ijassa-1367	214	25	stated	state	VERB
ijassa-1367	214	26	as	as	SCONJ
ijassa-1367	214	27	follows	follow	VERB
ijassa-1367	214	28	[	[	X
ijassa-1367	214	29	20	20	NUM
ijassa-1367	214	30	]	]	PUNCT
ijassa-1367	214	31	–	–	PUNCT
ijassa-1367	214	32	[	[	X
ijassa-1367	214	33	21	21	NUM
ijassa-1367	214	34	]	]	PUNCT
ijassa-1367	214	35	:	:	PUNCT
ijassa-1367	215	1	dx	dx	PROPN
ijassa-1367	216	1	dt	dt	X
ijassa-1367	217	1	=	=	SYM
ijassa-1367	217	2	ẋ	ẋ	PROPN
ijassa-1367	217	3	,	,	PUNCT
ijassa-1367	217	4	dẋ	dẋ	NOUN
ijassa-1367	217	5	dt	dt	X
ijassa-1367	218	1	=	=	SYM
ijassa-1367	218	2	u	u	PROPN
ijassa-1367	218	3	,	,	PUNCT
ijassa-1367	218	4	|u|	|u|	ADV
ijassa-1367	218	5	≤	≤	NUM
ijassa-1367	218	6	1	1	NUM
ijassa-1367	218	7	,	,	PUNCT
ijassa-1367	218	8	x(0	x(0	PROPN
ijassa-1367	218	9	)	)	PUNCT
ijassa-1367	218	10	=	=	PUNCT
ijassa-1367	218	11	x0	x0	PROPN
ijassa-1367	218	12	,	,	PUNCT
ijassa-1367	218	13	x(t	x(t	PROPN
ijassa-1367	218	14	)	)	PUNCT
ijassa-1367	219	1	=	=	PUNCT
ijassa-1367	219	2	x1	x1	PROPN
ijassa-1367	219	3	,	,	PUNCT
ijassa-1367	219	4	t	t	PROPN
ijassa-1367	219	5	→	→	SYM
ijassa-1367	219	6	min	min	PROPN
ijassa-1367	219	7	.	.	PUNCT
ijassa-1367	220	1	figure	figure	VERB
ijassa-1367	220	2	4.3	4.3	NUM
ijassa-1367	220	3	shows	show	VERB
ijassa-1367	220	4	the	the	DET
ijassa-1367	220	5	central	central	ADJ
ijassa-1367	220	6	extremal	extremal	ADJ
ijassa-1367	220	7	fields	field	NOUN
ijassa-1367	220	8	and	and	CCONJ
ijassa-1367	220	9	polygonal	polygonal	ADJ
ijassa-1367	220	10	lines	line	NOUN
ijassa-1367	220	11	for	for	ADP
ijassa-1367	220	12	the	the	DET
ijassa-1367	220	13	fixed	fix	VERB
ijassa-1367	220	14	initial	initial	ADJ
ijassa-1367	220	15	point	point	NOUN
ijassa-1367	221	1	[	[	X
ijassa-1367	221	2	17	17	NUM
ijassa-1367	221	3	]	]	SYM
ijassa-1367	221	4	.	.	PUNCT
ijassa-1367	222	1	4.2	4.2	NUM
ijassa-1367	222	2	.	.	PUNCT
ijassa-1367	222	3	car	car	NOUN
ijassa-1367	222	4	motion	motion	NOUN
ijassa-1367	222	5	to	to	ADP
ijassa-1367	222	6	the	the	DET
ijassa-1367	222	7	parking	parking	NOUN
ijassa-1367	222	8	place	place	NOUN
ijassa-1367	222	9	the	the	DET
ijassa-1367	222	10	detailed	detailed	ADJ
ijassa-1367	222	11	consideration	consideration	NOUN
ijassa-1367	222	12	of	of	ADP
ijassa-1367	222	13	this	this	DET
ijassa-1367	222	14	problem	problem	NOUN
ijassa-1367	222	15	can	can	AUX
ijassa-1367	222	16	be	be	AUX
ijassa-1367	222	17	found	find	VERB
ijassa-1367	222	18	in	in	ADP
ijassa-1367	222	19	[	[	X
ijassa-1367	222	20	3	3	NUM
ijassa-1367	222	21	]	]	PUNCT
ijassa-1367	222	22	.	.	PUNCT
ijassa-1367	223	1	at	at	ADP
ijassa-1367	223	2	first	first	ADJ
ijassa-1367	223	3	glance	glance	NOUN
ijassa-1367	223	4	,	,	PUNCT
ijassa-1367	223	5	it	it	PRON
ijassa-1367	223	6	seems	seem	VERB
ijassa-1367	223	7	that	that	SCONJ
ijassa-1367	223	8	at	at	ADP
ijassa-1367	223	9	each	each	DET
ijassa-1367	223	10	particular	particular	ADJ
ijassa-1367	223	11	case	case	NOUN
ijassa-1367	223	12	the	the	DET
ijassa-1367	223	13	problem	problem	NOUN
ijassa-1367	223	14	could	could	AUX
ijassa-1367	223	15	be	be	AUX
ijassa-1367	223	16	solved	solve	VERB
ijassa-1367	223	17	by	by	ADP
ijassa-1367	223	18	ruler	ruler	NOUN
ijassa-1367	223	19	-	-	PUNCT
ijassa-1367	223	20	and	and	CCONJ
ijassa-1367	223	21	-	-	PUNCT
ijassa-1367	223	22	compass	compass	NOUN
ijassa-1367	223	23	constructions	construction	NOUN
ijassa-1367	223	24	.	.	PUNCT
ijassa-1367	224	1	nevertheless	nevertheless	ADV
ijassa-1367	224	2	,	,	PUNCT
ijassa-1367	224	3	the	the	DET
ijassa-1367	224	4	authors	author	NOUN
ijassa-1367	224	5	are	be	AUX
ijassa-1367	224	6	not	not	PART
ijassa-1367	224	7	aware	aware	ADJ
ijassa-1367	224	8	of	of	ADP
ijassa-1367	224	9	the	the	DET
ijassa-1367	224	10	exact	exact	ADJ
ijassa-1367	224	11	analytic	analytic	ADJ
ijassa-1367	224	12	solution	solution	NOUN
ijassa-1367	224	13	of	of	ADP
ijassa-1367	224	14	this	this	DET
ijassa-1367	224	15	problem	problem	NOUN
ijassa-1367	224	16	.	.	PUNCT
ijassa-1367	225	1	assuming	assume	VERB
ijassa-1367	225	2	the	the	DET
ijassa-1367	225	3	speed	speed	NOUN
ijassa-1367	225	4	of	of	ADP
ijassa-1367	225	5	a	a	DET
ijassa-1367	225	6	material	material	NOUN
ijassa-1367	225	7	point	point	NOUN
ijassa-1367	225	8	(	(	PUNCT
ijassa-1367	225	9	x	x	NOUN
ijassa-1367	225	10	,	,	PUNCT
ijassa-1367	225	11	y	y	NOUN
ijassa-1367	225	12	)	)	PUNCT
ijassa-1367	225	13	is	be	AUX
ijassa-1367	225	14	constant	constant	ADJ
ijassa-1367	225	15	and	and	CCONJ
ijassa-1367	225	16	the	the	DET
ijassa-1367	225	17	curvature	curvature	NOUN
ijassa-1367	225	18	is	be	AUX
ijassa-1367	225	19	limited	limited	ADJ
ijassa-1367	225	20	,	,	PUNCT
ijassa-1367	225	21	we	we	PRON
ijassa-1367	225	22	can	can	AUX
ijassa-1367	225	23	describe	describe	VERB
ijassa-1367	225	24	the	the	DET
ijassa-1367	225	25	problem	problem	NOUN
ijassa-1367	225	26	as	as	SCONJ
ijassa-1367	225	27	follows	follow	VERB
ijassa-1367	225	28	:	:	PUNCT
ijassa-1367	225	29	dx	dx	PROPN
ijassa-1367	225	30	dt	dt	NOUN
ijassa-1367	225	31	=	=	SYM
ijassa-1367	225	32	cosφ	cosφ	NOUN
ijassa-1367	225	33	,	,	PUNCT
ijassa-1367	225	34	dy	dy	NOUN
ijassa-1367	225	35	dt	dt	NOUN
ijassa-1367	225	36	=	=	PUNCT
ijassa-1367	225	37	sinφ	sinφ	PROPN
ijassa-1367	225	38	,	,	PUNCT
ijassa-1367	225	39	dφ	dφ	ADP
ijassa-1367	225	40	dt	dt	X
ijassa-1367	225	41	=	=	SYM
ijassa-1367	225	42	u	u	PROPN
ijassa-1367	225	43	,	,	PUNCT
ijassa-1367	225	44	|u|	|u|	ADV
ijassa-1367	225	45	≤	≤	NUM
ijassa-1367	225	46	1	1	NUM
ijassa-1367	225	47	,	,	PUNCT
ijassa-1367	225	48	x(0	x(0	PROPN
ijassa-1367	225	49	)	)	PUNCT
ijassa-1367	225	50	=	=	PUNCT
ijassa-1367	226	1	x0	x0	PROPN
ijassa-1367	226	2	,	,	PUNCT
ijassa-1367	226	3	x(t	x(t	PROPN
ijassa-1367	226	4	)	)	PUNCT
ijassa-1367	227	1	∈	∈	PROPN
ijassa-1367	227	2	g	g	PROPN
ijassa-1367	227	3	,	,	PUNCT
ijassa-1367	227	4	t	t	PROPN
ijassa-1367	227	5	→	→	SYM
ijassa-1367	227	6	min	min	PROPN
ijassa-1367	227	7	.	.	PUNCT
ijassa-1367	228	1	here	here	ADV
ijassa-1367	228	2	by	by	ADP
ijassa-1367	228	3	a	a	DET
ijassa-1367	228	4	parking	parking	NOUN
ijassa-1367	228	5	place	place	NOUN
ijassa-1367	228	6	we	we	PRON
ijassa-1367	228	7	mean	mean	VERB
ijassa-1367	228	8	a	a	DET
ijassa-1367	228	9	point	point	NOUN
ijassa-1367	228	10	or	or	CCONJ
ijassa-1367	228	11	its	its	PRON
ijassa-1367	228	12	neighborhood	neighborhood	NOUN
ijassa-1367	228	13	.	.	PUNCT
ijassa-1367	229	1	note	note	VERB
ijassa-1367	229	2	that	that	SCONJ
ijassa-1367	229	3	the	the	DET
ijassa-1367	229	4	state	state	NOUN
ijassa-1367	229	5	space	space	NOUN
ijassa-1367	229	6	is	be	AUX
ijassa-1367	229	7	three	three	NUM
ijassa-1367	229	8	-	-	PUNCT
ijassa-1367	229	9	dimensional	dimensional	ADJ
ijassa-1367	229	10	,	,	PUNCT
ijassa-1367	229	11	so	so	SCONJ
ijassa-1367	229	12	a	a	DET
ijassa-1367	229	13	point	point	NOUN
ijassa-1367	229	14	(	(	PUNCT
ijassa-1367	229	15	x	x	NOUN
ijassa-1367	229	16	,	,	PUNCT
ijassa-1367	229	17	y	y	NOUN
ijassa-1367	229	18	)	)	PUNCT
ijassa-1367	229	19	in	in	ADP
ijassa-1367	229	20	plane	plane	NOUN
ijassa-1367	229	21	corresponds	correspond	VERB
ijassa-1367	229	22	to	to	ADP
ijassa-1367	229	23	an	an	DET
ijassa-1367	229	24	entire	entire	ADJ
ijassa-1367	229	25	state	state	NOUN
ijassa-1367	229	26	set	set	NOUN
ijassa-1367	229	27	(	(	PUNCT
ijassa-1367	229	28	x	x	X
ijassa-1367	229	29	,	,	PUNCT
ijassa-1367	229	30	y	y	PROPN
ijassa-1367	229	31	,	,	PUNCT
ijassa-1367	229	32	φ	φ	NOUN
ijassa-1367	229	33	)	)	PUNCT
ijassa-1367	229	34	,	,	PUNCT
ijassa-1367	229	35	where	where	SCONJ
ijassa-1367	229	36	φ	φ	PROPN
ijassa-1367	229	37	is	be	AUX
ijassa-1367	229	38	an	an	DET
ijassa-1367	229	39	arbitrary	arbitrary	ADJ
ijassa-1367	229	40	angle	angle	NOUN
ijassa-1367	229	41	.	.	PUNCT
ijassa-1367	230	1	figure	figure	NOUN
ijassa-1367	230	2	4.4	4.4	NUM
ijassa-1367	230	3	illustrates	illustrate	VERB
ijassa-1367	230	4	the	the	DET
ijassa-1367	230	5	results	result	NOUN
ijassa-1367	230	6	of	of	ADP
ijassa-1367	230	7	numerical	numerical	ADJ
ijassa-1367	230	8	solution	solution	NOUN
ijassa-1367	230	9	of	of	ADP
ijassa-1367	230	10	the	the	DET
ijassa-1367	230	11	problem	problem	NOUN
ijassa-1367	230	12	for	for	ADP
ijassa-1367	230	13	various	various	ADJ
ijassa-1367	230	14	initial	initial	ADJ
ijassa-1367	230	15	and	and	CCONJ
ijassa-1367	230	16	terminal	terminal	ADJ
ijassa-1367	230	17	conditions	condition	NOUN
ijassa-1367	230	18	.	.	PUNCT
ijassa-1367	231	1	in	in	ADP
ijassa-1367	231	2	all	all	DET
ijassa-1367	231	3	the	the	DET
ijassa-1367	231	4	cases	case	NOUN
ijassa-1367	231	5	,	,	PUNCT
ijassa-1367	231	6	we	we	PRON
ijassa-1367	231	7	must	must	AUX
ijassa-1367	231	8	eventually	eventually	ADV
ijassa-1367	231	9	reach	reach	VERB
ijassa-1367	231	10	a	a	DET
ijassa-1367	231	11	small	small	ADJ
ijassa-1367	231	12	square	square	NOUN
ijassa-1367	231	13	.	.	PUNCT
ijassa-1367	232	1	on	on	ADP
ijassa-1367	232	2	the	the	DET
ijassa-1367	232	3	left	left	ADJ
ijassa-1367	232	4	-	-	PUNCT
ijassa-1367	232	5	hand	hand	NOUN
ijassa-1367	232	6	part	part	NOUN
ijassa-1367	232	7	of	of	ADP
ijassa-1367	232	8	the	the	DET
ijassa-1367	232	9	figure	figure	NOUN
ijassa-1367	232	10	,	,	PUNCT
ijassa-1367	232	11	we	we	PRON
ijassa-1367	232	12	are	be	AUX
ijassa-1367	232	13	allowed	allow	VERB
ijassa-1367	232	14	to	to	PART
ijassa-1367	232	15	get	get	VERB
ijassa-1367	232	16	to	to	ADP
ijassa-1367	232	17	the	the	DET
ijassa-1367	232	18	square	square	NOUN
ijassa-1367	232	19	at	at	ADP
ijassa-1367	232	20	any	any	DET
ijassa-1367	232	21	slope	slope	NOUN
ijassa-1367	232	22	.	.	PUNCT
ijassa-1367	233	1	on	on	ADP
ijassa-1367	233	2	the	the	DET
ijassa-1367	233	3	right	right	NOUN
ijassa-1367	233	4	,	,	PUNCT
ijassa-1367	233	5	we	we	PRON
ijassa-1367	233	6	must	must	AUX
ijassa-1367	233	7	get	get	VERB
ijassa-1367	233	8	to	to	ADP
ijassa-1367	233	9	the	the	DET
ijassa-1367	233	10	square	square	NOUN
ijassa-1367	233	11	in	in	ADP
ijassa-1367	233	12	the	the	DET
ijassa-1367	233	13	direction	direction	NOUN
ijassa-1367	233	14	specified	specify	VERB
ijassa-1367	233	15	by	by	ADP
ijassa-1367	233	16	an	an	DET
ijassa-1367	233	17	arrow	arrow	NOUN
ijassa-1367	233	18	,	,	PUNCT
ijassa-1367	233	19	precisely	precisely	ADV
ijassa-1367	233	20	,	,	PUNCT
ijassa-1367	233	21	at	at	ADP
ijassa-1367	233	22	an	an	DET
ijassa-1367	233	23	angle	angle	NOUN
ijassa-1367	233	24	that	that	PRON
ijassa-1367	233	25	is	be	AUX
ijassa-1367	233	26	very	very	ADV
ijassa-1367	233	27	close	close	ADJ
ijassa-1367	233	28	to	to	ADP
ijassa-1367	233	29	the	the	DET
ijassa-1367	233	30	arrow	arrow	NOUN
ijassa-1367	233	31	.	.	PUNCT
ijassa-1367	234	1	thus	thus	ADV
ijassa-1367	234	2	,	,	PUNCT
ijassa-1367	234	3	in	in	ADP
ijassa-1367	234	4	the	the	DET
ijassa-1367	234	5	first	first	ADJ
ijassa-1367	234	6	case	case	NOUN
ijassa-1367	234	7	the	the	DET
ijassa-1367	234	8	target	target	NOUN
ijassa-1367	234	9	set	set	VERB
ijassa-1367	234	10	is	be	AUX
ijassa-1367	234	11	a	a	DET
ijassa-1367	234	12	two	two	NUM
ijassa-1367	234	13	-	-	PUNCT
ijassa-1367	234	14	dimensional	dimensional	ADJ
ijassa-1367	234	15	neighborhood	neighborhood	NOUN
ijassa-1367	234	16	of	of	ADP
ijassa-1367	234	17	a	a	DET
ijassa-1367	234	18	point	point	NOUN
ijassa-1367	234	19	(	(	PUNCT
ijassa-1367	234	20	x	x	NOUN
ijassa-1367	234	21	,	,	PUNCT
ijassa-1367	234	22	y	y	PROPN
ijassa-1367	234	23	)	)	PUNCT
ijassa-1367	234	24	,	,	PUNCT
ijassa-1367	234	25	in	in	ADP
ijassa-1367	234	26	the	the	DET
ijassa-1367	234	27	second	second	ADJ
ijassa-1367	234	28	case	case	NOUN
ijassa-1367	234	29	the	the	DET
ijassa-1367	234	30	target	target	NOUN
ijassa-1367	234	31	set	set	VERB
ijassa-1367	234	32	is	be	AUX
ijassa-1367	234	33	a	a	DET
ijassa-1367	234	34	three	three	NUM
ijassa-1367	234	35	-	-	PUNCT
ijassa-1367	234	36	dimensional	dimensional	ADJ
ijassa-1367	234	37	neighborhood	neighborhood	NOUN
ijassa-1367	234	38	of	of	ADP
ijassa-1367	234	39	a	a	DET
ijassa-1367	234	40	point	point	NOUN
ijassa-1367	234	41	copyright	copyright	NOUN
ijassa-1367	234	42	©	©	ADP
ijassa-1367	234	43	2023	2023	NUM
ijassa-1367	234	44	assa	assa	NOUN
ijassa-1367	234	45	.	.	PUNCT
ijassa-1367	235	1	adv	adv	PROPN
ijassa-1367	235	2	syst	syst	PROPN
ijassa-1367	235	3	sci	sci	PROPN
ijassa-1367	235	4	appl	appl	PROPN
ijassa-1367	235	5	(	(	PUNCT
ijassa-1367	235	6	2023	2023	NUM
ijassa-1367	235	7	)	)	PUNCT
ijassa-1367	235	8	44	44	NUM
ijassa-1367	235	9	o.	o.	PROPN
ijassa-1367	235	10	e.	e.	PROPN
ijassa-1367	235	11	orel	orel	PROPN
ijassa-1367	235	12	,	,	PUNCT
ijassa-1367	235	13	e.	e.	PROPN
ijassa-1367	235	14	n.	n.	PROPN
ijassa-1367	235	15	orel	orel	PROPN
ijassa-1367	235	16	fig	fig	PROPN
ijassa-1367	235	17	.	.	PUNCT
ijassa-1367	236	1	4.4	4.4	NUM
ijassa-1367	236	2	.	.	PUNCT
ijassa-1367	237	1	car	car	NOUN
ijassa-1367	237	2	motion	motion	NOUN
ijassa-1367	237	3	to	to	ADP
ijassa-1367	237	4	the	the	DET
ijassa-1367	237	5	parking	parking	NOUN
ijassa-1367	237	6	place	place	NOUN
ijassa-1367	237	7	fig	fig	NOUN
ijassa-1367	237	8	.	.	PUNCT
ijassa-1367	238	1	4.5	4.5	NUM
ijassa-1367	238	2	.	.	PUNCT
ijassa-1367	239	1	finding	find	VERB
ijassa-1367	239	2	a	a	DET
ijassa-1367	239	3	way	way	NOUN
ijassa-1367	239	4	out	out	ADP
ijassa-1367	239	5	of	of	ADP
ijassa-1367	239	6	the	the	DET
ijassa-1367	239	7	labyrinth	labyrinth	ADJ
ijassa-1367	239	8	(	(	PUNCT
ijassa-1367	239	9	x	x	X
ijassa-1367	239	10	,	,	PUNCT
ijassa-1367	239	11	y	y	PROPN
ijassa-1367	239	12	,	,	PUNCT
ijassa-1367	239	13	φ	φ	NOUN
ijassa-1367	239	14	)	)	PUNCT
ijassa-1367	239	15	.	.	PUNCT
ijassa-1367	240	1	obviously	obviously	ADV
ijassa-1367	240	2	,	,	PUNCT
ijassa-1367	240	3	on	on	ADP
ijassa-1367	240	4	the	the	DET
ijassa-1367	240	5	left	left	ADJ
ijassa-1367	240	6	-	-	PUNCT
ijassa-1367	240	7	hand	hand	NOUN
ijassa-1367	240	8	part	part	NOUN
ijassa-1367	240	9	of	of	ADP
ijassa-1367	240	10	the	the	DET
ijassa-1367	240	11	figure	figure	NOUN
ijassa-1367	240	12	the	the	DET
ijassa-1367	240	13	task	task	NOUN
ijassa-1367	240	14	is	be	AUX
ijassa-1367	240	15	a	a	DET
ijassa-1367	240	16	little	little	ADJ
ijassa-1367	240	17	simpler	simple	ADJ
ijassa-1367	240	18	than	than	ADP
ijassa-1367	240	19	on	on	ADP
ijassa-1367	240	20	the	the	DET
ijassa-1367	240	21	right	right	ADJ
ijassa-1367	240	22	-	-	PUNCT
ijassa-1367	240	23	hand	hand	NOUN
ijassa-1367	240	24	side	side	NOUN
ijassa-1367	240	25	.	.	PUNCT
ijassa-1367	241	1	this	this	PRON
ijassa-1367	241	2	can	can	AUX
ijassa-1367	241	3	be	be	AUX
ijassa-1367	241	4	seen	see	VERB
ijassa-1367	241	5	also	also	ADV
ijassa-1367	241	6	from	from	ADP
ijassa-1367	241	7	the	the	DET
ijassa-1367	241	8	form	form	NOUN
ijassa-1367	241	9	of	of	ADP
ijassa-1367	241	10	the	the	DET
ijassa-1367	241	11	“	"	PUNCT
ijassa-1367	241	12	polygonal	polygonal	ADJ
ijassa-1367	241	13	lines	line	NOUN
ijassa-1367	241	14	”	"	PUNCT
ijassa-1367	241	15	.	.	PUNCT
ijassa-1367	242	1	figure	figure	VERB
ijassa-1367	242	2	4.5	4.5	NUM
ijassa-1367	242	3	shows	show	VERB
ijassa-1367	242	4	the	the	DET
ijassa-1367	242	5	solution	solution	NOUN
ijassa-1367	242	6	of	of	ADP
ijassa-1367	242	7	the	the	DET
ijassa-1367	242	8	problem	problem	NOUN
ijassa-1367	242	9	on	on	ADP
ijassa-1367	242	10	finding	find	VERB
ijassa-1367	242	11	a	a	DET
ijassa-1367	242	12	way	way	NOUN
ijassa-1367	242	13	out	out	ADP
ijassa-1367	242	14	of	of	ADP
ijassa-1367	242	15	the	the	DET
ijassa-1367	242	16	labyrinth	labyrinth	NOUN
ijassa-1367	242	17	.	.	PUNCT
ijassa-1367	243	1	the	the	DET
ijassa-1367	243	2	car	car	NOUN
ijassa-1367	243	3	must	must	AUX
ijassa-1367	243	4	get	get	VERB
ijassa-1367	243	5	out	out	ADP
ijassa-1367	243	6	bypassing	bypass	VERB
ijassa-1367	243	7	all	all	DET
ijassa-1367	243	8	the	the	DET
ijassa-1367	243	9	obstacles	obstacle	NOUN
ijassa-1367	243	10	.	.	PUNCT
ijassa-1367	244	1	here	here	ADV
ijassa-1367	244	2	the	the	DET
ijassa-1367	244	3	region	region	NOUN
ijassa-1367	244	4	of	of	ADP
ijassa-1367	244	5	motion	motion	NOUN
ijassa-1367	244	6	,	,	PUNCT
ijassa-1367	244	7	which	which	PRON
ijassa-1367	244	8	is	be	AUX
ijassa-1367	244	9	a	a	DET
ijassa-1367	244	10	rectangle	rectangle	NOUN
ijassa-1367	244	11	of	of	ADP
ijassa-1367	244	12	size	size	NOUN
ijassa-1367	244	13	8×	8×	ADP
ijassa-1367	244	14	16	16	NUM
ijassa-1367	244	15	,	,	PUNCT
ijassa-1367	244	16	is	be	AUX
ijassa-1367	244	17	partitioned	partition	VERB
ijassa-1367	244	18	into	into	ADP
ijassa-1367	244	19	squares	square	NOUN
ijassa-1367	244	20	with	with	ADP
ijassa-1367	244	21	side	side	NOUN
ijassa-1367	244	22	8	8	NUM
ijassa-1367	244	23	10	10	NUM
ijassa-1367	244	24	,	,	PUNCT
ijassa-1367	244	25	and	and	CCONJ
ijassa-1367	244	26	the	the	DET
ijassa-1367	244	27	set	set	NOUN
ijassa-1367	244	28	of	of	ADP
ijassa-1367	244	29	directions	direction	NOUN
ijassa-1367	244	30	—	—	PUNCT
ijassa-1367	244	31	into	into	ADP
ijassa-1367	244	32	intervals	interval	NOUN
ijassa-1367	244	33	of	of	ADP
ijassa-1367	244	34	length	length	NOUN
ijassa-1367	244	35	2π	2π	PROPN
ijassa-1367	244	36	15	15	NUM
ijassa-1367	244	37	.	.	PUNCT
ijassa-1367	245	1	so	so	ADV
ijassa-1367	245	2	we	we	PRON
ijassa-1367	245	3	get	get	VERB
ijassa-1367	245	4	10×	10×	NUM
ijassa-1367	245	5	20×	20×	NUM
ijassa-1367	245	6	30	30	NUM
ijassa-1367	245	7	=	=	SYM
ijassa-1367	245	8	3000	3000	NUM
ijassa-1367	245	9	cells	cell	NOUN
ijassa-1367	245	10	.	.	PUNCT
ijassa-1367	246	1	this	this	DET
ijassa-1367	246	2	problem	problem	NOUN
ijassa-1367	246	3	and	and	CCONJ
ijassa-1367	246	4	its	its	PRON
ijassa-1367	246	5	solution	solution	NOUN
ijassa-1367	246	6	can	can	AUX
ijassa-1367	246	7	be	be	AUX
ijassa-1367	246	8	used	use	VERB
ijassa-1367	246	9	in	in	ADP
ijassa-1367	246	10	robotics	robotic	NOUN
ijassa-1367	246	11	and	and	CCONJ
ijassa-1367	246	12	artificial	artificial	ADJ
ijassa-1367	246	13	intelligence	intelligence	NOUN
ijassa-1367	246	14	.	.	PUNCT
ijassa-1367	247	1	therefore	therefore	ADV
ijassa-1367	247	2	,	,	PUNCT
ijassa-1367	247	3	in	in	ADP
ijassa-1367	247	4	[	[	PUNCT
ijassa-1367	247	5	9	9	NUM
ijassa-1367	247	6	]	]	PUNCT
ijassa-1367	247	7	,	,	PUNCT
ijassa-1367	247	8	[	[	X
ijassa-1367	247	9	11	11	NUM
ijassa-1367	247	10	]	]	PUNCT
ijassa-1367	247	11	there	there	PRON
ijassa-1367	247	12	was	be	VERB
ijassa-1367	247	13	suggested	suggest	VERB
ijassa-1367	247	14	to	to	PART
ijassa-1367	247	15	use	use	VERB
ijassa-1367	247	16	the	the	DET
ijassa-1367	247	17	model	model	NOUN
ijassa-1367	247	18	for	for	ADP
ijassa-1367	247	19	testing	testing	NOUN
ijassa-1367	247	20	methods	method	NOUN
ijassa-1367	247	21	of	of	ADP
ijassa-1367	247	22	solving	solve	VERB
ijassa-1367	247	23	dynamic	dynamic	ADJ
ijassa-1367	247	24	optimization	optimization	NOUN
ijassa-1367	247	25	problems	problem	NOUN
ijassa-1367	247	26	.	.	PUNCT
ijassa-1367	248	1	however	however	ADV
ijassa-1367	248	2	,	,	PUNCT
ijassa-1367	248	3	since	since	SCONJ
ijassa-1367	248	4	then	then	ADV
ijassa-1367	248	5	no	no	DET
ijassa-1367	248	6	method	method	NOUN
ijassa-1367	248	7	to	to	PART
ijassa-1367	248	8	solve	solve	VERB
ijassa-1367	248	9	the	the	DET
ijassa-1367	248	10	problem	problem	NOUN
ijassa-1367	248	11	on	on	ADP
ijassa-1367	248	12	finding	find	VERB
ijassa-1367	248	13	a	a	DET
ijassa-1367	248	14	way	way	NOUN
ijassa-1367	248	15	out	out	ADP
ijassa-1367	248	16	of	of	ADP
ijassa-1367	248	17	the	the	DET
ijassa-1367	248	18	labyrinth	labyrinth	NOUN
ijassa-1367	248	19	has	have	AUX
ijassa-1367	248	20	appeared	appear	VERB
ijassa-1367	248	21	.	.	PUNCT
ijassa-1367	249	1	copyright	copyright	NOUN
ijassa-1367	249	2	©	©	PROPN
ijassa-1367	249	3	2023	2023	NUM
ijassa-1367	249	4	assa	assa	NOUN
ijassa-1367	249	5	.	.	PUNCT
ijassa-1367	250	1	adv	adv	PROPN
ijassa-1367	250	2	syst	syst	PROPN
ijassa-1367	250	3	sci	sci	PROPN
ijassa-1367	250	4	appl	appl	PROPN
ijassa-1367	250	5	(	(	PUNCT
ijassa-1367	250	6	2023	2023	NUM
ijassa-1367	250	7	)	)	PUNCT
ijassa-1367	250	8	piecewise	piecewise	NOUN
ijassa-1367	250	9	constant	constant	ADJ
ijassa-1367	250	10	functions	function	NOUN
ijassa-1367	250	11	in	in	ADP
ijassa-1367	250	12	dynamic	dynamic	ADJ
ijassa-1367	250	13	optimization	optimization	NOUN
ijassa-1367	250	14	problems	problem	NOUN
ijassa-1367	250	15	45	45	NUM
ijassa-1367	250	16	5	5	NUM
ijassa-1367	250	17	.	.	PUNCT
ijassa-1367	250	18	differential	differential	ADJ
ijassa-1367	250	19	games	game	NOUN
ijassa-1367	250	20	now	now	ADV
ijassa-1367	250	21	we	we	PRON
ijassa-1367	250	22	consider	consider	VERB
ijassa-1367	250	23	three	three	NUM
ijassa-1367	250	24	differential	differential	ADJ
ijassa-1367	250	25	games	game	NOUN
ijassa-1367	250	26	with	with	ADP
ijassa-1367	250	27	two	two	NUM
ijassa-1367	250	28	players	player	NOUN
ijassa-1367	250	29	(	(	PUNCT
ijassa-1367	250	30	see	see	VERB
ijassa-1367	250	31	[	[	X
ijassa-1367	250	32	3	3	NUM
ijassa-1367	250	33	]	]	NUM
ijassa-1367	250	34	)	)	PUNCT
ijassa-1367	250	35	.	.	PUNCT
ijassa-1367	251	1	in	in	ADP
ijassa-1367	251	2	all	all	DET
ijassa-1367	251	3	three	three	NUM
ijassa-1367	251	4	games	game	NOUN
ijassa-1367	251	5	,	,	PUNCT
ijassa-1367	251	6	speeds	speed	NOUN
ijassa-1367	251	7	of	of	ADP
ijassa-1367	251	8	player	player	NOUN
ijassa-1367	251	9	p	p	NOUN
ijassa-1367	251	10	(	(	PUNCT
ijassa-1367	251	11	pursuer	pursuer	PROPN
ijassa-1367	251	12	)	)	PUNCT
ijassa-1367	251	13	and	and	CCONJ
ijassa-1367	251	14	of	of	ADP
ijassa-1367	251	15	player	player	NOUN
ijassa-1367	251	16	e	e	NOUN
ijassa-1367	251	17	(	(	PUNCT
ijassa-1367	251	18	evader	evader	NOUN
ijassa-1367	251	19	)	)	PUNCT
ijassa-1367	251	20	are	be	AUX
ijassa-1367	251	21	constant	constant	ADJ
ijassa-1367	251	22	.	.	PUNCT
ijassa-1367	252	1	in	in	ADP
ijassa-1367	252	2	addition	addition	NOUN
ijassa-1367	252	3	,	,	PUNCT
ijassa-1367	252	4	pursuer	pursuer	NOUN
ijassa-1367	252	5	p	p	NOUN
ijassa-1367	252	6	is	be	AUX
ijassa-1367	252	7	to	to	PART
ijassa-1367	252	8	be	be	AUX
ijassa-1367	252	9	faster	fast	ADJ
ijassa-1367	252	10	than	than	ADP
ijassa-1367	252	11	evader	evader	NOUN
ijassa-1367	252	12	e.	e.	PROPN
ijassa-1367	252	13	5.1	5.1	NUM
ijassa-1367	252	14	.	.	PUNCT
ijassa-1367	253	1	simplest	simple	ADJ
ijassa-1367	253	2	pursuit	pursuit	ADJ
ijassa-1367	253	3	game	game	NOUN
ijassa-1367	253	4	in	in	ADP
ijassa-1367	253	5	frames	frame	NOUN
ijassa-1367	253	6	of	of	ADP
ijassa-1367	253	7	this	this	DET
ijassa-1367	253	8	game	game	NOUN
ijassa-1367	253	9	,	,	PUNCT
ijassa-1367	253	10	the	the	DET
ijassa-1367	253	11	players	player	NOUN
ijassa-1367	253	12	make	make	VERB
ijassa-1367	253	13	a	a	DET
ijassa-1367	253	14	simple	simple	ADJ
ijassa-1367	253	15	motion	motion	NOUN
ijassa-1367	253	16	.	.	PUNCT
ijassa-1367	254	1	each	each	PRON
ijassa-1367	254	2	of	of	ADP
ijassa-1367	254	3	them	they	PRON
ijassa-1367	254	4	moves	move	VERB
ijassa-1367	254	5	with	with	ADP
ijassa-1367	254	6	its	its	PRON
ijassa-1367	254	7	own	own	ADJ
ijassa-1367	254	8	constant	constant	ADJ
ijassa-1367	254	9	speed	speed	NOUN
ijassa-1367	254	10	,	,	PUNCT
ijassa-1367	254	11	changing	change	VERB
ijassa-1367	254	12	the	the	DET
ijassa-1367	254	13	direction	direction	NOUN
ijassa-1367	254	14	at	at	ADP
ijassa-1367	254	15	his	his	PRON
ijassa-1367	254	16	own	own	ADJ
ijassa-1367	254	17	discretion	discretion	NOUN
ijassa-1367	254	18	.	.	PUNCT
ijassa-1367	255	1	the	the	DET
ijassa-1367	255	2	game	game	NOUN
ijassa-1367	255	3	terminates	terminate	VERB
ijassa-1367	255	4	when	when	SCONJ
ijassa-1367	255	5	p	p	NOUN
ijassa-1367	255	6	captures	capture	NOUN
ijassa-1367	255	7	e	e	NOUN
ijassa-1367	255	8	(	(	PUNCT
ijassa-1367	255	9	i.e.	i.e.	X
ijassa-1367	255	10	,	,	PUNCT
ijassa-1367	255	11	the	the	DET
ijassa-1367	255	12	distance	distance	NOUN
ijassa-1367	255	13	pe	pe	PROPN
ijassa-1367	255	14	becomes	become	VERB
ijassa-1367	255	15	less	less	ADJ
ijassa-1367	255	16	than	than	ADP
ijassa-1367	255	17	a	a	DET
ijassa-1367	255	18	certain	certain	ADJ
ijassa-1367	255	19	prescribed	prescribed	ADJ
ijassa-1367	255	20	positive	positive	ADJ
ijassa-1367	255	21	quantity	quantity	NOUN
ijassa-1367	255	22	)	)	PUNCT
ijassa-1367	255	23	.	.	PUNCT
ijassa-1367	256	1	write	write	VERB
ijassa-1367	256	2	kinematic	kinematic	ADJ
ijassa-1367	256	3	equations	equation	NOUN
ijassa-1367	256	4	:	:	PUNCT
ijassa-1367	257	1	ẋ1	ẋ1	PROPN
ijassa-1367	257	2	=	=	PUNCT
ijassa-1367	257	3	v1	v1	PROPN
ijassa-1367	257	4	cosφ1	cosφ1	NOUN
ijassa-1367	257	5	,	,	PUNCT
ijassa-1367	257	6	ẏ1	ẏ1	PROPN
ijassa-1367	257	7	=	=	SYM
ijassa-1367	257	8	v1	v1	PROPN
ijassa-1367	257	9	sinφ1	sinφ1	ADJ
ijassa-1367	257	10	,	,	PUNCT
ijassa-1367	257	11	ẋ2	ẋ2	PROPN
ijassa-1367	257	12	=	=	PUNCT
ijassa-1367	257	13	v2	v2	PROPN
ijassa-1367	257	14	cosφ2	cosφ2	NOUN
ijassa-1367	257	15	,	,	PUNCT
ijassa-1367	257	16	ẏ2	ẏ2	PROPN
ijassa-1367	257	17	=	=	SYM
ijassa-1367	257	18	v2	v2	PROPN
ijassa-1367	257	19	sinφ2	sinφ2	PROPN
ijassa-1367	257	20	,	,	PUNCT
ijassa-1367	257	21	v1	v1	VERB
ijassa-1367	257	22	>	>	X
ijassa-1367	257	23	v2	v2	PROPN
ijassa-1367	257	24	>	>	X
ijassa-1367	257	25	0	0	PROPN
ijassa-1367	257	26	,	,	PUNCT
ijassa-1367	257	27	where	where	SCONJ
ijassa-1367	257	28	φ1(t	φ1(t	X
ijassa-1367	257	29	)	)	PUNCT
ijassa-1367	257	30	and	and	CCONJ
ijassa-1367	257	31	φ2(t	φ2(t	NUM
ijassa-1367	257	32	)	)	PUNCT
ijassa-1367	257	33	are	be	AUX
ijassa-1367	257	34	controls	control	NOUN
ijassa-1367	257	35	of	of	ADP
ijassa-1367	257	36	the	the	DET
ijassa-1367	257	37	players	player	NOUN
ijassa-1367	257	38	.	.	PUNCT
ijassa-1367	258	1	for	for	ADP
ijassa-1367	258	2	each	each	DET
ijassa-1367	258	3	player	player	NOUN
ijassa-1367	258	4	,	,	PUNCT
ijassa-1367	258	5	motion	motion	NOUN
ijassa-1367	258	6	along	along	ADP
ijassa-1367	258	7	the	the	DET
ijassa-1367	258	8	straight	straight	ADJ
ijassa-1367	258	9	line	line	NOUN
ijassa-1367	258	10	pe	pe	PROPN
ijassa-1367	258	11	would	would	AUX
ijassa-1367	258	12	be	be	AUX
ijassa-1367	258	13	optimal	optimal	ADJ
ijassa-1367	258	14	,	,	PUNCT
ijassa-1367	258	15	where	where	SCONJ
ijassa-1367	258	16	p	p	NOUN
ijassa-1367	258	17	moves	move	VERB
ijassa-1367	258	18	toward	toward	ADP
ijassa-1367	258	19	e	e	NOUN
ijassa-1367	258	20	and	and	CCONJ
ijassa-1367	258	21	e	e	NOUN
ijassa-1367	258	22	moves	move	VERB
ijassa-1367	258	23	away	away	ADV
ijassa-1367	258	24	from	from	ADP
ijassa-1367	258	25	p	p	PROPN
ijassa-1367	258	26	.	.	PUNCT
ijassa-1367	259	1	the	the	DET
ijassa-1367	259	2	authors	author	NOUN
ijassa-1367	259	3	wrote	write	VERB
ijassa-1367	259	4	a	a	DET
ijassa-1367	259	5	program	program	NOUN
ijassa-1367	259	6	,	,	PUNCT
ijassa-1367	259	7	but	but	CCONJ
ijassa-1367	259	8	the	the	DET
ijassa-1367	259	9	game	game	NOUN
ijassa-1367	259	10	figure	figure	NOUN
ijassa-1367	259	11	is	be	AUX
ijassa-1367	259	12	not	not	PART
ijassa-1367	259	13	very	very	ADV
ijassa-1367	259	14	informative	informative	ADJ
ijassa-1367	259	15	:	:	PUNCT
ijassa-1367	259	16	one	one	PRON
ijassa-1367	259	17	would	would	AUX
ijassa-1367	259	18	see	see	VERB
ijassa-1367	259	19	only	only	ADV
ijassa-1367	259	20	the	the	DET
ijassa-1367	259	21	segments	segment	NOUN
ijassa-1367	259	22	of	of	ADP
ijassa-1367	259	23	the	the	DET
ijassa-1367	259	24	straight	straight	ADJ
ijassa-1367	259	25	line	line	NOUN
ijassa-1367	259	26	pe	pe	INTJ
ijassa-1367	259	27	.	.	PUNCT
ijassa-1367	260	1	the	the	DET
ijassa-1367	260	2	state	state	NOUN
ijassa-1367	260	3	space	space	NOUN
ijassa-1367	260	4	is	be	AUX
ijassa-1367	260	5	one	one	NUM
ijassa-1367	260	6	-	-	PUNCT
ijassa-1367	260	7	dimensional	dimensional	ADJ
ijassa-1367	260	8	,	,	PUNCT
ijassa-1367	260	9	because	because	SCONJ
ijassa-1367	260	10	the	the	DET
ijassa-1367	260	11	state	state	NOUN
ijassa-1367	260	12	is	be	AUX
ijassa-1367	260	13	completely	completely	ADV
ijassa-1367	260	14	defined	define	VERB
ijassa-1367	260	15	by	by	ADP
ijassa-1367	260	16	the	the	DET
ijassa-1367	260	17	distance	distance	NOUN
ijassa-1367	260	18	between	between	ADP
ijassa-1367	260	19	the	the	DET
ijassa-1367	260	20	players	player	NOUN
ijassa-1367	260	21	.	.	PUNCT
ijassa-1367	261	1	in	in	ADP
ijassa-1367	261	2	the	the	DET
ijassa-1367	261	3	program	program	NOUN
ijassa-1367	261	4	,	,	PUNCT
ijassa-1367	261	5	we	we	PRON
ijassa-1367	261	6	used	use	VERB
ijassa-1367	261	7	the	the	DET
ijassa-1367	261	8	largest	large	ADJ
ijassa-1367	261	9	distance	distance	NOUN
ijassa-1367	261	10	r	r	NOUN
ijassa-1367	261	11	(	(	PUNCT
ijassa-1367	261	12	i.e.	i.e.	X
ijassa-1367	261	13	,	,	PUNCT
ijassa-1367	261	14	the	the	DET
ijassa-1367	261	15	distance	distance	NOUN
ijassa-1367	261	16	at	at	ADP
ijassa-1367	261	17	which	which	PRON
ijassa-1367	261	18	the	the	DET
ijassa-1367	261	19	game	game	NOUN
ijassa-1367	261	20	terminates	terminate	VERB
ijassa-1367	261	21	with	with	ADP
ijassa-1367	261	22	the	the	DET
ijassa-1367	261	23	win	win	NOUN
ijassa-1367	261	24	for	for	ADP
ijassa-1367	261	25	player	player	NOUN
ijassa-1367	261	26	p	p	PROPN
ijassa-1367	261	27	)	)	PUNCT
ijassa-1367	261	28	,	,	PUNCT
ijassa-1367	261	29	and	and	CCONJ
ijassa-1367	261	30	the	the	DET
ijassa-1367	261	31	segment	segment	NOUN
ijassa-1367	261	32	[	[	X
ijassa-1367	261	33	0	0	NUM
ijassa-1367	261	34	,	,	PUNCT
ijassa-1367	261	35	r	r	NOUN
ijassa-1367	261	36	]	]	X
ijassa-1367	261	37	was	be	AUX
ijassa-1367	261	38	,	,	PUNCT
ijassa-1367	261	39	as	as	ADV
ijassa-1367	261	40	usual	usual	ADJ
ijassa-1367	261	41	,	,	PUNCT
ijassa-1367	261	42	divided	divide	VERB
ijassa-1367	261	43	into	into	ADP
ijassa-1367	261	44	finite	finite	ADJ
ijassa-1367	261	45	number	number	NOUN
ijassa-1367	261	46	of	of	ADP
ijassa-1367	261	47	cells	cell	NOUN
ijassa-1367	261	48	.	.	PUNCT
ijassa-1367	262	1	5.2	5.2	NUM
ijassa-1367	262	2	.	.	PUNCT
ijassa-1367	262	3	homicidal	homicidal	ADJ
ijassa-1367	262	4	chauffeur	chauffeur	PROPN
ijassa-1367	262	5	game	game	NOUN
ijassa-1367	262	6	a	a	DET
ijassa-1367	262	7	driver	driver	NOUN
ijassa-1367	262	8	attempts	attempt	VERB
ijassa-1367	262	9	to	to	PART
ijassa-1367	262	10	run	run	VERB
ijassa-1367	262	11	down	down	ADP
ijassa-1367	262	12	a	a	DET
ijassa-1367	262	13	pedestrian	pedestrian	NOUN
ijassa-1367	262	14	at	at	ADP
ijassa-1367	262	15	minimum	minimum	ADJ
ijassa-1367	262	16	time	time	NOUN
ijassa-1367	262	17	;	;	PUNCT
ijassa-1367	262	18	the	the	DET
ijassa-1367	262	19	motion	motion	NOUN
ijassa-1367	262	20	is	be	AUX
ijassa-1367	262	21	described	describe	VERB
ijassa-1367	262	22	by	by	ADP
ijassa-1367	262	23	the	the	DET
ijassa-1367	262	24	following	follow	VERB
ijassa-1367	262	25	kinematic	kinematic	ADJ
ijassa-1367	262	26	equations	equation	NOUN
ijassa-1367	262	27	:	:	PUNCT
ijassa-1367	263	1	ẋ1	ẋ1	PROPN
ijassa-1367	263	2	=	=	PUNCT
ijassa-1367	263	3	v1	v1	PROPN
ijassa-1367	263	4	cosφ1	cosφ1	NOUN
ijassa-1367	263	5	,	,	PUNCT
ijassa-1367	263	6	ẏ1	ẏ1	PROPN
ijassa-1367	263	7	=	=	SYM
ijassa-1367	263	8	v1	v1	PROPN
ijassa-1367	263	9	sinφ1	sinφ1	ADJ
ijassa-1367	263	10	,	,	PUNCT
ijassa-1367	263	11	φ̇1	φ̇1	PROPN
ijassa-1367	263	12	=	=	SYM
ijassa-1367	263	13	v1	v1	PROPN
ijassa-1367	263	14	r	r	NOUN
ijassa-1367	263	15	u	u	NOUN
ijassa-1367	263	16	,	,	PUNCT
ijassa-1367	263	17	ẋ2	ẋ2	PROPN
ijassa-1367	263	18	=	=	SYM
ijassa-1367	263	19	v2	v2	PROPN
ijassa-1367	263	20	cosφ2	cosφ2	NOUN
ijassa-1367	263	21	,	,	PUNCT
ijassa-1367	263	22	ẏ2	ẏ2	PROPN
ijassa-1367	263	23	=	=	SYM
ijassa-1367	263	24	v2	v2	PROPN
ijassa-1367	263	25	sinφ2	sinφ2	PROPN
ijassa-1367	263	26	,	,	PUNCT
ijassa-1367	263	27	v1	v1	VERB
ijassa-1367	263	28	>	>	X
ijassa-1367	263	29	v2	v2	PROPN
ijassa-1367	263	30	>	>	X
ijassa-1367	263	31	0	0	X
ijassa-1367	263	32	.	.	PUNCT
ijassa-1367	264	1	this	this	DET
ijassa-1367	264	2	game	game	NOUN
ijassa-1367	264	3	was	be	AUX
ijassa-1367	264	4	studied	study	VERB
ijassa-1367	264	5	by	by	ADP
ijassa-1367	264	6	several	several	ADJ
ijassa-1367	264	7	authors	author	NOUN
ijassa-1367	264	8	[	[	X
ijassa-1367	264	9	1	1	NUM
ijassa-1367	264	10	]	]	PUNCT
ijassa-1367	264	11	,	,	PUNCT
ijassa-1367	265	1	[	[	X
ijassa-1367	265	2	3	3	NUM
ijassa-1367	265	3	]	]	PUNCT
ijassa-1367	265	4	,	,	PUNCT
ijassa-1367	265	5	however	however	ADV
ijassa-1367	265	6	an	an	DET
ijassa-1367	265	7	exact	exact	ADJ
ijassa-1367	265	8	analytic	analytic	ADJ
ijassa-1367	265	9	solution	solution	NOUN
ijassa-1367	265	10	has	have	AUX
ijassa-1367	265	11	not	not	PART
ijassa-1367	265	12	been	be	AUX
ijassa-1367	265	13	found	find	VERB
ijassa-1367	265	14	as	as	ADP
ijassa-1367	265	15	yet	yet	ADV
ijassa-1367	265	16	.	.	PUNCT
ijassa-1367	266	1	figure	figure	NOUN
ijassa-1367	266	2	5.6	5.6	NUM
ijassa-1367	266	3	represents	represent	VERB
ijassa-1367	266	4	some	some	DET
ijassa-1367	266	5	parties	party	NOUN
ijassa-1367	266	6	constructed	construct	VERB
ijassa-1367	266	7	by	by	ADP
ijassa-1367	266	8	computer	computer	NOUN
ijassa-1367	266	9	.	.	PUNCT
ijassa-1367	267	1	after	after	ADP
ijassa-1367	267	2	self	self	NOUN
ijassa-1367	267	3	-	-	PUNCT
ijassa-1367	267	4	learning	learning	NOUN
ijassa-1367	267	5	,	,	PUNCT
ijassa-1367	267	6	each	each	DET
ijassa-1367	267	7	player	player	NOUN
ijassa-1367	267	8	acts	act	VERB
ijassa-1367	267	9	optimally	optimally	ADV
ijassa-1367	267	10	himself	himself	PRON
ijassa-1367	267	11	.	.	PUNCT
ijassa-1367	268	1	in	in	ADP
ijassa-1367	268	2	this	this	DET
ijassa-1367	268	3	game	game	NOUN
ijassa-1367	268	4	,	,	PUNCT
ijassa-1367	268	5	the	the	DET
ijassa-1367	268	6	state	state	NOUN
ijassa-1367	268	7	space	space	NOUN
ijassa-1367	268	8	is	be	AUX
ijassa-1367	268	9	two	two	NUM
ijassa-1367	268	10	-	-	PUNCT
ijassa-1367	268	11	dimensional	dimensional	ADJ
ijassa-1367	268	12	,	,	PUNCT
ijassa-1367	268	13	since	since	SCONJ
ijassa-1367	268	14	it	it	PRON
ijassa-1367	268	15	is	be	AUX
ijassa-1367	268	16	completely	completely	ADV
ijassa-1367	268	17	determined	determine	VERB
ijassa-1367	268	18	by	by	ADP
ijassa-1367	268	19	the	the	DET
ijassa-1367	268	20	distance	distance	NOUN
ijassa-1367	268	21	between	between	ADP
ijassa-1367	268	22	the	the	DET
ijassa-1367	268	23	players	player	NOUN
ijassa-1367	268	24	and	and	CCONJ
ijassa-1367	268	25	the	the	DET
ijassa-1367	268	26	angle	angle	NOUN
ijassa-1367	268	27	between	between	ADP
ijassa-1367	268	28	the	the	DET
ijassa-1367	268	29	sight	sight	NOUN
ijassa-1367	268	30	line	line	NOUN
ijassa-1367	268	31	pe	pe	PROPN
ijassa-1367	268	32	and	and	CCONJ
ijassa-1367	268	33	the	the	DET
ijassa-1367	268	34	velocity	velocity	NOUN
ijassa-1367	268	35	of	of	ADP
ijassa-1367	268	36	p	p	PROPN
ijassa-1367	268	37	.	.	PUNCT
ijassa-1367	269	1	figure	figure	VERB
ijassa-1367	269	2	5.6	5.6	NUM
ijassa-1367	269	3	shows	show	NOUN
ijassa-1367	269	4	8	8	NUM
ijassa-1367	269	5	parties	party	NOUN
ijassa-1367	269	6	,	,	PUNCT
ijassa-1367	269	7	each	each	PRON
ijassa-1367	269	8	terminates	terminate	VERB
ijassa-1367	269	9	with	with	ADP
ijassa-1367	269	10	the	the	DET
ijassa-1367	269	11	victory	victory	NOUN
ijassa-1367	269	12	of	of	ADP
ijassa-1367	269	13	pursuer	pursuer	NOUN
ijassa-1367	269	14	p	p	NOUN
ijassa-1367	269	15	.	.	PUNCT
ijassa-1367	270	1	the	the	DET
ijassa-1367	270	2	trajectory	trajectory	NOUN
ijassa-1367	270	3	of	of	ADP
ijassa-1367	270	4	p	p	NOUN
ijassa-1367	270	5	is	be	AUX
ijassa-1367	270	6	depicted	depict	VERB
ijassa-1367	270	7	by	by	ADP
ijassa-1367	270	8	an	an	DET
ijassa-1367	270	9	ordinary	ordinary	ADJ
ijassa-1367	270	10	line	line	NOUN
ijassa-1367	270	11	,	,	PUNCT
ijassa-1367	270	12	whereas	whereas	SCONJ
ijassa-1367	270	13	the	the	DET
ijassa-1367	270	14	trajectory	trajectory	NOUN
ijassa-1367	270	15	of	of	ADP
ijassa-1367	270	16	e	e	PROPN
ijassa-1367	270	17	—	—	PUNCT
ijassa-1367	270	18	by	by	ADP
ijassa-1367	270	19	a	a	DET
ijassa-1367	270	20	bold	bold	ADJ
ijassa-1367	270	21	line	line	NOUN
ijassa-1367	270	22	.	.	PUNCT
ijassa-1367	271	1	in	in	ADP
ijassa-1367	271	2	addition	addition	NOUN
ijassa-1367	271	3	,	,	PUNCT
ijassa-1367	271	4	along	along	ADP
ijassa-1367	271	5	the	the	DET
ijassa-1367	271	6	path	path	NOUN
ijassa-1367	271	7	of	of	ADP
ijassa-1367	271	8	each	each	DET
ijassa-1367	271	9	player	player	NOUN
ijassa-1367	271	10	,	,	PUNCT
ijassa-1367	271	11	we	we	PRON
ijassa-1367	271	12	put	put	VERB
ijassa-1367	271	13	markers	marker	NOUN
ijassa-1367	271	14	at	at	ADP
ijassa-1367	271	15	equal	equal	ADJ
ijassa-1367	271	16	intervals	interval	NOUN
ijassa-1367	271	17	of	of	ADP
ijassa-1367	271	18	time	time	NOUN
ijassa-1367	271	19	.	.	PUNCT
ijassa-1367	272	1	the	the	DET
ijassa-1367	272	2	markers	marker	NOUN
ijassa-1367	272	3	of	of	ADP
ijassa-1367	272	4	pursuer	pursuer	NOUN
ijassa-1367	272	5	p	p	NOUN
ijassa-1367	272	6	are	be	AUX
ijassa-1367	272	7	depicted	depict	VERB
ijassa-1367	272	8	by	by	ADP
ijassa-1367	272	9	deleted	delete	VERB
ijassa-1367	272	10	circles	circle	NOUN
ijassa-1367	272	11	,	,	PUNCT
ijassa-1367	272	12	whereas	whereas	SCONJ
ijassa-1367	272	13	the	the	DET
ijassa-1367	272	14	markers	marker	NOUN
ijassa-1367	272	15	of	of	ADP
ijassa-1367	272	16	evader	evader	NOUN
ijassa-1367	272	17	e	e	NOUN
ijassa-1367	272	18	are	be	AUX
ijassa-1367	272	19	represented	represent	VERB
ijassa-1367	272	20	by	by	ADP
ijassa-1367	272	21	solid	solid	ADJ
ijassa-1367	272	22	squares	square	NOUN
ijassa-1367	272	23	.	.	PUNCT
ijassa-1367	273	1	therefore	therefore	ADV
ijassa-1367	273	2	,	,	PUNCT
ijassa-1367	273	3	at	at	ADP
ijassa-1367	273	4	each	each	DET
ijassa-1367	273	5	party	party	NOUN
ijassa-1367	273	6	,	,	PUNCT
ijassa-1367	273	7	the	the	DET
ijassa-1367	273	8	numbers	number	NOUN
ijassa-1367	273	9	of	of	ADP
ijassa-1367	273	10	circles	circle	NOUN
ijassa-1367	273	11	and	and	CCONJ
ijassa-1367	273	12	squares	square	NOUN
ijassa-1367	273	13	are	be	AUX
ijassa-1367	273	14	the	the	DET
ijassa-1367	273	15	same	same	ADJ
ijassa-1367	273	16	(	(	PUNCT
ijassa-1367	273	17	sometimes	sometimes	ADV
ijassa-1367	273	18	,	,	PUNCT
ijassa-1367	273	19	the	the	DET
ijassa-1367	273	20	last	last	ADJ
ijassa-1367	273	21	and	and	CCONJ
ijassa-1367	273	22	the	the	DET
ijassa-1367	273	23	first	first	ADJ
ijassa-1367	273	24	markers	marker	NOUN
ijassa-1367	273	25	are	be	AUX
ijassa-1367	273	26	not	not	PART
ijassa-1367	273	27	printed	print	VERB
ijassa-1367	273	28	well	well	ADV
ijassa-1367	273	29	)	)	PUNCT
ijassa-1367	273	30	.	.	PUNCT
ijassa-1367	274	1	the	the	DET
ijassa-1367	274	2	initial	initial	ADJ
ijassa-1367	274	3	location	location	NOUN
ijassa-1367	274	4	of	of	ADP
ijassa-1367	274	5	p	p	NOUN
ijassa-1367	274	6	is	be	AUX
ijassa-1367	274	7	always	always	ADV
ijassa-1367	274	8	the	the	DET
ijassa-1367	274	9	origin	origin	NOUN
ijassa-1367	274	10	,	,	PUNCT
ijassa-1367	274	11	but	but	CCONJ
ijassa-1367	274	12	the	the	DET
ijassa-1367	274	13	initial	initial	ADJ
ijassa-1367	274	14	direction	direction	NOUN
ijassa-1367	274	15	of	of	ADP
ijassa-1367	274	16	p	p	NOUN
ijassa-1367	274	17	and	and	CCONJ
ijassa-1367	274	18	the	the	DET
ijassa-1367	274	19	initial	initial	ADJ
ijassa-1367	274	20	coordinates	coordinate	NOUN
ijassa-1367	274	21	of	of	ADP
ijassa-1367	274	22	e	e	PROPN
ijassa-1367	274	23	are	be	AUX
ijassa-1367	274	24	specified	specify	VERB
ijassa-1367	274	25	at	at	ADP
ijassa-1367	274	26	random	random	ADJ
ijassa-1367	274	27	.	.	PUNCT
ijassa-1367	275	1	in	in	ADP
ijassa-1367	275	2	parties	party	NOUN
ijassa-1367	275	3	2	2	NUM
ijassa-1367	275	4	,	,	PUNCT
ijassa-1367	275	5	3	3	NUM
ijassa-1367	275	6	,	,	PUNCT
ijassa-1367	275	7	5	5	NUM
ijassa-1367	275	8	,	,	PUNCT
ijassa-1367	275	9	6	6	NUM
ijassa-1367	275	10	,	,	PUNCT
ijassa-1367	275	11	and	and	CCONJ
ijassa-1367	275	12	7	7	NUM
ijassa-1367	275	13	player	player	NOUN
ijassa-1367	275	14	p	p	PROPN
ijassa-1367	275	15	captured	capture	VERB
ijassa-1367	275	16	the	the	DET
ijassa-1367	275	17	opponent	opponent	NOUN
ijassa-1367	275	18	easily	easily	ADV
ijassa-1367	275	19	,	,	PUNCT
ijassa-1367	275	20	since	since	SCONJ
ijassa-1367	275	21	he	he	PRON
ijassa-1367	275	22	did	do	AUX
ijassa-1367	275	23	n’t	not	PART
ijassa-1367	275	24	need	need	VERB
ijassa-1367	275	25	to	to	PART
ijassa-1367	275	26	perform	perform	VERB
ijassa-1367	275	27	a	a	DET
ijassa-1367	275	28	sharp	sharp	ADJ
ijassa-1367	275	29	turn	turn	NOUN
ijassa-1367	275	30	as	as	SCONJ
ijassa-1367	275	31	the	the	DET
ijassa-1367	275	32	initial	initial	ADJ
ijassa-1367	275	33	velocity	velocity	NOUN
ijassa-1367	275	34	of	of	ADP
ijassa-1367	275	35	p	p	NOUN
ijassa-1367	275	36	was	be	AUX
ijassa-1367	275	37	directed	direct	VERB
ijassa-1367	275	38	approximately	approximately	ADV
ijassa-1367	275	39	toward	toward	ADP
ijassa-1367	275	40	e.	e.	PROPN
ijassa-1367	275	41	notice	notice	VERB
ijassa-1367	275	42	that	that	SCONJ
ijassa-1367	275	43	in	in	ADP
ijassa-1367	275	44	parties	party	NOUN
ijassa-1367	275	45	1	1	NUM
ijassa-1367	275	46	and	and	CCONJ
ijassa-1367	275	47	4	4	NUM
ijassa-1367	275	48	,	,	PUNCT
ijassa-1367	275	49	player	player	NOUN
ijassa-1367	275	50	p	p	PROPN
ijassa-1367	275	51	made	make	VERB
ijassa-1367	275	52	a	a	DET
ijassa-1367	275	53	turn	turn	NOUN
ijassa-1367	275	54	maneuver	maneuver	NOUN
ijassa-1367	275	55	immediately	immediately	ADV
ijassa-1367	275	56	.	.	PUNCT
ijassa-1367	276	1	in	in	ADP
ijassa-1367	276	2	the	the	DET
ijassa-1367	276	3	beginning	beginning	NOUN
ijassa-1367	276	4	of	of	ADP
ijassa-1367	276	5	party	party	NOUN
ijassa-1367	276	6	8	8	NUM
ijassa-1367	276	7	,	,	PUNCT
ijassa-1367	276	8	evader	evader	NOUN
ijassa-1367	276	9	e	e	NOUN
ijassa-1367	276	10	caught	catch	VERB
ijassa-1367	276	11	the	the	DET
ijassa-1367	276	12	tail	tail	NOUN
ijassa-1367	276	13	of	of	ADP
ijassa-1367	276	14	p	p	NOUN
ijassa-1367	276	15	to	to	PART
ijassa-1367	276	16	prohibit	prohibit	VERB
ijassa-1367	276	17	him	he	PRON
ijassa-1367	276	18	from	from	ADP
ijassa-1367	276	19	turning	turn	VERB
ijassa-1367	276	20	.	.	PUNCT
ijassa-1367	277	1	however	however	ADV
ijassa-1367	277	2	p	p	X
ijassa-1367	277	3	,	,	PUNCT
ijassa-1367	277	4	who	who	PRON
ijassa-1367	277	5	has	have	VERB
ijassa-1367	277	6	a	a	DET
ijassa-1367	277	7	larger	large	ADJ
ijassa-1367	277	8	speed	speed	NOUN
ijassa-1367	277	9	,	,	PUNCT
ijassa-1367	277	10	broke	break	VERB
ijassa-1367	277	11	away	away	ADV
ijassa-1367	277	12	from	from	ADP
ijassa-1367	277	13	the	the	DET
ijassa-1367	277	14	pursuit	pursuit	NOUN
ijassa-1367	277	15	and	and	CCONJ
ijassa-1367	277	16	,	,	PUNCT
ijassa-1367	277	17	having	having	AUX
ijassa-1367	277	18	made	make	VERB
ijassa-1367	277	19	a	a	DET
ijassa-1367	277	20	loop	loop	NOUN
ijassa-1367	277	21	,	,	PUNCT
ijassa-1367	277	22	aimed	aim	VERB
ijassa-1367	277	23	for	for	SCONJ
ijassa-1367	277	24	e.	e.	PROPN
ijassa-1367	277	25	to	to	PART
ijassa-1367	277	26	extend	extend	VERB
ijassa-1367	277	27	the	the	DET
ijassa-1367	277	28	time	time	NOUN
ijassa-1367	277	29	of	of	ADP
ijassa-1367	277	30	the	the	DET
ijassa-1367	277	31	game	game	NOUN
ijassa-1367	277	32	,	,	PUNCT
ijassa-1367	277	33	evader	evader	NOUN
ijassa-1367	277	34	e	e	NOUN
ijassa-1367	277	35	has	have	AUX
ijassa-1367	277	36	changed	change	VERB
ijassa-1367	277	37	the	the	DET
ijassa-1367	277	38	direction	direction	NOUN
ijassa-1367	277	39	,	,	PUNCT
ijassa-1367	277	40	but	but	CCONJ
ijassa-1367	277	41	this	this	PRON
ijassa-1367	277	42	has	have	AUX
ijassa-1367	277	43	only	only	ADV
ijassa-1367	277	44	delayed	delay	VERB
ijassa-1367	277	45	his	his	PRON
ijassa-1367	277	46	defeat	defeat	NOUN
ijassa-1367	277	47	.	.	PUNCT
ijassa-1367	278	1	the	the	DET
ijassa-1367	278	2	situation	situation	NOUN
ijassa-1367	278	3	just	just	ADV
ijassa-1367	278	4	described	describe	VERB
ijassa-1367	278	5	is	be	AUX
ijassa-1367	278	6	represented	represent	VERB
ijassa-1367	278	7	in	in	ADP
ijassa-1367	278	8	5.7	5.7	NUM
ijassa-1367	278	9	.	.	PUNCT
ijassa-1367	279	1	5.3	5.3	NUM
ijassa-1367	279	2	.	.	PUNCT
ijassa-1367	279	3	game	game	NOUN
ijassa-1367	279	4	of	of	ADP
ijassa-1367	279	5	two	two	NUM
ijassa-1367	279	6	cars	car	NOUN
ijassa-1367	279	7	the	the	DET
ijassa-1367	279	8	kinematic	kinematic	ADJ
ijassa-1367	279	9	equations	equation	NOUN
ijassa-1367	279	10	of	of	ADP
ijassa-1367	279	11	players	player	NOUN
ijassa-1367	279	12	are	be	AUX
ijassa-1367	279	13	similar	similar	ADJ
ijassa-1367	279	14	:	:	PUNCT
ijassa-1367	279	15	if	if	SCONJ
ijassa-1367	279	16	speeds	speed	NOUN
ijassa-1367	279	17	satisfy	satisfy	VERB
ijassa-1367	279	18	the	the	DET
ijassa-1367	279	19	inequality	inequality	NOUN
ijassa-1367	279	20	v1	v1	PROPN
ijassa-1367	279	21	>	>	X
ijassa-1367	279	22	v2	v2	PROPN
ijassa-1367	279	23	>	>	X
ijassa-1367	279	24	0	0	NUM
ijassa-1367	279	25	,	,	PUNCT
ijassa-1367	279	26	then	then	ADV
ijassa-1367	279	27	the	the	DET
ijassa-1367	279	28	following	follow	VERB
ijassa-1367	279	29	equations	equation	NOUN
ijassa-1367	279	30	are	be	AUX
ijassa-1367	279	31	valid	valid	ADJ
ijassa-1367	279	32	:	:	PUNCT
ijassa-1367	279	33	ẋ1	ẋ1	PROPN
ijassa-1367	279	34	=	=	PUNCT
ijassa-1367	279	35	v1	v1	PROPN
ijassa-1367	279	36	cosφ1	cosφ1	NOUN
ijassa-1367	279	37	,	,	PUNCT
ijassa-1367	279	38	ẏ1	ẏ1	PROPN
ijassa-1367	279	39	=	=	SYM
ijassa-1367	279	40	v1	v1	PROPN
ijassa-1367	279	41	sinφ1	sinφ1	ADJ
ijassa-1367	279	42	,	,	PUNCT
ijassa-1367	279	43	φ̇1	φ̇1	PROPN
ijassa-1367	279	44	=	=	SYM
ijassa-1367	279	45	v1	v1	PROPN
ijassa-1367	279	46	r1	r1	NOUN
ijassa-1367	279	47	u1	u1	NOUN
ijassa-1367	279	48	,	,	PUNCT
ijassa-1367	279	49	ẋ2	ẋ2	PROPN
ijassa-1367	279	50	=	=	SYM
ijassa-1367	279	51	v2	v2	PROPN
ijassa-1367	279	52	cosφ2	cosφ2	NOUN
ijassa-1367	279	53	,	,	PUNCT
ijassa-1367	279	54	ẏ2	ẏ2	PROPN
ijassa-1367	279	55	=	=	SYM
ijassa-1367	279	56	v2	v2	PROPN
ijassa-1367	279	57	sinφ2	sinφ2	PROPN
ijassa-1367	279	58	,	,	PUNCT
ijassa-1367	279	59	φ̇2	φ̇2	PROPN
ijassa-1367	279	60	=	=	SYM
ijassa-1367	279	61	v2	v2	PROPN
ijassa-1367	279	62	r2	r2	PROPN
ijassa-1367	279	63	u2	u2	PROPN
ijassa-1367	279	64	.	.	PUNCT
ijassa-1367	280	1	copyright	copyright	NOUN
ijassa-1367	280	2	©	©	PROPN
ijassa-1367	280	3	2023	2023	NUM
ijassa-1367	280	4	assa	assa	NOUN
ijassa-1367	280	5	.	.	PUNCT
ijassa-1367	281	1	adv	adv	PROPN
ijassa-1367	281	2	syst	syst	PROPN
ijassa-1367	281	3	sci	sci	PROPN
ijassa-1367	281	4	appl	appl	PROPN
ijassa-1367	281	5	(	(	PUNCT
ijassa-1367	281	6	2023	2023	NUM
ijassa-1367	281	7	)	)	PUNCT
ijassa-1367	281	8	46	46	NUM
ijassa-1367	282	1	o.	o.	PROPN
ijassa-1367	282	2	e.	e.	PROPN
ijassa-1367	282	3	orel	orel	PROPN
ijassa-1367	282	4	,	,	PUNCT
ijassa-1367	282	5	e.	e.	PROPN
ijassa-1367	282	6	n.	n.	PROPN
ijassa-1367	282	7	orel	orel	PROPN
ijassa-1367	282	8	fig	fig	PROPN
ijassa-1367	282	9	.	.	PUNCT
ijassa-1367	283	1	5.6	5.6	NUM
ijassa-1367	283	2	.	.	PUNCT
ijassa-1367	284	1	several	several	ADJ
ijassa-1367	284	2	parties	party	NOUN
ijassa-1367	284	3	of	of	ADP
ijassa-1367	284	4	the	the	DET
ijassa-1367	284	5	homicidal	homicidal	ADJ
ijassa-1367	284	6	chauffeur	chauffeur	NOUN
ijassa-1367	284	7	game	game	NOUN
ijassa-1367	284	8	fig	fig	NOUN
ijassa-1367	284	9	.	.	PUNCT
ijassa-1367	285	1	5.7	5.7	NUM
ijassa-1367	285	2	.	.	PUNCT
ijassa-1367	285	3	homicidal	homicidal	ADJ
ijassa-1367	285	4	chauffeur	chauffeur	NOUN
ijassa-1367	285	5	game	game	NOUN
ijassa-1367	285	6	.	.	PUNCT
ijassa-1367	286	1	evader	evader	NOUN
ijassa-1367	286	2	e	e	PROPN
ijassa-1367	286	3	is	be	AUX
ijassa-1367	286	4	catching	catch	VERB
ijassa-1367	286	5	the	the	DET
ijassa-1367	286	6	tail	tail	NOUN
ijassa-1367	286	7	of	of	ADP
ijassa-1367	286	8	p	p	DET
ijassa-1367	286	9	fig	fig	NOUN
ijassa-1367	286	10	.	.	PUNCT
ijassa-1367	287	1	5.8	5.8	NUM
ijassa-1367	287	2	.	.	PUNCT
ijassa-1367	288	1	two	two	NUM
ijassa-1367	288	2	parties	party	NOUN
ijassa-1367	288	3	of	of	ADP
ijassa-1367	288	4	the	the	DET
ijassa-1367	288	5	game	game	NOUN
ijassa-1367	288	6	of	of	ADP
ijassa-1367	288	7	two	two	NUM
ijassa-1367	288	8	cars	car	NOUN
ijassa-1367	288	9	the	the	DET
ijassa-1367	288	10	state	state	NOUN
ijassa-1367	288	11	space	space	NOUN
ijassa-1367	288	12	is	be	AUX
ijassa-1367	288	13	three	three	NUM
ijassa-1367	288	14	-	-	PUNCT
ijassa-1367	288	15	dimensional	dimensional	ADJ
ijassa-1367	288	16	.	.	PUNCT
ijassa-1367	289	1	the	the	DET
ijassa-1367	289	2	coordinates	coordinate	NOUN
ijassa-1367	289	3	are	be	AUX
ijassa-1367	289	4	completely	completely	ADV
ijassa-1367	289	5	determined	determine	VERB
ijassa-1367	289	6	by	by	ADP
ijassa-1367	289	7	distances	distance	NOUN
ijassa-1367	289	8	between	between	ADP
ijassa-1367	289	9	players	player	NOUN
ijassa-1367	289	10	and	and	CCONJ
ijassa-1367	289	11	angles	angle	NOUN
ijassa-1367	289	12	between	between	ADP
ijassa-1367	289	13	the	the	DET
ijassa-1367	289	14	sight	sight	NOUN
ijassa-1367	289	15	line	line	NOUN
ijassa-1367	289	16	pe	pe	PROPN
ijassa-1367	289	17	and	and	CCONJ
ijassa-1367	289	18	the	the	DET
ijassa-1367	289	19	velocities	velocity	NOUN
ijassa-1367	289	20	of	of	ADP
ijassa-1367	289	21	players	player	NOUN
ijassa-1367	289	22	.	.	PUNCT
ijassa-1367	290	1	optimal	optimal	ADJ
ijassa-1367	290	2	behaviours	behaviour	NOUN
ijassa-1367	290	3	of	of	ADP
ijassa-1367	290	4	players	player	NOUN
ijassa-1367	290	5	found	find	VERB
ijassa-1367	290	6	by	by	ADP
ijassa-1367	290	7	the	the	DET
ijassa-1367	290	8	program	program	NOUN
ijassa-1367	290	9	in	in	ADP
ijassa-1367	290	10	two	two	NUM
ijassa-1367	290	11	parties	party	NOUN
ijassa-1367	290	12	are	be	AUX
ijassa-1367	290	13	shown	show	VERB
ijassa-1367	290	14	in	in	ADP
ijassa-1367	290	15	figure	figure	NOUN
ijassa-1367	290	16	5.8	5.8	NUM
ijassa-1367	290	17	.	.	PUNCT
ijassa-1367	291	1	limitations	limitation	NOUN
ijassa-1367	291	2	of	of	ADP
ijassa-1367	291	3	turning	turn	VERB
ijassa-1367	291	4	radii	radius	NOUN
ijassa-1367	291	5	are	be	AUX
ijassa-1367	291	6	the	the	DET
ijassa-1367	291	7	same	same	ADJ
ijassa-1367	291	8	for	for	ADP
ijassa-1367	291	9	both	both	DET
ijassa-1367	291	10	players	player	NOUN
ijassa-1367	291	11	.	.	PUNCT
ijassa-1367	292	1	in	in	ADP
ijassa-1367	292	2	the	the	DET
ijassa-1367	292	3	first	first	ADJ
ijassa-1367	292	4	party	party	NOUN
ijassa-1367	292	5	,	,	PUNCT
ijassa-1367	292	6	the	the	DET
ijassa-1367	292	7	motion	motion	NOUN
ijassa-1367	292	8	is	be	AUX
ijassa-1367	292	9	to	to	ADP
ijassa-1367	292	10	copyright	copyright	NOUN
ijassa-1367	292	11	©	©	PROPN
ijassa-1367	292	12	2023	2023	NUM
ijassa-1367	292	13	assa	assa	NOUN
ijassa-1367	292	14	.	.	PUNCT
ijassa-1367	293	1	adv	adv	PROPN
ijassa-1367	293	2	syst	syst	PROPN
ijassa-1367	293	3	sci	sci	PROPN
ijassa-1367	293	4	appl	appl	PROPN
ijassa-1367	293	5	(	(	PUNCT
ijassa-1367	293	6	2023	2023	NUM
ijassa-1367	293	7	)	)	PUNCT
ijassa-1367	293	8	piecewise	piecewise	NOUN
ijassa-1367	293	9	constant	constant	ADJ
ijassa-1367	293	10	functions	function	NOUN
ijassa-1367	293	11	in	in	ADP
ijassa-1367	293	12	dynamic	dynamic	ADJ
ijassa-1367	293	13	optimization	optimization	NOUN
ijassa-1367	293	14	problems	problem	NOUN
ijassa-1367	293	15	47	47	NUM
ijassa-1367	293	16	fig	fig	NOUN
ijassa-1367	293	17	.	.	PUNCT
ijassa-1367	294	1	6.9	6.9	NUM
ijassa-1367	294	2	.	.	PUNCT
ijassa-1367	294	3	inverted	invert	VERB
ijassa-1367	294	4	pendulum	pendulum	NOUN
ijassa-1367	294	5	on	on	ADP
ijassa-1367	294	6	the	the	DET
ijassa-1367	294	7	cart	cart	NOUN
ijassa-1367	294	8	some	some	DET
ijassa-1367	294	9	extent	extent	NOUN
ijassa-1367	294	10	toward	toward	ADP
ijassa-1367	294	11	each	each	DET
ijassa-1367	294	12	other	other	ADJ
ijassa-1367	294	13	.	.	PUNCT
ijassa-1367	295	1	in	in	ADP
ijassa-1367	295	2	the	the	DET
ijassa-1367	295	3	second	second	ADJ
ijassa-1367	295	4	game	game	NOUN
ijassa-1367	295	5	,	,	PUNCT
ijassa-1367	295	6	player	player	NOUN
ijassa-1367	295	7	e	e	PROPN
ijassa-1367	295	8	appeared	appear	VERB
ijassa-1367	295	9	in	in	ADP
ijassa-1367	295	10	the	the	DET
ijassa-1367	295	11	back	back	NOUN
ijassa-1367	295	12	of	of	ADP
ijassa-1367	295	13	p	p	NOUN
ijassa-1367	295	14	and	and	CCONJ
ijassa-1367	295	15	caught	catch	VERB
ijassa-1367	295	16	his	his	PRON
ijassa-1367	295	17	tail	tail	NOUN
ijassa-1367	295	18	,	,	PUNCT
ijassa-1367	295	19	but	but	CCONJ
ijassa-1367	295	20	then	then	ADV
ijassa-1367	295	21	he	he	PRON
ijassa-1367	295	22	had	have	VERB
ijassa-1367	295	23	to	to	PART
ijassa-1367	295	24	change	change	VERB
ijassa-1367	295	25	direction	direction	NOUN
ijassa-1367	295	26	.	.	PUNCT
ijassa-1367	296	1	in	in	ADP
ijassa-1367	296	2	all	all	DET
ijassa-1367	296	3	three	three	NUM
ijassa-1367	296	4	parties	party	NOUN
ijassa-1367	296	5	,	,	PUNCT
ijassa-1367	296	6	the	the	DET
ijassa-1367	296	7	program	program	NOUN
ijassa-1367	296	8	involves	involve	VERB
ijassa-1367	296	9	two	two	NUM
ijassa-1367	296	10	steps	step	NOUN
ijassa-1367	296	11	.	.	PUNCT
ijassa-1367	297	1	at	at	ADP
ijassa-1367	297	2	the	the	DET
ijassa-1367	297	3	first	first	ADJ
ijassa-1367	297	4	step	step	NOUN
ijassa-1367	297	5	(	(	PUNCT
ijassa-1367	297	6	imitation	imitation	NOUN
ijassa-1367	297	7	modelling	modelling	NOUN
ijassa-1367	297	8	)	)	PUNCT
ijassa-1367	297	9	,	,	PUNCT
ijassa-1367	297	10	for	for	ADP
ijassa-1367	297	11	one	one	NUM
ijassa-1367	297	12	-	-	PUNCT
ijassa-1367	297	13	step	step	NOUN
ijassa-1367	297	14	scenarios	scenario	NOUN
ijassa-1367	297	15	we	we	PRON
ijassa-1367	297	16	used	use	VERB
ijassa-1367	297	17	monte	monte	PROPN
ijassa-1367	297	18	–	–	PUNCT
ijassa-1367	297	19	carlo	carlo	NOUN
ijassa-1367	297	20	method	method	NOUN
ijassa-1367	297	21	,	,	PUNCT
ijassa-1367	297	22	whereas	whereas	SCONJ
ijassa-1367	297	23	at	at	ADP
ijassa-1367	297	24	the	the	DET
ijassa-1367	297	25	second	second	ADJ
ijassa-1367	297	26	step	step	NOUN
ijassa-1367	297	27	testing	testing	NOUN
ijassa-1367	297	28	was	be	AUX
ijassa-1367	297	29	conducted	conduct	VERB
ijassa-1367	297	30	.	.	PUNCT
ijassa-1367	298	1	each	each	DET
ijassa-1367	298	2	player	player	NOUN
ijassa-1367	298	3	did	do	AUX
ijassa-1367	298	4	n’t	not	PART
ijassa-1367	298	5	know	know	VERB
ijassa-1367	298	6	actual	actual	ADJ
ijassa-1367	298	7	strategy	strategy	NOUN
ijassa-1367	298	8	of	of	ADP
ijassa-1367	298	9	the	the	DET
ijassa-1367	298	10	other	other	ADJ
ijassa-1367	298	11	and	and	CCONJ
ijassa-1367	298	12	produced	produce	VERB
ijassa-1367	298	13	its	its	PRON
ijassa-1367	298	14	own	own	ADJ
ijassa-1367	298	15	payoff	payoff	NOUN
ijassa-1367	298	16	.	.	PUNCT
ijassa-1367	299	1	it	it	PRON
ijassa-1367	299	2	was	be	AUX
ijassa-1367	299	3	a	a	DET
ijassa-1367	299	4	payoff	payoff	NOUN
ijassa-1367	299	5	when	when	SCONJ
ijassa-1367	299	6	both	both	DET
ijassa-1367	299	7	players	player	NOUN
ijassa-1367	299	8	act	act	VERB
ijassa-1367	299	9	optimally	optimally	ADV
ijassa-1367	299	10	.	.	PUNCT
ijassa-1367	300	1	at	at	ADP
ijassa-1367	300	2	the	the	DET
ijassa-1367	300	3	initial	initial	ADJ
ijassa-1367	300	4	instant	instant	NOUN
ijassa-1367	300	5	,	,	PUNCT
ijassa-1367	300	6	player	player	NOUN
ijassa-1367	300	7	p	p	PROPN
ijassa-1367	300	8	took	take	VERB
ijassa-1367	300	9	the	the	DET
ijassa-1367	300	10	payoff	payoff	NOUN
ijassa-1367	300	11	to	to	PART
ijassa-1367	300	12	be	be	AUX
ijassa-1367	300	13	identical	identical	ADJ
ijassa-1367	300	14	zero	zero	NUM
ijassa-1367	300	15	,	,	PUNCT
ijassa-1367	300	16	whereas	whereas	SCONJ
ijassa-1367	300	17	for	for	ADP
ijassa-1367	300	18	player	player	NOUN
ijassa-1367	300	19	e	e	NOUN
ijassa-1367	300	20	the	the	DET
ijassa-1367	300	21	payoff	payoff	NOUN
ijassa-1367	300	22	was	be	AUX
ijassa-1367	300	23	infinite	infinite	ADJ
ijassa-1367	300	24	.	.	PUNCT
ijassa-1367	301	1	in	in	ADP
ijassa-1367	301	2	what	what	PRON
ijassa-1367	301	3	follows	follow	VERB
ijassa-1367	301	4	,	,	PUNCT
ijassa-1367	301	5	the	the	DET
ijassa-1367	301	6	payoff	payoff	NOUN
ijassa-1367	301	7	for	for	ADP
ijassa-1367	301	8	p	p	PROPN
ijassa-1367	301	9	was	be	AUX
ijassa-1367	301	10	increasing	increase	VERB
ijassa-1367	301	11	,	,	PUNCT
ijassa-1367	301	12	and	and	CCONJ
ijassa-1367	301	13	for	for	ADP
ijassa-1367	301	14	e	e	NOUN
ijassa-1367	301	15	it	it	PRON
ijassa-1367	301	16	was	be	AUX
ijassa-1367	301	17	decreasing	decrease	VERB
ijassa-1367	301	18	.	.	PUNCT
ijassa-1367	302	1	as	as	SCONJ
ijassa-1367	302	2	the	the	DET
ijassa-1367	302	3	self	self	NOUN
ijassa-1367	302	4	-	-	PUNCT
ijassa-1367	302	5	learning	learning	NOUN
ijassa-1367	302	6	progressed	progress	VERB
ijassa-1367	302	7	,	,	PUNCT
ijassa-1367	302	8	pursuer	pursuer	NOUN
ijassa-1367	302	9	p	p	NOUN
ijassa-1367	302	10	was	be	AUX
ijassa-1367	302	11	working	work	VERB
ijassa-1367	302	12	out	out	ADP
ijassa-1367	302	13	his	his	PRON
ijassa-1367	302	14	own	own	ADJ
ijassa-1367	302	15	strategy	strategy	NOUN
ijassa-1367	302	16	by	by	ADP
ijassa-1367	302	17	minimax	minimax	NOUN
ijassa-1367	302	18	principle	principle	NOUN
ijassa-1367	302	19	,	,	PUNCT
ijassa-1367	302	20	whereas	whereas	SCONJ
ijassa-1367	302	21	evader	evader	NOUN
ijassa-1367	302	22	e	e	NOUN
ijassa-1367	302	23	—	—	PUNCT
ijassa-1367	302	24	by	by	ADP
ijassa-1367	302	25	maximin	maximin	NOUN
ijassa-1367	302	26	one	one	NUM
ijassa-1367	302	27	.	.	PUNCT
ijassa-1367	303	1	6	6	NUM
ijassa-1367	303	2	.	.	X
ijassa-1367	303	3	optimization	optimization	NOUN
ijassa-1367	303	4	in	in	ADP
ijassa-1367	303	5	lack	lack	NOUN
ijassa-1367	303	6	of	of	ADP
ijassa-1367	303	7	information	information	NOUN
ijassa-1367	303	8	dynamic	dynamic	ADJ
ijassa-1367	303	9	optimization	optimization	NOUN
ijassa-1367	303	10	problems	problem	NOUN
ijassa-1367	303	11	are	be	AUX
ijassa-1367	303	12	not	not	PART
ijassa-1367	303	13	limited	limit	VERB
ijassa-1367	303	14	to	to	ADP
ijassa-1367	303	15	optimal	optimal	ADJ
ijassa-1367	303	16	control	control	NOUN
ijassa-1367	303	17	models	model	NOUN
ijassa-1367	303	18	when	when	SCONJ
ijassa-1367	303	19	decisions	decision	NOUN
ijassa-1367	303	20	are	be	AUX
ijassa-1367	303	21	made	make	VERB
ijassa-1367	303	22	in	in	ADP
ijassa-1367	303	23	conditions	condition	NOUN
ijassa-1367	303	24	of	of	ADP
ijassa-1367	303	25	complete	complete	ADJ
ijassa-1367	303	26	information	information	NOUN
ijassa-1367	303	27	,	,	PUNCT
ijassa-1367	303	28	or	or	CCONJ
ijassa-1367	303	29	dynamic	dynamic	ADJ
ijassa-1367	303	30	games	game	NOUN
ijassa-1367	303	31	when	when	SCONJ
ijassa-1367	303	32	we	we	PRON
ijassa-1367	303	33	have	have	VERB
ijassa-1367	303	34	no	no	DET
ijassa-1367	303	35	information	information	NOUN
ijassa-1367	303	36	about	about	ADP
ijassa-1367	303	37	the	the	DET
ijassa-1367	303	38	behavior	behavior	NOUN
ijassa-1367	303	39	of	of	ADP
ijassa-1367	303	40	the	the	DET
ijassa-1367	303	41	opponent	opponent	NOUN
ijassa-1367	303	42	.	.	PUNCT
ijassa-1367	304	1	some	some	DET
ijassa-1367	304	2	other	other	ADJ
ijassa-1367	304	3	kinds	kind	NOUN
ijassa-1367	304	4	of	of	ADP
ijassa-1367	304	5	lack	lack	NOUN
ijassa-1367	304	6	of	of	ADP
ijassa-1367	304	7	information	information	NOUN
ijassa-1367	304	8	are	be	AUX
ijassa-1367	304	9	possible	possible	ADJ
ijassa-1367	304	10	.	.	PUNCT
ijassa-1367	305	1	for	for	ADP
ijassa-1367	305	2	example	example	NOUN
ijassa-1367	305	3	,	,	PUNCT
ijassa-1367	305	4	the	the	DET
ijassa-1367	305	5	behavior	behavior	NOUN
ijassa-1367	305	6	of	of	ADP
ijassa-1367	305	7	the	the	DET
ijassa-1367	305	8	environment	environment	NOUN
ijassa-1367	305	9	could	could	AUX
ijassa-1367	305	10	be	be	AUX
ijassa-1367	305	11	described	describe	VERB
ijassa-1367	305	12	by	by	ADP
ijassa-1367	305	13	random	random	ADJ
ijassa-1367	305	14	laws	law	NOUN
ijassa-1367	305	15	.	.	PUNCT
ijassa-1367	306	1	we	we	PRON
ijassa-1367	306	2	will	will	AUX
ijassa-1367	306	3	focus	focus	VERB
ijassa-1367	306	4	on	on	ADP
ijassa-1367	306	5	a	a	DET
ijassa-1367	306	6	model	model	NOUN
ijassa-1367	306	7	,	,	PUNCT
ijassa-1367	306	8	in	in	ADP
ijassa-1367	306	9	which	which	PRON
ijassa-1367	306	10	the	the	DET
ijassa-1367	306	11	control	control	NOUN
ijassa-1367	306	12	block	block	NOUN
ijassa-1367	306	13	has	have	VERB
ijassa-1367	306	14	no	no	DET
ijassa-1367	306	15	information	information	NOUN
ijassa-1367	306	16	about	about	ADP
ijassa-1367	306	17	kinematic	kinematic	ADJ
ijassa-1367	306	18	equations	equation	NOUN
ijassa-1367	306	19	of	of	ADP
ijassa-1367	306	20	an	an	DET
ijassa-1367	306	21	object	object	NOUN
ijassa-1367	306	22	.	.	PUNCT
ijassa-1367	307	1	this	this	PRON
ijassa-1367	307	2	is	be	AUX
ijassa-1367	307	3	the	the	DET
ijassa-1367	307	4	case	case	NOUN
ijassa-1367	307	5	for	for	ADP
ijassa-1367	307	6	the	the	DET
ijassa-1367	307	7	biological	biological	ADJ
ijassa-1367	307	8	systems	system	NOUN
ijassa-1367	307	9	.	.	PUNCT
ijassa-1367	308	1	consider	consider	VERB
ijassa-1367	308	2	a	a	DET
ijassa-1367	308	3	well	well	ADV
ijassa-1367	308	4	-	-	PUNCT
ijassa-1367	308	5	known	know	VERB
ijassa-1367	308	6	example	example	NOUN
ijassa-1367	308	7	of	of	ADP
ijassa-1367	308	8	holding	hold	VERB
ijassa-1367	308	9	a	a	DET
ijassa-1367	308	10	pole	pole	NOUN
ijassa-1367	308	11	in	in	ADP
ijassa-1367	308	12	an	an	DET
ijassa-1367	308	13	unstable	unstable	ADJ
ijassa-1367	308	14	vertical	vertical	ADJ
ijassa-1367	308	15	equilibrium	equilibrium	NOUN
ijassa-1367	309	1	[	[	X
ijassa-1367	309	2	6	6	NUM
ijassa-1367	309	3	]	]	PUNCT
ijassa-1367	309	4	,	,	PUNCT
ijassa-1367	309	5	[	[	X
ijassa-1367	309	6	8	8	NUM
ijassa-1367	309	7	]	]	PUNCT
ijassa-1367	309	8	.	.	PUNCT
ijassa-1367	310	1	6.1	6.1	NUM
ijassa-1367	310	2	.	.	PUNCT
ijassa-1367	310	3	problem	problem	NOUN
ijassa-1367	310	4	on	on	ADP
ijassa-1367	310	5	plane	plane	NOUN
ijassa-1367	310	6	inverted	invert	VERB
ijassa-1367	310	7	pendulum	pendulum	NOUN
ijassa-1367	310	8	the	the	DET
ijassa-1367	310	9	system	system	NOUN
ijassa-1367	310	10	in	in	ADP
ijassa-1367	310	11	this	this	DET
ijassa-1367	310	12	example	example	NOUN
ijassa-1367	310	13	consists	consist	VERB
ijassa-1367	310	14	of	of	ADP
ijassa-1367	310	15	an	an	DET
ijassa-1367	310	16	inverted	inverted	ADJ
ijassa-1367	310	17	pendulum	pendulum	NOUN
ijassa-1367	310	18	mounted	mount	VERB
ijassa-1367	310	19	to	to	ADP
ijassa-1367	310	20	a	a	DET
ijassa-1367	310	21	motorized	motorized	ADJ
ijassa-1367	310	22	cart	cart	NOUN
ijassa-1367	310	23	.	.	PUNCT
ijassa-1367	311	1	the	the	DET
ijassa-1367	311	2	pendulum	pendulum	NOUN
ijassa-1367	311	3	will	will	AUX
ijassa-1367	311	4	simply	simply	ADV
ijassa-1367	311	5	fall	fall	VERB
ijassa-1367	311	6	over	over	ADP
ijassa-1367	311	7	if	if	SCONJ
ijassa-1367	311	8	the	the	DET
ijassa-1367	311	9	cart	cart	NOUN
ijassa-1367	311	10	is	be	AUX
ijassa-1367	311	11	n’t	not	PART
ijassa-1367	311	12	moved	move	VERB
ijassa-1367	311	13	to	to	PART
ijassa-1367	311	14	balance	balance	VERB
ijassa-1367	311	15	it	it	PRON
ijassa-1367	311	16	.	.	PUNCT
ijassa-1367	312	1	the	the	DET
ijassa-1367	312	2	objective	objective	NOUN
ijassa-1367	312	3	of	of	ADP
ijassa-1367	312	4	the	the	DET
ijassa-1367	312	5	control	control	NOUN
ijassa-1367	312	6	system	system	NOUN
ijassa-1367	312	7	is	be	AUX
ijassa-1367	312	8	to	to	PART
ijassa-1367	312	9	balance	balance	VERB
ijassa-1367	312	10	the	the	DET
ijassa-1367	312	11	inverted	inverted	ADJ
ijassa-1367	312	12	pendulum	pendulum	NOUN
ijassa-1367	312	13	by	by	ADP
ijassa-1367	312	14	applying	apply	VERB
ijassa-1367	312	15	a	a	DET
ijassa-1367	312	16	force	force	NOUN
ijassa-1367	312	17	to	to	ADP
ijassa-1367	312	18	the	the	DET
ijassa-1367	312	19	cart	cart	NOUN
ijassa-1367	312	20	that	that	PRON
ijassa-1367	312	21	the	the	DET
ijassa-1367	312	22	pendulum	pendulum	NOUN
ijassa-1367	312	23	is	be	AUX
ijassa-1367	312	24	attached	attach	VERB
ijassa-1367	312	25	to	to	ADP
ijassa-1367	312	26	.	.	PUNCT
ijassa-1367	313	1	one	one	PRON
ijassa-1367	313	2	wants	want	VERB
ijassa-1367	313	3	to	to	PART
ijassa-1367	313	4	maximize	maximize	VERB
ijassa-1367	313	5	the	the	DET
ijassa-1367	313	6	time	time	NOUN
ijassa-1367	313	7	during	during	ADP
ijassa-1367	313	8	which	which	PRON
ijassa-1367	313	9	the	the	DET
ijassa-1367	313	10	pendulum	pendulum	NOUN
ijassa-1367	313	11	is	be	AUX
ijassa-1367	313	12	balanced	balance	VERB
ijassa-1367	313	13	.	.	PUNCT
ijassa-1367	314	1	regarding	regard	VERB
ijassa-1367	314	2	the	the	DET
ijassa-1367	314	3	cart	cart	NOUN
ijassa-1367	314	4	as	as	ADP
ijassa-1367	314	5	a	a	DET
ijassa-1367	314	6	massive	massive	ADJ
ijassa-1367	314	7	body	body	NOUN
ijassa-1367	314	8	,	,	PUNCT
ijassa-1367	314	9	we	we	PRON
ijassa-1367	314	10	get	get	VERB
ijassa-1367	314	11	the	the	DET
ijassa-1367	314	12	system	system	NOUN
ijassa-1367	314	13	of	of	ADP
ijassa-1367	314	14	lagrange	lagrange	PROPN
ijassa-1367	314	15	’s	’s	PART
ijassa-1367	314	16	equations	equation	NOUN
ijassa-1367	314	17	of	of	ADP
ijassa-1367	314	18	second	second	ADJ
ijassa-1367	314	19	kind	kind	NOUN
ijassa-1367	314	20	:	:	PUNCT
ijassa-1367	314	21	ẍ	ẍ	X
ijassa-1367	315	1	=	=	SYM
ijassa-1367	315	2	u	u	PROPN
ijassa-1367	315	3	,	,	PUNCT
ijassa-1367	315	4	l0θ̈	l0θ̈	PROPN
ijassa-1367	315	5	+	+	CCONJ
ijassa-1367	315	6	u	u	X
ijassa-1367	315	7	cos	cos	PROPN
ijassa-1367	315	8	θ	θ	PROPN
ijassa-1367	315	9	−	−	PROPN
ijassa-1367	315	10	g	g	PROPN
ijassa-1367	315	11	sin	sin	NOUN
ijassa-1367	315	12	θ	θ	NOUN
ijassa-1367	315	13	=	=	SYM
ijassa-1367	315	14	0	0	NUM
ijassa-1367	315	15	,	,	PUNCT
ijassa-1367	315	16	(	(	PUNCT
ijassa-1367	315	17	6.8	6.8	NUM
ijassa-1367	315	18	)	)	PUNCT
ijassa-1367	315	19	where	where	SCONJ
ijassa-1367	315	20	x	x	PRON
ijassa-1367	315	21	is	be	AUX
ijassa-1367	315	22	a	a	DET
ijassa-1367	315	23	cart	cart	NOUN
ijassa-1367	315	24	position	position	NOUN
ijassa-1367	315	25	coordinate	coordinate	NOUN
ijassa-1367	315	26	;	;	PUNCT
ijassa-1367	315	27	u	u	NOUN
ijassa-1367	315	28	is	be	AUX
ijassa-1367	315	29	an	an	DET
ijassa-1367	315	30	acceleration	acceleration	NOUN
ijassa-1367	315	31	of	of	ADP
ijassa-1367	315	32	the	the	DET
ijassa-1367	315	33	cart	cart	NOUN
ijassa-1367	315	34	,	,	PUNCT
ijassa-1367	315	35	which	which	PRON
ijassa-1367	315	36	is	be	AUX
ijassa-1367	315	37	a	a	DET
ijassa-1367	315	38	control	control	NOUN
ijassa-1367	315	39	;	;	PUNCT
ijassa-1367	315	40	θ	θ	PROPN
ijassa-1367	315	41	is	be	AUX
ijassa-1367	315	42	a	a	DET
ijassa-1367	315	43	pendulum	pendulum	NOUN
ijassa-1367	315	44	angle	angle	NOUN
ijassa-1367	315	45	from	from	ADP
ijassa-1367	315	46	vertical	vertical	ADJ
ijassa-1367	315	47	oy	oy	PROPN
ijassa-1367	315	48	;	;	PUNCT
ijassa-1367	315	49	l0	l0	PROPN
ijassa-1367	315	50	is	be	AUX
ijassa-1367	315	51	a	a	DET
ijassa-1367	315	52	reduced	reduce	VERB
ijassa-1367	315	53	length	length	NOUN
ijassa-1367	315	54	to	to	ADP
ijassa-1367	315	55	pendulum	pendulum	NOUN
ijassa-1367	315	56	center	center	NOUN
ijassa-1367	315	57	of	of	ADP
ijassa-1367	315	58	mass	mass	PROPN
ijassa-1367	315	59	;	;	PUNCT
ijassa-1367	315	60	g	g	PROPN
ijassa-1367	315	61	is	be	AUX
ijassa-1367	315	62	the	the	DET
ijassa-1367	315	63	acceleration	acceleration	NOUN
ijassa-1367	315	64	of	of	ADP
ijassa-1367	315	65	gravity	gravity	NOUN
ijassa-1367	315	66	.	.	PUNCT
ijassa-1367	316	1	in	in	ADP
ijassa-1367	316	2	frames	frame	NOUN
ijassa-1367	316	3	of	of	ADP
ijassa-1367	316	4	numerical	numerical	ADJ
ijassa-1367	316	5	experiments	experiment	NOUN
ijassa-1367	316	6	,	,	PUNCT
ijassa-1367	316	7	we	we	PRON
ijassa-1367	316	8	choose	choose	VERB
ijassa-1367	316	9	the	the	DET
ijassa-1367	316	10	following	follow	VERB
ijassa-1367	316	11	values	value	NOUN
ijassa-1367	316	12	of	of	ADP
ijassa-1367	316	13	parameters	parameter	NOUN
ijassa-1367	316	14	and	and	CCONJ
ijassa-1367	316	15	ranges	range	NOUN
ijassa-1367	316	16	of	of	ADP
ijassa-1367	316	17	phase	phase	NOUN
ijassa-1367	316	18	coordinates	coordinate	NOUN
ijassa-1367	316	19	:	:	PUNCT
ijassa-1367	316	20	g	g	NOUN
ijassa-1367	316	21	=	=	SYM
ijassa-1367	316	22	980	980	NUM
ijassa-1367	316	23	cm	cm	NOUN
ijassa-1367	316	24	/	/	SYM
ijassa-1367	316	25	s2	s2	PROPN
ijassa-1367	316	26	,	,	PUNCT
ijassa-1367	316	27	u	u	NOUN
ijassa-1367	316	28	=	=	NOUN
ijassa-1367	316	29	±1000	±1000	PROPN
ijassa-1367	316	30	cm	cm	NOUN
ijassa-1367	316	31	/	/	SYM
ijassa-1367	316	32	s2	s2	PROPN
ijassa-1367	316	33	,	,	PUNCT
ijassa-1367	316	34	l0	l0	NOUN
ijassa-1367	316	35	=	=	NOUN
ijassa-1367	316	36	100	100	NUM
ijassa-1367	316	37	cm	cm	NOUN
ijassa-1367	316	38	,	,	PUNCT
ijassa-1367	317	1	|θ|	|θ|	PROPN
ijassa-1367	317	2	≤	≤	NOUN
ijassa-1367	317	3	0.2	0.2	NUM
ijassa-1367	317	4	rad	rad	NOUN
ijassa-1367	317	5	.	.	PROPN
ijassa-1367	317	6	,	,	PUNCT
ijassa-1367	317	7	|x|	|x|	PROPN
ijassa-1367	317	8	≤	≤	ADV
ijassa-1367	317	9	240	240	NUM
ijassa-1367	317	10	cm	cm	NOUN
ijassa-1367	317	11	,	,	PUNCT
ijassa-1367	317	12	∆τ	∆τ	PROPN
ijassa-1367	317	13	=	=	PROPN
ijassa-1367	317	14	0.02	0.02	NUM
ijassa-1367	317	15	s.	s.	PROPN
ijassa-1367	317	16	the	the	DET
ijassa-1367	317	17	state	state	NOUN
ijassa-1367	317	18	space	space	NOUN
ijassa-1367	317	19	is	be	AUX
ijassa-1367	317	20	four	four	NUM
ijassa-1367	317	21	-	-	PUNCT
ijassa-1367	317	22	dimensional	dimensional	ADJ
ijassa-1367	317	23	,	,	PUNCT
ijassa-1367	317	24	the	the	DET
ijassa-1367	317	25	state	state	NOUN
ijassa-1367	317	26	coordinates	coordinate	NOUN
ijassa-1367	317	27	are	be	AUX
ijassa-1367	317	28	position	position	NOUN
ijassa-1367	317	29	(	(	PUNCT
ijassa-1367	317	30	x	x	NOUN
ijassa-1367	317	31	)	)	PUNCT
ijassa-1367	317	32	and	and	CCONJ
ijassa-1367	317	33	velocity	velocity	NOUN
ijassa-1367	317	34	(	(	PUNCT
ijassa-1367	317	35	ẋ	ẋ	PROPN
ijassa-1367	317	36	)	)	PUNCT
ijassa-1367	317	37	of	of	ADP
ijassa-1367	317	38	the	the	DET
ijassa-1367	317	39	cart	cart	NOUN
ijassa-1367	317	40	,	,	PUNCT
ijassa-1367	317	41	pendulum	pendulum	NOUN
ijassa-1367	317	42	angle	angle	VERB
ijassa-1367	317	43	from	from	ADP
ijassa-1367	317	44	vertical	vertical	ADJ
ijassa-1367	317	45	(	(	PUNCT
ijassa-1367	317	46	θ	θ	NOUN
ijassa-1367	317	47	)	)	PUNCT
ijassa-1367	317	48	and	and	CCONJ
ijassa-1367	317	49	its	its	PRON
ijassa-1367	317	50	angular	angular	ADJ
ijassa-1367	317	51	velocity	velocity	NOUN
ijassa-1367	317	52	(	(	PUNCT
ijassa-1367	317	53	θ̇	θ̇	NOUN
ijassa-1367	317	54	)	)	PUNCT
ijassa-1367	317	55	.	.	PUNCT
ijassa-1367	318	1	following	follow	VERB
ijassa-1367	318	2	copyright	copyright	NOUN
ijassa-1367	318	3	©	©	PROPN
ijassa-1367	318	4	2023	2023	NUM
ijassa-1367	318	5	assa	assa	NOUN
ijassa-1367	318	6	.	.	PUNCT
ijassa-1367	319	1	adv	adv	PROPN
ijassa-1367	319	2	syst	syst	PROPN
ijassa-1367	319	3	sci	sci	PROPN
ijassa-1367	319	4	appl	appl	PROPN
ijassa-1367	319	5	(	(	PUNCT
ijassa-1367	319	6	2023	2023	NUM
ijassa-1367	319	7	)	)	PUNCT
ijassa-1367	319	8	48	48	NUM
ijassa-1367	319	9	o.	o.	PROPN
ijassa-1367	319	10	e.	e.	PROPN
ijassa-1367	319	11	orel	orel	PROPN
ijassa-1367	319	12	,	,	PUNCT
ijassa-1367	319	13	e.	e.	PROPN
ijassa-1367	319	14	n.	n.	PROPN
ijassa-1367	319	15	orel	orel	PROPN
ijassa-1367	320	1	michie	michie	PROPN
ijassa-1367	321	1	[	[	X
ijassa-1367	321	2	6	6	NUM
ijassa-1367	321	3	]	]	PUNCT
ijassa-1367	321	4	,	,	PUNCT
ijassa-1367	321	5	we	we	PRON
ijassa-1367	321	6	divide	divide	VERB
ijassa-1367	321	7	the	the	DET
ijassa-1367	321	8	state	state	NOUN
ijassa-1367	321	9	space	space	NOUN
ijassa-1367	321	10	into	into	ADP
ijassa-1367	321	11	162	162	NUM
ijassa-1367	321	12	classes	class	NOUN
ijassa-1367	321	13	according	accord	VERB
ijassa-1367	321	14	to	to	ADP
ijassa-1367	321	15	threshold	threshold	NOUN
ijassa-1367	321	16	values	value	NOUN
ijassa-1367	321	17	:	:	PUNCT
ijassa-1367	321	18	in	in	ADP
ijassa-1367	321	19	angle	angle	NOUN
ijassa-1367	321	20	±0.1	±0.1	PROPN
ijassa-1367	321	21	;	;	PUNCT
ijassa-1367	321	22	±0.017	±0.017	X
ijassa-1367	321	23	;	;	PUNCT
ijassa-1367	321	24	0	0	NUM
ijassa-1367	321	25	,	,	PUNCT
ijassa-1367	321	26	in	in	ADP
ijassa-1367	321	27	angular	angular	ADJ
ijassa-1367	321	28	velocity	velocity	NOUN
ijassa-1367	321	29	±0.87	±0.87	PROPN
ijassa-1367	321	30	;	;	PUNCT
ijassa-1367	321	31	in	in	ADP
ijassa-1367	321	32	position	position	NOUN
ijassa-1367	321	33	of	of	ADP
ijassa-1367	321	34	the	the	DET
ijassa-1367	321	35	cart	cart	NOUN
ijassa-1367	321	36	±80	±80	PROPN
ijassa-1367	321	37	,	,	PUNCT
ijassa-1367	321	38	in	in	ADP
ijassa-1367	321	39	the	the	DET
ijassa-1367	321	40	velocity	velocity	NOUN
ijassa-1367	321	41	of	of	ADP
ijassa-1367	321	42	the	the	DET
ijassa-1367	321	43	cart	cart	NOUN
ijassa-1367	321	44	±50	±50	NOUN
ijassa-1367	321	45	.	.	PUNCT
ijassa-1367	322	1	at	at	ADP
ijassa-1367	322	2	each	each	DET
ijassa-1367	322	3	instant	instant	NOUN
ijassa-1367	322	4	of	of	ADP
ijassa-1367	322	5	processing	processing	NOUN
ijassa-1367	322	6	,	,	PUNCT
ijassa-1367	322	7	the	the	DET
ijassa-1367	322	8	control	control	NOUN
ijassa-1367	322	9	block	block	NOUN
ijassa-1367	322	10	knows	know	VERB
ijassa-1367	322	11	only	only	ADV
ijassa-1367	322	12	the	the	DET
ijassa-1367	322	13	ordinal	ordinal	ADJ
ijassa-1367	322	14	number	number	NOUN
ijassa-1367	322	15	of	of	ADP
ijassa-1367	322	16	class	class	NOUN
ijassa-1367	322	17	,	,	PUNCT
ijassa-1367	322	18	in	in	ADP
ijassa-1367	322	19	which	which	PRON
ijassa-1367	322	20	the	the	DET
ijassa-1367	322	21	object	object	NOUN
ijassa-1367	322	22	is	be	AUX
ijassa-1367	322	23	located	locate	VERB
ijassa-1367	322	24	.	.	PUNCT
ijassa-1367	323	1	on	on	ADP
ijassa-1367	323	2	the	the	DET
ijassa-1367	323	3	basis	basis	NOUN
ijassa-1367	323	4	of	of	ADP
ijassa-1367	323	5	only	only	ADV
ijassa-1367	323	6	this	this	DET
ijassa-1367	323	7	consistent	consistent	ADJ
ijassa-1367	323	8	information	information	NOUN
ijassa-1367	323	9	,	,	PUNCT
ijassa-1367	323	10	the	the	DET
ijassa-1367	323	11	block	block	NOUN
ijassa-1367	323	12	must	must	AUX
ijassa-1367	323	13	make	make	VERB
ijassa-1367	323	14	a	a	DET
ijassa-1367	323	15	decision	decision	NOUN
ijassa-1367	323	16	:	:	PUNCT
ijassa-1367	323	17	u	u	NOUN
ijassa-1367	323	18	=	=	NOUN
ijassa-1367	323	19	1000	1000	NUM
ijassa-1367	323	20	or	or	CCONJ
ijassa-1367	323	21	u	u	NOUN
ijassa-1367	323	22	=	=	PROPN
ijassa-1367	323	23	−1000	−1000	PROPN
ijassa-1367	323	24	.	.	PUNCT
ijassa-1367	324	1	the	the	DET
ijassa-1367	324	2	cost	cost	NOUN
ijassa-1367	324	3	for	for	ADP
ijassa-1367	324	4	the	the	DET
ijassa-1367	324	5	lack	lack	NOUN
ijassa-1367	324	6	of	of	ADP
ijassa-1367	324	7	knowledge	knowledge	NOUN
ijassa-1367	324	8	of	of	ADP
ijassa-1367	324	9	dynamics	dynamic	NOUN
ijassa-1367	324	10	is	be	AUX
ijassa-1367	324	11	a	a	DET
ijassa-1367	324	12	doubling	doubling	NOUN
ijassa-1367	324	13	of	of	ADP
ijassa-1367	324	14	the	the	DET
ijassa-1367	324	15	random	random	ADJ
ijassa-1367	324	16	access	access	NOUN
ijassa-1367	324	17	memory	memory	NOUN
ijassa-1367	324	18	:	:	PUNCT
ijassa-1367	324	19	action	action	NOUN
ijassa-1367	324	20	now	now	ADV
ijassa-1367	324	21	depends	depend	VERB
ijassa-1367	324	22	not	not	PART
ijassa-1367	324	23	only	only	ADV
ijassa-1367	324	24	on	on	ADP
ijassa-1367	324	25	the	the	DET
ijassa-1367	324	26	state	state	NOUN
ijassa-1367	324	27	classes	class	NOUN
ijassa-1367	324	28	,	,	PUNCT
ijassa-1367	324	29	but	but	CCONJ
ijassa-1367	324	30	also	also	ADV
ijassa-1367	324	31	on	on	ADP
ijassa-1367	324	32	the	the	DET
ijassa-1367	324	33	control	control	NOUN
ijassa-1367	324	34	±1000	±1000	PROPN
ijassa-1367	324	35	.	.	PUNCT
ijassa-1367	325	1	the	the	DET
ijassa-1367	325	2	algorithms	algorithm	NOUN
ijassa-1367	325	3	of	of	ADP
ijassa-1367	325	4	decision	decision	NOUN
ijassa-1367	325	5	making	making	NOUN
ijassa-1367	325	6	and	and	CCONJ
ijassa-1367	325	7	self	self	NOUN
ijassa-1367	325	8	-	-	PUNCT
ijassa-1367	325	9	learning	learning	NOUN
ijassa-1367	325	10	could	could	AUX
ijassa-1367	325	11	be	be	AUX
ijassa-1367	325	12	different	different	ADJ
ijassa-1367	325	13	.	.	PUNCT
ijassa-1367	326	1	in	in	ADP
ijassa-1367	326	2	the	the	DET
ijassa-1367	326	3	michie	michie	PROPN
ijassa-1367	326	4	program	program	PROPN
ijassa-1367	326	5	,	,	PUNCT
ijassa-1367	326	6	self	self	NOUN
ijassa-1367	326	7	-	-	PUNCT
ijassa-1367	326	8	learning	learning	NOUN
ijassa-1367	326	9	is	be	AUX
ijassa-1367	326	10	based	base	VERB
ijassa-1367	326	11	on	on	ADP
ijassa-1367	326	12	the	the	DET
ijassa-1367	326	13	empiric	empiric	ADJ
ijassa-1367	326	14	approach	approach	NOUN
ijassa-1367	326	15	.	.	PUNCT
ijassa-1367	327	1	after	after	ADP
ijassa-1367	327	2	some	some	DET
ijassa-1367	327	3	learning	learning	NOUN
ijassa-1367	327	4	period	period	NOUN
ijassa-1367	327	5	,	,	PUNCT
ijassa-1367	327	6	the	the	DET
ijassa-1367	327	7	pendulum	pendulum	NOUN
ijassa-1367	327	8	eventually	eventually	ADV
ijassa-1367	327	9	fell	fall	VERB
ijassa-1367	327	10	down	down	ADP
ijassa-1367	327	11	though	though	SCONJ
ijassa-1367	327	12	it	it	PRON
ijassa-1367	327	13	has	have	AUX
ijassa-1367	327	14	been	be	AUX
ijassa-1367	327	15	balanced	balance	VERB
ijassa-1367	327	16	for	for	ADP
ijassa-1367	327	17	a	a	DET
ijassa-1367	327	18	long	long	ADJ
ijassa-1367	327	19	time	time	NOUN
ijassa-1367	327	20	.	.	PUNCT
ijassa-1367	328	1	the	the	DET
ijassa-1367	328	2	authors	author	NOUN
ijassa-1367	328	3	used	use	VERB
ijassa-1367	328	4	another	another	DET
ijassa-1367	328	5	program	program	NOUN
ijassa-1367	328	6	that	that	PRON
ijassa-1367	328	7	is	be	AUX
ijassa-1367	328	8	based	base	VERB
ijassa-1367	328	9	on	on	ADP
ijassa-1367	328	10	the	the	DET
ijassa-1367	328	11	idea	idea	NOUN
ijassa-1367	328	12	of	of	ADP
ijassa-1367	328	13	a	a	DET
ijassa-1367	328	14	priori	priori	ADJ
ijassa-1367	328	15	optimism	optimism	NOUN
ijassa-1367	328	16	and	and	CCONJ
ijassa-1367	328	17	the	the	DET
ijassa-1367	328	18	method	method	NOUN
ijassa-1367	328	19	of	of	ADP
ijassa-1367	328	20	forward	forward	ADJ
ijassa-1367	328	21	error	error	NOUN
ijassa-1367	328	22	correction	correction	NOUN
ijassa-1367	328	23	[	[	X
ijassa-1367	328	24	13	13	NUM
ijassa-1367	328	25	]	]	PUNCT
ijassa-1367	328	26	.	.	PUNCT
ijassa-1367	329	1	as	as	ADP
ijassa-1367	329	2	a	a	DET
ijassa-1367	329	3	result	result	NOUN
ijassa-1367	329	4	,	,	PUNCT
ijassa-1367	329	5	at	at	ADP
ijassa-1367	329	6	the	the	DET
ijassa-1367	329	7	end	end	NOUN
ijassa-1367	329	8	of	of	ADP
ijassa-1367	329	9	self	self	NOUN
ijassa-1367	329	10	-	-	PUNCT
ijassa-1367	329	11	learning	learning	NOUN
ijassa-1367	329	12	,	,	PUNCT
ijassa-1367	329	13	the	the	DET
ijassa-1367	329	14	pendulum	pendulum	NOUN
ijassa-1367	329	15	was	be	AUX
ijassa-1367	329	16	balanced	balance	VERB
ijassa-1367	329	17	about	about	ADP
ijassa-1367	329	18	vertical	vertical	ADJ
ijassa-1367	329	19	position	position	NOUN
ijassa-1367	329	20	forever	forever	ADV
ijassa-1367	329	21	.	.	PUNCT
ijassa-1367	330	1	7	7	X
ijassa-1367	330	2	.	.	X
ijassa-1367	330	3	conclusion	conclusion	VERB
ijassa-1367	330	4	direct	direct	ADJ
ijassa-1367	330	5	methods	method	NOUN
ijassa-1367	330	6	of	of	ADP
ijassa-1367	330	7	dynamic	dynamic	ADJ
ijassa-1367	330	8	optimization	optimization	NOUN
ijassa-1367	330	9	considered	consider	VERB
ijassa-1367	330	10	in	in	ADP
ijassa-1367	330	11	the	the	DET
ijassa-1367	330	12	paper	paper	NOUN
ijassa-1367	330	13	are	be	AUX
ijassa-1367	330	14	efficient	efficient	ADJ
ijassa-1367	330	15	in	in	ADP
ijassa-1367	330	16	the	the	DET
ijassa-1367	330	17	problem	problem	NOUN
ijassa-1367	330	18	on	on	ADP
ijassa-1367	330	19	global	global	ADJ
ijassa-1367	330	20	extremum	extremum	NOUN
ijassa-1367	330	21	rather	rather	ADV
ijassa-1367	330	22	than	than	ADP
ijassa-1367	330	23	on	on	ADP
ijassa-1367	330	24	local	local	ADJ
ijassa-1367	330	25	extremum	extremum	NOUN
ijassa-1367	330	26	.	.	PUNCT
ijassa-1367	331	1	moreover	moreover	ADV
ijassa-1367	331	2	,	,	PUNCT
ijassa-1367	331	3	this	this	DET
ijassa-1367	331	4	method	method	NOUN
ijassa-1367	331	5	can	can	AUX
ijassa-1367	331	6	be	be	AUX
ijassa-1367	331	7	used	use	VERB
ijassa-1367	331	8	in	in	ADP
ijassa-1367	331	9	the	the	DET
ijassa-1367	331	10	case	case	NOUN
ijassa-1367	331	11	when	when	SCONJ
ijassa-1367	331	12	searching	search	VERB
ijassa-1367	331	13	analytic	analytic	ADJ
ijassa-1367	331	14	solution	solution	NOUN
ijassa-1367	331	15	involves	involve	VERB
ijassa-1367	331	16	enormous	enormous	ADJ
ijassa-1367	331	17	time	time	NOUN
ijassa-1367	331	18	costs	cost	NOUN
ijassa-1367	331	19	.	.	PUNCT
ijassa-1367	332	1	partition	partition	NOUN
ijassa-1367	332	2	of	of	ADP
ijassa-1367	332	3	the	the	DET
ijassa-1367	332	4	state	state	NOUN
ijassa-1367	332	5	set	set	VERB
ijassa-1367	332	6	into	into	ADP
ijassa-1367	332	7	classes	class	NOUN
ijassa-1367	332	8	must	must	AUX
ijassa-1367	332	9	be	be	AUX
ijassa-1367	332	10	such	such	ADJ
ijassa-1367	332	11	that	that	SCONJ
ijassa-1367	332	12	the	the	DET
ijassa-1367	332	13	corresponding	correspond	VERB
ijassa-1367	332	14	data	datum	NOUN
ijassa-1367	332	15	set	set	VERB
ijassa-1367	332	16	could	could	AUX
ijassa-1367	332	17	be	be	AUX
ijassa-1367	332	18	stored	store	VERB
ijassa-1367	332	19	in	in	ADP
ijassa-1367	332	20	the	the	DET
ijassa-1367	332	21	computer	computer	NOUN
ijassa-1367	332	22	memory	memory	NOUN
ijassa-1367	332	23	.	.	PUNCT
ijassa-1367	333	1	diameters	diameter	NOUN
ijassa-1367	333	2	of	of	ADP
ijassa-1367	333	3	classes	class	NOUN
ijassa-1367	333	4	must	must	AUX
ijassa-1367	333	5	be	be	AUX
ijassa-1367	333	6	as	as	ADV
ijassa-1367	333	7	small	small	ADJ
ijassa-1367	333	8	as	as	ADP
ijassa-1367	333	9	possible	possible	ADJ
ijassa-1367	333	10	.	.	PUNCT
ijassa-1367	334	1	creating	create	VERB
ijassa-1367	334	2	piecewise	piecewise	NOUN
ijassa-1367	334	3	constant	constant	ADJ
ijassa-1367	334	4	functions	function	NOUN
ijassa-1367	334	5	most	most	ADJ
ijassa-1367	334	6	of	of	ADP
ijassa-1367	334	7	all	all	PRON
ijassa-1367	334	8	resembles	resemble	VERB
ijassa-1367	334	9	imitation	imitation	NOUN
ijassa-1367	334	10	modelling	modelling	NOUN
ijassa-1367	334	11	.	.	PUNCT
ijassa-1367	335	1	as	as	SCONJ
ijassa-1367	335	2	is	be	AUX
ijassa-1367	335	3	known	know	VERB
ijassa-1367	335	4	,	,	PUNCT
ijassa-1367	335	5	piecewise	piecewise	NOUN
ijassa-1367	335	6	constant	constant	ADJ
ijassa-1367	335	7	functions	function	NOUN
ijassa-1367	335	8	are	be	AUX
ijassa-1367	335	9	used	use	VERB
ijassa-1367	335	10	when	when	SCONJ
ijassa-1367	335	11	it	it	PRON
ijassa-1367	335	12	is	be	AUX
ijassa-1367	335	13	difficult	difficult	ADJ
ijassa-1367	335	14	to	to	PART
ijassa-1367	335	15	obtain	obtain	VERB
ijassa-1367	335	16	the	the	DET
ijassa-1367	335	17	solution	solution	NOUN
ijassa-1367	335	18	in	in	ADP
ijassa-1367	335	19	the	the	DET
ijassa-1367	335	20	form	form	NOUN
ijassa-1367	335	21	of	of	ADP
ijassa-1367	335	22	mathematical	mathematical	ADJ
ijassa-1367	335	23	equations	equation	NOUN
ijassa-1367	335	24	.	.	PUNCT
ijassa-1367	336	1	if	if	SCONJ
ijassa-1367	336	2	assumptions	assumption	NOUN
ijassa-1367	336	3	of	of	ADP
ijassa-1367	336	4	theorem	theorem	NOUN
ijassa-1367	336	5	,	,	PUNCT
ijassa-1367	336	6	which	which	PRON
ijassa-1367	336	7	was	be	AUX
ijassa-1367	336	8	proved	prove	VERB
ijassa-1367	336	9	in	in	ADP
ijassa-1367	336	10	the	the	DET
ijassa-1367	336	11	paper	paper	NOUN
ijassa-1367	336	12	,	,	PUNCT
ijassa-1367	336	13	are	be	AUX
ijassa-1367	336	14	satisfied	satisfied	ADJ
ijassa-1367	336	15	,	,	PUNCT
ijassa-1367	336	16	the	the	DET
ijassa-1367	336	17	algorithm	algorithm	NOUN
ijassa-1367	336	18	constructs	construct	VERB
ijassa-1367	336	19	the	the	DET
ijassa-1367	336	20	optimal	optimal	ADJ
ijassa-1367	336	21	curve	curve	NOUN
ijassa-1367	336	22	in	in	ADP
ijassa-1367	336	23	the	the	DET
ijassa-1367	336	24	class	class	NOUN
ijassa-1367	336	25	of	of	ADP
ijassa-1367	336	26	polygonal	polygonal	ADJ
ijassa-1367	336	27	lines	line	NOUN
ijassa-1367	336	28	.	.	PUNCT
ijassa-1367	337	1	if	if	SCONJ
ijassa-1367	337	2	the	the	DET
ijassa-1367	337	3	assumptions	assumption	NOUN
ijassa-1367	337	4	are	be	AUX
ijassa-1367	337	5	not	not	PART
ijassa-1367	337	6	satisfied	satisfied	ADJ
ijassa-1367	337	7	,	,	PUNCT
ijassa-1367	337	8	it	it	PRON
ijassa-1367	337	9	is	be	AUX
ijassa-1367	337	10	still	still	ADV
ijassa-1367	337	11	possible	possible	ADJ
ijassa-1367	337	12	to	to	PART
ijassa-1367	337	13	speak	speak	VERB
ijassa-1367	337	14	about	about	ADP
ijassa-1367	337	15	optimization	optimization	NOUN
ijassa-1367	337	16	if	if	SCONJ
ijassa-1367	337	17	we	we	PRON
ijassa-1367	337	18	recognize	recognize	VERB
ijassa-1367	337	19	it	it	PRON
ijassa-1367	337	20	as	as	ADP
ijassa-1367	337	21	a	a	DET
ijassa-1367	337	22	process	process	NOUN
ijassa-1367	337	23	,	,	PUNCT
ijassa-1367	337	24	at	at	ADP
ijassa-1367	337	25	which	which	PRON
ijassa-1367	337	26	extra	extra	ADJ
ijassa-1367	337	27	resources	resource	NOUN
ijassa-1367	337	28	of	of	ADP
ijassa-1367	337	29	time	time	NOUN
ijassa-1367	337	30	and	and	CCONJ
ijassa-1367	337	31	memory	memory	NOUN
ijassa-1367	337	32	appear	appear	NOUN
ijassa-1367	337	33	.	.	PUNCT
ijassa-1367	338	1	note	note	VERB
ijassa-1367	338	2	that	that	SCONJ
ijassa-1367	338	3	in	in	ADP
ijassa-1367	338	4	the	the	DET
ijassa-1367	338	5	simpler	simple	ADJ
ijassa-1367	338	6	problem	problem	NOUN
ijassa-1367	338	7	on	on	ADP
ijassa-1367	338	8	searching	search	VERB
ijassa-1367	338	9	global	global	ADJ
ijassa-1367	338	10	extremum	extremum	NOUN
ijassa-1367	338	11	of	of	ADP
ijassa-1367	338	12	functions	function	NOUN
ijassa-1367	338	13	of	of	ADP
ijassa-1367	338	14	several	several	ADJ
ijassa-1367	338	15	variables	variable	NOUN
ijassa-1367	338	16	,	,	PUNCT
ijassa-1367	338	17	it	it	PRON
ijassa-1367	338	18	is	be	AUX
ijassa-1367	338	19	enough	enough	ADJ
ijassa-1367	338	20	to	to	PART
ijassa-1367	338	21	equate	equate	VERB
ijassa-1367	338	22	the	the	DET
ijassa-1367	338	23	gradient	gradient	NOUN
ijassa-1367	338	24	to	to	ADP
ijassa-1367	338	25	zero	zero	NUM
ijassa-1367	338	26	and	and	CCONJ
ijassa-1367	338	27	after	after	ADP
ijassa-1367	338	28	that	that	PRON
ijassa-1367	338	29	to	to	PART
ijassa-1367	338	30	test	test	VERB
ijassa-1367	338	31	critical	critical	ADJ
ijassa-1367	338	32	points	point	NOUN
ijassa-1367	338	33	.	.	PUNCT
ijassa-1367	339	1	at	at	ADP
ijassa-1367	339	2	that	that	DET
ijassa-1367	339	3	case	case	NOUN
ijassa-1367	339	4	,	,	PUNCT
ijassa-1367	339	5	direct	direct	ADJ
ijassa-1367	339	6	methods	method	NOUN
ijassa-1367	339	7	are	be	AUX
ijassa-1367	339	8	not	not	PART
ijassa-1367	339	9	required	require	VERB
ijassa-1367	339	10	.	.	PUNCT
ijassa-1367	340	1	it	it	PRON
ijassa-1367	340	2	is	be	AUX
ijassa-1367	340	3	shown	show	VERB
ijassa-1367	340	4	in	in	ADP
ijassa-1367	340	5	textbooks	textbook	NOUN
ijassa-1367	340	6	on	on	ADP
ijassa-1367	340	7	mathematical	mathematical	ADJ
ijassa-1367	340	8	analysis	analysis	NOUN
ijassa-1367	340	9	.	.	PUNCT
ijassa-1367	341	1	the	the	DET
ijassa-1367	341	2	picture	picture	NOUN
ijassa-1367	341	3	changes	change	VERB
ijassa-1367	341	4	drastically	drastically	ADV
ijassa-1367	341	5	and	and	CCONJ
ijassa-1367	341	6	direct	direct	ADJ
ijassa-1367	341	7	methods	method	NOUN
ijassa-1367	341	8	have	have	AUX
ijassa-1367	341	9	become	become	VERB
ijassa-1367	341	10	very	very	ADV
ijassa-1367	341	11	actual	actual	ADJ
ijassa-1367	341	12	,	,	PUNCT
ijassa-1367	341	13	when	when	SCONJ
ijassa-1367	341	14	we	we	PRON
ijassa-1367	341	15	pass	pass	VERB
ijassa-1367	341	16	to	to	ADP
ijassa-1367	341	17	problems	problem	NOUN
ijassa-1367	341	18	of	of	ADP
ijassa-1367	341	19	dynamic	dynamic	ADJ
ijassa-1367	341	20	optimization	optimization	NOUN
ijassa-1367	341	21	,	,	PUNCT
ijassa-1367	341	22	since	since	SCONJ
ijassa-1367	341	23	otherwise	otherwise	ADV
ijassa-1367	341	24	we	we	PRON
ijassa-1367	341	25	have	have	VERB
ijassa-1367	341	26	to	to	PART
ijassa-1367	341	27	construct	construct	VERB
ijassa-1367	341	28	and	and	CCONJ
ijassa-1367	341	29	analyse	analyse	VERB
ijassa-1367	341	30	central	central	ADJ
ijassa-1367	341	31	field	field	NOUN
ijassa-1367	341	32	of	of	ADP
ijassa-1367	341	33	extremals	extremal	NOUN
ijassa-1367	341	34	,	,	PUNCT
ijassa-1367	341	35	and	and	CCONJ
ijassa-1367	341	36	common	common	ADJ
ijassa-1367	341	37	approaches	approach	NOUN
ijassa-1367	341	38	have	have	AUX
ijassa-1367	341	39	not	not	PART
ijassa-1367	341	40	been	be	AUX
ijassa-1367	341	41	worked	work	VERB
ijassa-1367	341	42	out	out	ADP
ijassa-1367	341	43	yet	yet	ADV
ijassa-1367	341	44	.	.	PUNCT
ijassa-1367	342	1	in	in	ADP
ijassa-1367	342	2	the	the	DET
ijassa-1367	342	3	paper	paper	NOUN
ijassa-1367	342	4	,	,	PUNCT
ijassa-1367	342	5	we	we	PRON
ijassa-1367	342	6	showed	show	VERB
ijassa-1367	342	7	not	not	PART
ijassa-1367	342	8	only	only	ADV
ijassa-1367	342	9	relevance	relevance	NOUN
ijassa-1367	342	10	and	and	CCONJ
ijassa-1367	342	11	efficiency	efficiency	NOUN
ijassa-1367	342	12	of	of	ADP
ijassa-1367	342	13	direct	direct	ADJ
ijassa-1367	342	14	methods	method	NOUN
ijassa-1367	342	15	in	in	ADP
ijassa-1367	342	16	the	the	DET
ijassa-1367	342	17	dynamic	dynamic	ADJ
ijassa-1367	342	18	optimization	optimization	NOUN
ijassa-1367	342	19	problems	problem	NOUN
ijassa-1367	342	20	of	of	ADP
ijassa-1367	342	21	various	various	ADJ
ijassa-1367	342	22	types	type	NOUN
ijassa-1367	342	23	,	,	PUNCT
ijassa-1367	342	24	but	but	CCONJ
ijassa-1367	342	25	also	also	ADV
ijassa-1367	342	26	demonstrated	demonstrate	VERB
ijassa-1367	342	27	internal	internal	ADJ
ijassa-1367	342	28	and	and	CCONJ
ijassa-1367	342	29	external	external	ADJ
ijassa-1367	342	30	similarity	similarity	NOUN
ijassa-1367	342	31	of	of	ADP
ijassa-1367	342	32	analytic	analytic	ADJ
ijassa-1367	342	33	and	and	CCONJ
ijassa-1367	342	34	direct	direct	ADJ
ijassa-1367	342	35	methods	method	NOUN
ijassa-1367	342	36	.	.	PUNCT
ijassa-1367	343	1	this	this	PRON
ijassa-1367	343	2	suggests	suggest	VERB
ijassa-1367	343	3	the	the	DET
ijassa-1367	343	4	idea	idea	NOUN
ijassa-1367	343	5	that	that	SCONJ
ijassa-1367	343	6	in	in	ADP
ijassa-1367	343	7	particular	particular	ADJ
ijassa-1367	343	8	cases	case	NOUN
ijassa-1367	343	9	,	,	PUNCT
ijassa-1367	343	10	combination	combination	NOUN
ijassa-1367	343	11	of	of	ADP
ijassa-1367	343	12	both	both	DET
ijassa-1367	343	13	methods	method	NOUN
ijassa-1367	343	14	would	would	AUX
ijassa-1367	343	15	be	be	AUX
ijassa-1367	343	16	fruitful	fruitful	ADJ
ijassa-1367	343	17	.	.	PUNCT
ijassa-1367	344	1	the	the	DET
ijassa-1367	344	2	presented	present	VERB
ijassa-1367	344	3	algorithms	algorithm	NOUN
ijassa-1367	344	4	and	and	CCONJ
ijassa-1367	344	5	programs	program	NOUN
ijassa-1367	344	6	can	can	AUX
ijassa-1367	344	7	be	be	AUX
ijassa-1367	344	8	applied	apply	VERB
ijassa-1367	344	9	to	to	ADP
ijassa-1367	344	10	various	various	ADJ
ijassa-1367	344	11	engineering	engineering	NOUN
ijassa-1367	344	12	problems	problem	NOUN
ijassa-1367	344	13	connected	connect	VERB
ijassa-1367	344	14	with	with	ADP
ijassa-1367	344	15	optimal	optimal	ADJ
ijassa-1367	344	16	control	control	NOUN
ijassa-1367	344	17	;	;	PUNCT
ijassa-1367	344	18	see	see	VERB
ijassa-1367	344	19	,	,	PUNCT
ijassa-1367	344	20	for	for	ADP
ijassa-1367	344	21	instance	instance	NOUN
ijassa-1367	344	22	,	,	PUNCT
ijassa-1367	344	23	the	the	DET
ijassa-1367	344	24	recent	recent	ADJ
ijassa-1367	344	25	papers	paper	NOUN
ijassa-1367	344	26	[	[	X
ijassa-1367	344	27	4	4	NUM
ijassa-1367	344	28	,	,	PUNCT
ijassa-1367	344	29	5	5	NUM
ijassa-1367	344	30	]	]	PUNCT
ijassa-1367	344	31	.	.	PUNCT
ijassa-1367	345	1	references	reference	NOUN
ijassa-1367	345	2	1	1	NUM
ijassa-1367	345	3	.	.	PUNCT
ijassa-1367	345	4	breakwell	breakwell	PROPN
ijassa-1367	345	5	,	,	PUNCT
ijassa-1367	345	6	j.	j.	PROPN
ijassa-1367	345	7	v.	v.	PROPN
ijassa-1367	345	8	,	,	PUNCT
ijassa-1367	345	9	speyer	speyer	PROPN
ijassa-1367	345	10	,	,	PUNCT
ijassa-1367	345	11	j.	j.	PROPN
ijassa-1367	345	12	l.	l.	PROPN
ijassa-1367	345	13	,	,	PUNCT
ijassa-1367	345	14	&	&	CCONJ
ijassa-1367	345	15	bryson	bryson	PROPN
ijassa-1367	345	16	,	,	PUNCT
ijassa-1367	345	17	a.	a.	PROPN
ijassa-1367	345	18	e.	e.	PROPN
ijassa-1367	345	19	(	(	PUNCT
ijassa-1367	345	20	1963	1963	NUM
ijassa-1367	345	21	)	)	PUNCT
ijassa-1367	345	22	.	.	PUNCT
ijassa-1367	346	1	optimization	optimization	NOUN
ijassa-1367	346	2	and	and	CCONJ
ijassa-1367	346	3	control	control	NOUN
ijassa-1367	346	4	of	of	ADP
ijassa-1367	346	5	nonlinear	nonlinear	ADJ
ijassa-1367	346	6	systems	system	NOUN
ijassa-1367	346	7	using	use	VERB
ijassa-1367	346	8	the	the	DET
ijassa-1367	346	9	second	second	ADJ
ijassa-1367	346	10	variations	variation	NOUN
ijassa-1367	346	11	,	,	PUNCT
ijassa-1367	346	12	siam	siam	PROPN
ijassa-1367	346	13	j.	j.	PROPN
ijassa-1367	346	14	control	control	PROPN
ijassa-1367	346	15	,	,	PUNCT
ijassa-1367	346	16	1	1	NUM
ijassa-1367	346	17	,	,	PUNCT
ijassa-1367	346	18	193–223	193–223	NUM
ijassa-1367	346	19	.	.	PUNCT
ijassa-1367	347	1	2	2	X
ijassa-1367	347	2	.	.	NUM
ijassa-1367	347	3	elsgolts	elsgolt	NOUN
ijassa-1367	347	4	,	,	PUNCT
ijassa-1367	347	5	l.	l.	PROPN
ijassa-1367	347	6	e.	e.	PROPN
ijassa-1367	347	7	(	(	PUNCT
ijassa-1367	347	8	1970	1970	NUM
ijassa-1367	347	9	)	)	PUNCT
ijassa-1367	347	10	differential	differential	ADJ
ijassa-1367	347	11	equations	equation	NOUN
ijassa-1367	347	12	and	and	CCONJ
ijassa-1367	347	13	calculus	calculus	NOUN
ijassa-1367	347	14	of	of	ADP
ijassa-1367	347	15	variations	variation	NOUN
ijassa-1367	347	16	,	,	PUNCT
ijassa-1367	347	17	moscow	moscow	PROPN
ijassa-1367	347	18	,	,	PUNCT
ijassa-1367	347	19	russia	russia	PROPN
ijassa-1367	347	20	:	:	PUNCT
ijassa-1367	347	21	mir	mir	NOUN
ijassa-1367	347	22	publishers	publisher	NOUN
ijassa-1367	347	23	.	.	PUNCT
ijassa-1367	348	1	3	3	X
ijassa-1367	348	2	.	.	X
ijassa-1367	348	3	isaacs	isaacs	PROPN
ijassa-1367	348	4	,	,	PUNCT
ijassa-1367	348	5	r.	r.	PROPN
ijassa-1367	348	6	(	(	PUNCT
ijassa-1367	348	7	1965	1965	NUM
ijassa-1367	348	8	)	)	PUNCT
ijassa-1367	348	9	.	.	PUNCT
ijassa-1367	349	1	differential	differential	PROPN
ijassa-1367	349	2	games	games	PROPN
ijassa-1367	349	3	,	,	PUNCT
ijassa-1367	349	4	new	new	PROPN
ijassa-1367	349	5	york	york	PROPN
ijassa-1367	349	6	,	,	PUNCT
ijassa-1367	349	7	ny	ny	PROPN
ijassa-1367	349	8	:	:	PUNCT
ijassa-1367	349	9	john	john	PROPN
ijassa-1367	349	10	wiley	wiley	PROPN
ijassa-1367	349	11	and	and	CCONJ
ijassa-1367	349	12	sons	son	NOUN
ijassa-1367	349	13	.	.	PUNCT
ijassa-1367	350	1	4	4	X
ijassa-1367	350	2	.	.	X
ijassa-1367	350	3	kramar	kramar	PROPN
ijassa-1367	350	4	,	,	PUNCT
ijassa-1367	350	5	v.	v.	PROPN
ijassa-1367	350	6	,	,	PUNCT
ijassa-1367	350	7	alchakov	alchakov	PROPN
ijassa-1367	350	8	,	,	PUNCT
ijassa-1367	350	9	v.	v.	PROPN
ijassa-1367	350	10	,	,	PUNCT
ijassa-1367	350	11	&	&	CCONJ
ijassa-1367	350	12	osadchenko	osadchenko	PROPN
ijassa-1367	350	13	,	,	PUNCT
ijassa-1367	350	14	a.	a.	NOUN
ijassa-1367	350	15	(	(	PUNCT
ijassa-1367	350	16	2021	2021	NUM
ijassa-1367	350	17	)	)	PUNCT
ijassa-1367	350	18	.	.	PUNCT
ijassa-1367	351	1	the	the	DET
ijassa-1367	351	2	optimal	optimal	ADJ
ijassa-1367	351	3	control	control	NOUN
ijassa-1367	351	4	of	of	ADP
ijassa-1367	351	5	the	the	DET
ijassa-1367	351	6	vessel	vessel	NOUN
ijassa-1367	351	7	’s	’s	PART
ijassa-1367	351	8	automatic	automatic	ADJ
ijassa-1367	351	9	dynamic	dynamic	ADJ
ijassa-1367	351	10	positioning	positioning	NOUN
ijassa-1367	351	11	system	system	NOUN
ijassa-1367	351	12	under	under	ADP
ijassa-1367	351	13	deviation	deviation	NOUN
ijassa-1367	351	14	,	,	PUNCT
ijassa-1367	351	15	adv	adv	PROPN
ijassa-1367	351	16	.	.	PUNCT
ijassa-1367	351	17	syst	syst	PROPN
ijassa-1367	351	18	.	.	PUNCT
ijassa-1367	352	1	sci	sci	PROPN
ijassa-1367	352	2	.	.	PUNCT
ijassa-1367	352	3	appl	appl	PROPN
ijassa-1367	352	4	.	.	PROPN
ijassa-1367	352	5	,	,	PUNCT
ijassa-1367	352	6	21(1	21(1	NUM
ijassa-1367	352	7	)	)	PUNCT
ijassa-1367	352	8	,	,	PUNCT
ijassa-1367	352	9	1–10	1–10	NOUN
ijassa-1367	352	10	.	.	PUNCT
ijassa-1367	353	1	5	5	NUM
ijassa-1367	353	2	.	.	X
ijassa-1367	353	3	mitrishkin	mitrishkin	PROPN
ijassa-1367	353	4	,	,	PUNCT
ijassa-1367	353	5	y.	y.	PROPN
ijassa-1367	353	6	(	(	PUNCT
ijassa-1367	353	7	2021	2021	NUM
ijassa-1367	353	8	)	)	PUNCT
ijassa-1367	353	9	.	.	PUNCT
ijassa-1367	354	1	plasma	plasma	PROPN
ijassa-1367	354	2	magnetic	magnetic	PROPN
ijassa-1367	354	3	control	control	NOUN
ijassa-1367	354	4	systems	system	NOUN
ijassa-1367	354	5	in	in	ADP
ijassa-1367	354	6	d	d	ADV
ijassa-1367	354	7	-	-	PUNCT
ijassa-1367	354	8	shaped	shape	VERB
ijassa-1367	354	9	tokamaks	tokamak	NOUN
ijassa-1367	354	10	and	and	CCONJ
ijassa-1367	354	11	imitation	imitation	NOUN
ijassa-1367	354	12	digital	digital	ADJ
ijassa-1367	354	13	computer	computer	NOUN
ijassa-1367	354	14	platform	platform	NOUN
ijassa-1367	354	15	in	in	ADP
ijassa-1367	354	16	real	real	ADJ
ijassa-1367	354	17	time	time	NOUN
ijassa-1367	354	18	for	for	ADP
ijassa-1367	354	19	controlling	control	VERB
ijassa-1367	354	20	plasma	plasma	NOUN
ijassa-1367	354	21	current	current	NOUN
ijassa-1367	354	22	and	and	CCONJ
ijassa-1367	354	23	copyright	copyright	NOUN
ijassa-1367	354	24	©	©	PROPN
ijassa-1367	354	25	2023	2023	NUM
ijassa-1367	354	26	assa	assa	NOUN
ijassa-1367	354	27	.	.	PUNCT
ijassa-1367	355	1	adv	adv	PROPN
ijassa-1367	355	2	syst	syst	PROPN
ijassa-1367	355	3	sci	sci	PROPN
ijassa-1367	355	4	appl	appl	PROPN
ijassa-1367	355	5	(	(	PUNCT
ijassa-1367	355	6	2023	2023	NUM
ijassa-1367	355	7	)	)	PUNCT
ijassa-1367	355	8	piecewise	piecewise	NOUN
ijassa-1367	355	9	constant	constant	ADJ
ijassa-1367	355	10	functions	function	NOUN
ijassa-1367	355	11	in	in	ADP
ijassa-1367	355	12	dynamic	dynamic	ADJ
ijassa-1367	355	13	optimization	optimization	NOUN
ijassa-1367	355	14	problems	problem	NOUN
ijassa-1367	355	15	49	49	NUM
ijassa-1367	355	16	shape	shape	NOUN
ijassa-1367	355	17	,	,	PUNCT
ijassa-1367	355	18	adv	adv	PROPN
ijassa-1367	355	19	.	.	PUNCT
ijassa-1367	355	20	syst	syst	PROPN
ijassa-1367	355	21	.	.	PUNCT
ijassa-1367	356	1	sci	sci	PROPN
ijassa-1367	356	2	.	.	PUNCT
ijassa-1367	356	3	appl	appl	PROPN
ijassa-1367	356	4	.	.	PROPN
ijassa-1367	356	5	,	,	PUNCT
ijassa-1367	356	6	22(1	22(1	NUM
ijassa-1367	356	7	)	)	PUNCT
ijassa-1367	356	8	,	,	PUNCT
ijassa-1367	356	9	1–14	1–14	PROPN
ijassa-1367	356	10	.	.	PROPN
ijassa-1367	357	1	6	6	NUM
ijassa-1367	357	2	.	.	X
ijassa-1367	357	3	michie	michie	PROPN
ijassa-1367	357	4	,	,	PUNCT
ijassa-1367	357	5	d.	d.	PROPN
ijassa-1367	357	6	,	,	PUNCT
ijassa-1367	357	7	johnston	johnston	PROPN
ijassa-1367	357	8	,	,	PUNCT
ijassa-1367	357	9	r.	r.	PROPN
ijassa-1367	357	10	(	(	PUNCT
ijassa-1367	357	11	1984	1984	NUM
ijassa-1367	357	12	)	)	PUNCT
ijassa-1367	357	13	.	.	PUNCT
ijassa-1367	358	1	the	the	DET
ijassa-1367	358	2	creative	creative	ADJ
ijassa-1367	358	3	computer	computer	NOUN
ijassa-1367	358	4	.	.	PUNCT
ijassa-1367	359	1	machine	machine	NOUN
ijassa-1367	359	2	intelligence	intelligence	NOUN
ijassa-1367	359	3	and	and	CCONJ
ijassa-1367	359	4	human	human	ADJ
ijassa-1367	359	5	knowledge	knowledge	NOUN
ijassa-1367	359	6	,	,	PUNCT
ijassa-1367	359	7	new	new	PROPN
ijassa-1367	359	8	york	york	PROPN
ijassa-1367	359	9	,	,	PUNCT
ijassa-1367	359	10	ny	ny	PROPN
ijassa-1367	359	11	:	:	PUNCT
ijassa-1367	359	12	the	the	DET
ijassa-1367	359	13	viking	viking	PROPN
ijassa-1367	359	14	press	press	NOUN
ijassa-1367	359	15	.	.	PUNCT
ijassa-1367	360	1	7	7	X
ijassa-1367	360	2	.	.	X
ijassa-1367	360	3	moiseev	moiseev	PROPN
ijassa-1367	360	4	,	,	PUNCT
ijassa-1367	360	5	n.	n.	NOUN
ijassa-1367	360	6	n.	n.	PROPN
ijassa-1367	360	7	(	(	PUNCT
ijassa-1367	360	8	1975	1975	NUM
ijassa-1367	360	9	)	)	PUNCT
ijassa-1367	360	10	elements	element	NOUN
ijassa-1367	360	11	of	of	ADP
ijassa-1367	360	12	the	the	DET
ijassa-1367	360	13	theory	theory	NOUN
ijassa-1367	360	14	of	of	ADP
ijassa-1367	360	15	optimas	optimas	PROPN
ijassa-1367	360	16	systems	system	NOUN
ijassa-1367	360	17	,	,	PUNCT
ijassa-1367	360	18	moscow	moscow	PROPN
ijassa-1367	360	19	,	,	PUNCT
ijassa-1367	360	20	russia	russia	PROPN
ijassa-1367	360	21	:	:	PUNCT
ijassa-1367	360	22	nauka	nauka	PROPN
ijassa-1367	360	23	.	.	PROPN
ijassa-1367	361	1	8	8	X
ijassa-1367	361	2	.	.	X
ijassa-1367	361	3	neimark	neimark	PROPN
ijassa-1367	361	4	,	,	PUNCT
ijassa-1367	361	5	u.	u.	PROPN
ijassa-1367	361	6	i.	i.	PROPN
ijassa-1367	361	7	,	,	PUNCT
ijassa-1367	361	8	kogan	kogan	PROPN
ijassa-1367	361	9	,	,	PUNCT
ijassa-1367	361	10	n.	n.	PROPN
ijassa-1367	361	11	ya	ya	PROPN
ijassa-1367	361	12	.	.	PROPN
ijassa-1367	361	13	,	,	PUNCT
ijassa-1367	361	14	&	&	CCONJ
ijassa-1367	361	15	savelyev	savelyev	PROPN
ijassa-1367	361	16	,	,	PUNCT
ijassa-1367	361	17	v.	v.	PROPN
ijassa-1367	362	1	p.	p.	NOUN
ijassa-1367	362	2	(	(	PUNCT
ijassa-1367	362	3	1985	1985	NUM
ijassa-1367	362	4	)	)	PUNCT
ijassa-1367	362	5	.	.	PUNCT
ijassa-1367	363	1	dynamics	dynamic	NOUN
ijassa-1367	363	2	models	model	NOUN
ijassa-1367	363	3	of	of	ADP
ijassa-1367	363	4	control	control	NOUN
ijassa-1367	363	5	theory	theory	NOUN
ijassa-1367	363	6	,	,	PUNCT
ijassa-1367	363	7	moscow	moscow	PROPN
ijassa-1367	363	8	,	,	PUNCT
ijassa-1367	363	9	russia	russia	PROPN
ijassa-1367	363	10	:	:	PUNCT
ijassa-1367	363	11	nauka	nauka	PROPN
ijassa-1367	363	12	.	.	PUNCT
ijassa-1367	364	1	9	9	X
ijassa-1367	364	2	.	.	X
ijassa-1367	364	3	orel	orel	PROPN
ijassa-1367	364	4	,	,	PUNCT
ijassa-1367	364	5	e.	e.	PROPN
ijassa-1367	364	6	n.	n.	PROPN
ijassa-1367	364	7	(	(	PUNCT
ijassa-1367	364	8	1989	1989	NUM
ijassa-1367	364	9	)	)	PUNCT
ijassa-1367	364	10	a	a	DET
ijassa-1367	364	11	method	method	NOUN
ijassa-1367	364	12	for	for	ADP
ijassa-1367	364	13	solving	solve	VERB
ijassa-1367	364	14	optimal	optimal	ADJ
ijassa-1367	364	15	control	control	NOUN
ijassa-1367	364	16	problems	problem	NOUN
ijassa-1367	364	17	,	,	PUNCT
ijassa-1367	364	18	sov	sov	NOUN
ijassa-1367	364	19	.	.	PUNCT
ijassa-1367	365	1	math	math	NOUN
ijassa-1367	365	2	.	.	PUNCT
ijassa-1367	365	3	,	,	PUNCT
ijassa-1367	366	1	dokl	dokl	NOUN
ijassa-1367	366	2	.	.	PUNCT
ijassa-1367	366	3	,	,	PUNCT
ijassa-1367	366	4	39(3	39(3	NUM
ijassa-1367	366	5	)	)	PUNCT
ijassa-1367	366	6	,	,	PUNCT
ijassa-1367	366	7	614–617	614–617	NUM
ijassa-1367	366	8	.	.	PUNCT
ijassa-1367	367	1	10	10	NUM
ijassa-1367	367	2	.	.	X
ijassa-1367	368	1	orel	orel	PROPN
ijassa-1367	368	2	,	,	PUNCT
ijassa-1367	368	3	e.	e.	PROPN
ijassa-1367	368	4	n.	n.	PROPN
ijassa-1367	368	5	(	(	PUNCT
ijassa-1367	368	6	1991	1991	NUM
ijassa-1367	368	7	)	)	PUNCT
ijassa-1367	368	8	.	.	PUNCT
ijassa-1367	369	1	adjustment	adjustment	NOUN
ijassa-1367	369	2	of	of	ADP
ijassa-1367	369	3	heuristic	heuristic	ADJ
ijassa-1367	369	4	functions	function	NOUN
ijassa-1367	369	5	in	in	ADP
ijassa-1367	369	6	search	search	NOUN
ijassa-1367	369	7	and	and	CCONJ
ijassa-1367	369	8	decision	decision	NOUN
ijassa-1367	369	9	-	-	PUNCT
ijassa-1367	369	10	making	make	VERB
ijassa-1367	369	11	processes	process	NOUN
ijassa-1367	369	12	.	.	PUNCT
ijassa-1367	370	1	sov	sov	NOUN
ijassa-1367	370	2	.	.	PUNCT
ijassa-1367	371	1	phys	phy	NOUN
ijassa-1367	371	2	.	.	PUNCT
ijassa-1367	371	3	,	,	PUNCT
ijassa-1367	371	4	dokl	dokl	NOUN
ijassa-1367	371	5	.	.	PUNCT
ijassa-1367	371	6	,	,	PUNCT
ijassa-1367	371	7	36(4	36(4	NUM
ijassa-1367	371	8	)	)	PUNCT
ijassa-1367	371	9	,	,	PUNCT
ijassa-1367	371	10	272–273	272–273	NUM
ijassa-1367	371	11	.	.	NOUN
ijassa-1367	371	12	11	11	NUM
ijassa-1367	371	13	.	.	X
ijassa-1367	372	1	orel	orel	PROPN
ijassa-1367	372	2	,	,	PUNCT
ijassa-1367	372	3	e.	e.	PROPN
ijassa-1367	372	4	n.	n.	PROPN
ijassa-1367	372	5	(	(	PUNCT
ijassa-1367	372	6	1990	1990	NUM
ijassa-1367	372	7	)	)	PUNCT
ijassa-1367	372	8	algorithms	algorithm	NOUN
ijassa-1367	372	9	for	for	ADP
ijassa-1367	372	10	searching	search	VERB
ijassa-1367	372	11	quasioptimal	quasioptimal	ADJ
ijassa-1367	372	12	control	control	NOUN
ijassa-1367	372	13	using	use	VERB
ijassa-1367	372	14	partitioning	partitioning	NOUN
ijassa-1367	372	15	of	of	ADP
ijassa-1367	372	16	the	the	DET
ijassa-1367	372	17	state	state	NOUN
ijassa-1367	372	18	space	space	NOUN
ijassa-1367	372	19	,	,	PUNCT
ijassa-1367	372	20	zh	zh	PROPN
ijassa-1367	372	21	.	.	PUNCT
ijassa-1367	372	22	vychisl	vychisl	PROPN
ijassa-1367	372	23	.	.	PUNCT
ijassa-1367	373	1	mat	mat	NOUN
ijassa-1367	373	2	.	.	PUNCT
ijassa-1367	373	3	mat	mat	PROPN
ijassa-1367	373	4	.	.	PUNCT
ijassa-1367	373	5	fiz	fiz	PROPN
ijassa-1367	373	6	.	.	PROPN
ijassa-1367	373	7	,	,	PUNCT
ijassa-1367	373	8	30(9	30(9	NUM
ijassa-1367	373	9	)	)	PUNCT
ijassa-1367	373	10	,	,	PUNCT
ijassa-1367	373	11	1283–1293	1283–1293	NUM
ijassa-1367	373	12	.	.	PUNCT
ijassa-1367	374	1	12	12	NUM
ijassa-1367	374	2	.	.	PUNCT
ijassa-1367	375	1	orel	orel	PROPN
ijassa-1367	375	2	,	,	PUNCT
ijassa-1367	375	3	e.	e.	PROPN
ijassa-1367	375	4	n.	n.	PROPN
ijassa-1367	375	5	(	(	PUNCT
ijassa-1367	375	6	1979	1979	NUM
ijassa-1367	375	7	)	)	PUNCT
ijassa-1367	375	8	approximation	approximation	NOUN
ijassa-1367	375	9	of	of	ADP
ijassa-1367	375	10	bellman	bellman	NOUN
ijassa-1367	375	11	’s	’s	PART
ijassa-1367	375	12	function	function	NOUN
ijassa-1367	375	13	by	by	ADP
ijassa-1367	375	14	piecewise	piecewise	NOUN
ijassa-1367	375	15	constant	constant	ADJ
ijassa-1367	375	16	functions	function	NOUN
ijassa-1367	375	17	,	,	PUNCT
ijassa-1367	375	18	u.s.s.r	u.s.s.r	PROPN
ijassa-1367	375	19	.	.	PROPN
ijassa-1367	375	20	comput	comput	PROPN
ijassa-1367	375	21	.	.	PUNCT
ijassa-1367	376	1	math	math	NOUN
ijassa-1367	376	2	.	.	PUNCT
ijassa-1367	377	1	math	math	NOUN
ijassa-1367	377	2	.	.	PUNCT
ijassa-1367	378	1	phys	phy	NOUN
ijassa-1367	378	2	.	.	PUNCT
ijassa-1367	378	3	,	,	PUNCT
ijassa-1367	378	4	18(4	18(4	NUM
ijassa-1367	378	5	)	)	PUNCT
ijassa-1367	378	6	,	,	PUNCT
ijassa-1367	378	7	95–107	95–107	PROPN
ijassa-1367	378	8	.	.	NOUN
ijassa-1367	378	9	13	13	NUM
ijassa-1367	378	10	.	.	X
ijassa-1367	379	1	orel	orel	PROPN
ijassa-1367	379	2	,	,	PUNCT
ijassa-1367	379	3	e.	e.	PROPN
ijassa-1367	379	4	n.	n.	PROPN
ijassa-1367	379	5	(	(	PUNCT
ijassa-1367	379	6	1998	1998	NUM
ijassa-1367	379	7	)	)	PUNCT
ijassa-1367	379	8	.	.	PUNCT
ijassa-1367	380	1	discrete	discrete	ADJ
ijassa-1367	380	2	boundary	boundary	ADJ
ijassa-1367	380	3	problems	problem	NOUN
ijassa-1367	380	4	and	and	CCONJ
ijassa-1367	380	5	optimization	optimization	NOUN
ijassa-1367	380	6	processes	process	NOUN
ijassa-1367	380	7	on	on	ADP
ijassa-1367	380	8	graphs	graph	NOUN
ijassa-1367	380	9	,	,	PUNCT
ijassa-1367	380	10	artificial	artificial	ADJ
ijassa-1367	380	11	intelligence	intelligence	NOUN
ijassa-1367	380	12	in	in	ADP
ijassa-1367	380	13	engineering	engineering	NOUN
ijassa-1367	380	14	systems	system	NOUN
ijassa-1367	380	15	,	,	PUNCT
ijassa-1367	380	16	3–33	3–33	NOUN
ijassa-1367	380	17	.	.	PUNCT
ijassa-1367	381	1	14	14	NUM
ijassa-1367	381	2	.	.	PUNCT
ijassa-1367	382	1	orel	orel	PROPN
ijassa-1367	382	2	,	,	PUNCT
ijassa-1367	382	3	e.	e.	PROPN
ijassa-1367	382	4	n.	n.	PROPN
ijassa-1367	382	5	(	(	PUNCT
ijassa-1367	382	6	1977	1977	NUM
ijassa-1367	382	7	)	)	PUNCT
ijassa-1367	382	8	.	.	PUNCT
ijassa-1367	383	1	finding	find	VERB
ijassa-1367	383	2	a	a	DET
ijassa-1367	383	3	shortest	short	ADJ
ijassa-1367	383	4	path	path	NOUN
ijassa-1367	383	5	in	in	ADP
ijassa-1367	383	6	a	a	DET
ijassa-1367	383	7	graph	graph	NOUN
ijassa-1367	383	8	using	use	VERB
ijassa-1367	383	9	the	the	DET
ijassa-1367	383	10	minorant	minorant	NOUN
ijassa-1367	383	11	of	of	ADP
ijassa-1367	383	12	the	the	DET
ijassa-1367	383	13	bellman	bellman	NOUN
ijassa-1367	383	14	function	function	NOUN
ijassa-1367	383	15	,	,	PUNCT
ijassa-1367	383	16	autom	autom	PROPN
ijassa-1367	383	17	.	.	PUNCT
ijassa-1367	384	1	remote	remote	ADJ
ijassa-1367	384	2	control	control	NOUN
ijassa-1367	384	3	,	,	PUNCT
ijassa-1367	384	4	38	38	NUM
ijassa-1367	384	5	,	,	PUNCT
ijassa-1367	384	6	235–237	235–237	NUM
ijassa-1367	384	7	.	.	PUNCT
ijassa-1367	385	1	15	15	NUM
ijassa-1367	385	2	.	.	X
ijassa-1367	386	1	orel	orel	PROPN
ijassa-1367	386	2	,	,	PUNCT
ijassa-1367	386	3	e.	e.	PROPN
ijassa-1367	386	4	n.	n.	PROPN
ijassa-1367	386	5	(	(	PUNCT
ijassa-1367	386	6	1992	1992	NUM
ijassa-1367	386	7	)	)	PUNCT
ijassa-1367	386	8	.	.	PUNCT
ijassa-1367	387	1	heuristic	heuristic	NOUN
ijassa-1367	387	2	of	of	ADP
ijassa-1367	387	3	teaching	teaching	NOUN
ijassa-1367	387	4	in	in	ADP
ijassa-1367	387	5	search	search	NOUN
ijassa-1367	387	6	problems	problem	NOUN
ijassa-1367	387	7	,	,	PUNCT
ijassa-1367	387	8	engineering	engineering	NOUN
ijassa-1367	387	9	cybernetics	cybernetic	NOUN
ijassa-1367	387	10	,	,	PUNCT
ijassa-1367	387	11	1(5	1(5	NUM
ijassa-1367	387	12	)	)	PUNCT
ijassa-1367	387	13	,	,	PUNCT
ijassa-1367	387	14	69–81	69–81	NUM
ijassa-1367	387	15	.	.	PUNCT
ijassa-1367	388	1	16	16	NUM
ijassa-1367	388	2	.	.	PUNCT
ijassa-1367	389	1	orel	orel	PROPN
ijassa-1367	389	2	,	,	PUNCT
ijassa-1367	389	3	e.	e.	PROPN
ijassa-1367	389	4	n.	n.	PROPN
ijassa-1367	389	5	,	,	PUNCT
ijassa-1367	389	6	orel	orel	PROPN
ijassa-1367	389	7	,	,	PUNCT
ijassa-1367	389	8	o.	o.	PROPN
ijassa-1367	389	9	e.	e.	PROPN
ijassa-1367	389	10	(	(	PUNCT
ijassa-1367	389	11	2015	2015	NUM
ijassa-1367	389	12	)	)	PUNCT
ijassa-1367	389	13	.	.	PUNCT
ijassa-1367	390	1	central	central	ADJ
ijassa-1367	390	2	field	field	NOUN
ijassa-1367	390	3	of	of	ADP
ijassa-1367	390	4	trajectories	trajectory	NOUN
ijassa-1367	390	5	in	in	ADP
ijassa-1367	390	6	problems	problem	NOUN
ijassa-1367	390	7	of	of	ADP
ijassa-1367	390	8	optimal	optimal	ADJ
ijassa-1367	390	9	control	control	NOUN
ijassa-1367	390	10	and	and	CCONJ
ijassa-1367	390	11	calculus	calculus	NOUN
ijassa-1367	390	12	of	of	ADP
ijassa-1367	390	13	variations	variation	NOUN
ijassa-1367	390	14	,	,	PUNCT
ijassa-1367	390	15	accounting	accounting	NOUN
ijassa-1367	390	16	.	.	PUNCT
ijassa-1367	391	1	analysis	analysis	NOUN
ijassa-1367	391	2	.	.	PUNCT
ijassa-1367	392	1	audit	audit	NOUN
ijassa-1367	392	2	,	,	PUNCT
ijassa-1367	392	3	3	3	NUM
ijassa-1367	392	4	,	,	PUNCT
ijassa-1367	392	5	35–42	35–42	NUM
ijassa-1367	392	6	.	.	NOUN
ijassa-1367	392	7	17	17	NUM
ijassa-1367	392	8	.	.	PUNCT
ijassa-1367	393	1	orel	orel	PROPN
ijassa-1367	393	2	,	,	PUNCT
ijassa-1367	393	3	e.	e.	PROPN
ijassa-1367	393	4	n.	n.	PROPN
ijassa-1367	393	5	,	,	PUNCT
ijassa-1367	393	6	orel	orel	PROPN
ijassa-1367	393	7	,	,	PUNCT
ijassa-1367	393	8	o.	o.	PROPN
ijassa-1367	393	9	e.	e.	PROPN
ijassa-1367	393	10	(	(	PUNCT
ijassa-1367	393	11	2014	2014	NUM
ijassa-1367	393	12	)	)	PUNCT
ijassa-1367	393	13	.	.	PUNCT
ijassa-1367	394	1	central	central	ADJ
ijassa-1367	394	2	fields	field	NOUN
ijassa-1367	394	3	of	of	ADP
ijassa-1367	394	4	optimal	optimal	ADJ
ijassa-1367	394	5	trajectories	trajectory	NOUN
ijassa-1367	394	6	,	,	PUNCT
ijassa-1367	394	7	dokl	dokl	NOUN
ijassa-1367	394	8	.	.	PUNCT
ijassa-1367	394	9	math	math	NOUN
ijassa-1367	394	10	.	.	PUNCT
ijassa-1367	394	11	,	,	PUNCT
ijassa-1367	394	12	90(2	90(2	NUM
ijassa-1367	394	13	)	)	PUNCT
ijassa-1367	394	14	,	,	PUNCT
ijassa-1367	394	15	651–653	651–653	NUM
ijassa-1367	394	16	.	.	NOUN
ijassa-1367	394	17	18	18	NUM
ijassa-1367	394	18	.	.	X
ijassa-1367	394	19	orel	orel	PROPN
ijassa-1367	394	20	,	,	PUNCT
ijassa-1367	394	21	e.	e.	PROPN
ijassa-1367	394	22	n.	n.	PROPN
ijassa-1367	394	23	,	,	PUNCT
ijassa-1367	394	24	orel	orel	PROPN
ijassa-1367	394	25	,	,	PUNCT
ijassa-1367	394	26	o.	o.	PROPN
ijassa-1367	394	27	e.	e.	PROPN
ijassa-1367	394	28	(	(	PUNCT
ijassa-1367	394	29	2017	2017	NUM
ijassa-1367	394	30	)	)	PUNCT
ijassa-1367	394	31	optimality	optimality	NOUN
ijassa-1367	394	32	conditions	condition	NOUN
ijassa-1367	394	33	for	for	ADP
ijassa-1367	394	34	central	central	ADJ
ijassa-1367	394	35	fields	field	NOUN
ijassa-1367	394	36	of	of	ADP
ijassa-1367	394	37	trajectories	trajectory	NOUN
ijassa-1367	394	38	,	,	PUNCT
ijassa-1367	394	39	diff	diff	PROPN
ijassa-1367	394	40	.	.	PUNCT
ijassa-1367	395	1	eq	eq	NOUN
ijassa-1367	395	2	.	.	PROPN
ijassa-1367	395	3	cont	cont	PROPN
ijassa-1367	395	4	.	.	PUNCT
ijassa-1367	396	1	proc	proc	PROPN
ijassa-1367	396	2	.	.	PROPN
ijassa-1367	397	1	,	,	PUNCT
ijassa-1367	397	2	1	1	NUM
ijassa-1367	397	3	,	,	PUNCT
ijassa-1367	397	4	53–77	53–77	NUM
ijassa-1367	397	5	.	.	PUNCT
ijassa-1367	398	1	19	19	NUM
ijassa-1367	398	2	.	.	X
ijassa-1367	398	3	orel	orel	PROPN
ijassa-1367	398	4	,	,	PUNCT
ijassa-1367	398	5	e.	e.	PROPN
ijassa-1367	398	6	n.	n.	PROPN
ijassa-1367	398	7	,	,	PUNCT
ijassa-1367	398	8	orel	orel	PROPN
ijassa-1367	398	9	,	,	PUNCT
ijassa-1367	398	10	o.	o.	PROPN
ijassa-1367	398	11	e.	e.	PROPN
ijassa-1367	398	12	(	(	PUNCT
ijassa-1367	398	13	2016	2016	NUM
ijassa-1367	398	14	)	)	PUNCT
ijassa-1367	398	15	.	.	PUNCT
ijassa-1367	399	1	optimal	optimal	ADJ
ijassa-1367	399	2	control	control	NOUN
ijassa-1367	399	3	of	of	ADP
ijassa-1367	399	4	the	the	DET
ijassa-1367	399	5	production	production	NOUN
ijassa-1367	399	6	process	process	NOUN
ijassa-1367	399	7	when	when	SCONJ
ijassa-1367	399	8	fulfilling	fulfil	VERB
ijassa-1367	399	9	an	an	DET
ijassa-1367	399	10	order	order	NOUN
ijassa-1367	399	11	by	by	ADP
ijassa-1367	399	12	a	a	DET
ijassa-1367	399	13	given	give	VERB
ijassa-1367	399	14	deadline	deadline	NOUN
ijassa-1367	399	15	,	,	PUNCT
ijassa-1367	399	16	econom	econom	PROPN
ijassa-1367	399	17	.	.	PROPN
ijassa-1367	399	18	math	math	PROPN
ijassa-1367	399	19	,	,	PUNCT
ijassa-1367	399	20	met	meet	VERB
ijassa-1367	399	21	.	.	PUNCT
ijassa-1367	399	22	,	,	PUNCT
ijassa-1367	399	23	52(2	52(2	NUM
ijassa-1367	399	24	)	)	PUNCT
ijassa-1367	399	25	,	,	PUNCT
ijassa-1367	399	26	65–77	65–77	PROPN
ijassa-1367	399	27	.	.	PUNCT
ijassa-1367	400	1	20	20	NUM
ijassa-1367	400	2	.	.	X
ijassa-1367	400	3	pontryagin	pontryagin	NOUN
ijassa-1367	400	4	,	,	PUNCT
ijassa-1367	400	5	l.	l.	PROPN
ijassa-1367	400	6	s.	s.	PROPN
ijassa-1367	400	7	,	,	PUNCT
ijassa-1367	400	8	boltyanskii	boltyanskii	PROPN
ijassa-1367	400	9	,	,	PUNCT
ijassa-1367	400	10	v.	v.	PROPN
ijassa-1367	400	11	g.	g.	PROPN
ijassa-1367	400	12	,	,	PUNCT
ijassa-1367	400	13	gamkrelidze	gamkrelidze	PROPN
ijassa-1367	400	14	,	,	PUNCT
ijassa-1367	400	15	r.	r.	PROPN
ijassa-1367	400	16	v.	v.	PROPN
ijassa-1367	400	17	,	,	PUNCT
ijassa-1367	400	18	&	&	CCONJ
ijassa-1367	400	19	mischenko	mischenko	PROPN
ijassa-1367	400	20	,	,	PUNCT
ijassa-1367	400	21	e.	e.	PROPN
ijassa-1367	400	22	f.	f.	PROPN
ijassa-1367	400	23	(	(	PUNCT
ijassa-1367	400	24	1962	1962	NUM
ijassa-1367	400	25	)	)	PUNCT
ijassa-1367	400	26	.	.	PUNCT
ijassa-1367	401	1	the	the	DET
ijassa-1367	401	2	mathematical	mathematical	ADJ
ijassa-1367	401	3	theory	theory	NOUN
ijassa-1367	401	4	of	of	ADP
ijassa-1367	401	5	optimal	optimal	ADJ
ijassa-1367	401	6	processes	process	NOUN
ijassa-1367	401	7	,	,	PUNCT
ijassa-1367	401	8	new	new	PROPN
ijassa-1367	401	9	york	york	PROPN
ijassa-1367	401	10	,	,	PUNCT
ijassa-1367	401	11	ny	ny	PROPN
ijassa-1367	401	12	:	:	PUNCT
ijassa-1367	401	13	john	john	PROPN
ijassa-1367	401	14	wiley	wiley	PROPN
ijassa-1367	401	15	and	and	CCONJ
ijassa-1367	401	16	sons	son	NOUN
ijassa-1367	401	17	.	.	PUNCT
ijassa-1367	402	1	21	21	NUM
ijassa-1367	402	2	.	.	PUNCT
ijassa-1367	403	1	zelikin	zelikin	NOUN
ijassa-1367	403	2	,	,	PUNCT
ijassa-1367	403	3	m.	m.	NOUN
ijassa-1367	403	4	i.	i.	PROPN
ijassa-1367	403	5	(	(	PUNCT
ijassa-1367	403	6	2004	2004	NUM
ijassa-1367	403	7	)	)	PUNCT
ijassa-1367	403	8	.	.	PUNCT
ijassa-1367	404	1	optimal	optimal	ADJ
ijassa-1367	404	2	control	control	NOUN
ijassa-1367	404	3	theory	theory	NOUN
ijassa-1367	404	4	and	and	CCONJ
ijassa-1367	404	5	calculus	calculus	NOUN
ijassa-1367	404	6	of	of	ADP
ijassa-1367	404	7	varianions	varianion	NOUN
ijassa-1367	404	8	,	,	PUNCT
ijassa-1367	404	9	moscow	moscow	PROPN
ijassa-1367	404	10	,	,	PUNCT
ijassa-1367	404	11	russia	russia	PROPN
ijassa-1367	404	12	:	:	PUNCT
ijassa-1367	404	13	editorial	editorial	ADJ
ijassa-1367	404	14	urss	urss	NOUN
ijassa-1367	404	15	.	.	PUNCT
ijassa-1367	405	1	copyright	copyright	NOUN
ijassa-1367	405	2	©	©	ADP
ijassa-1367	405	3	2023	2023	NUM
ijassa-1367	405	4	assa	assa	NOUN
ijassa-1367	405	5	.	.	PUNCT
ijassa-1367	406	1	adv	adv	PROPN
ijassa-1367	406	2	syst	syst	PROPN
ijassa-1367	406	3	sci	sci	PROPN
ijassa-1367	406	4	appl	appl	PROPN
ijassa-1367	406	5	(	(	PUNCT
ijassa-1367	406	6	2023	2023	NUM
ijassa-1367	406	7	)	)	PUNCT
ijassa-1367	406	8	introduction	introduction	NOUN
ijassa-1367	406	9	euler	euler	NOUN
ijassa-1367	406	10	field	field	NOUN
ijassa-1367	406	11	of	of	ADP
ijassa-1367	406	12	optimal	optimal	ADJ
ijassa-1367	406	13	polygonal	polygonal	ADJ
ijassa-1367	406	14	lines	line	NOUN
ijassa-1367	406	15	fixed	fix	VERB
ijassa-1367	406	16	time	time	NOUN
ijassa-1367	406	17	optimal	optimal	ADJ
ijassa-1367	406	18	control	control	NOUN
ijassa-1367	406	19	problems	problem	NOUN
ijassa-1367	406	20	generalized	generalize	VERB
ijassa-1367	406	21	polygonal	polygonal	ADJ
ijassa-1367	406	22	lines	line	NOUN
ijassa-1367	406	23	splitting	split	VERB
ijassa-1367	406	24	into	into	ADP
ijassa-1367	406	25	cells	cell	NOUN
ijassa-1367	406	26	optimization	optimization	NOUN
ijassa-1367	406	27	algorithm	algorithm	NOUN
ijassa-1367	406	28	justification	justification	NOUN
ijassa-1367	406	29	of	of	ADP
ijassa-1367	406	30	the	the	DET
ijassa-1367	406	31	algorithm	algorithm	NOUN
ijassa-1367	406	32	economic	economic	ADJ
ijassa-1367	406	33	example	example	NOUN
ijassa-1367	406	34	autonomous	autonomous	ADJ
ijassa-1367	406	35	problems	problem	NOUN
ijassa-1367	406	36	of	of	ADP
ijassa-1367	406	37	optimal	optimal	ADJ
ijassa-1367	406	38	control	control	NOUN
ijassa-1367	406	39	fel'dbaum	fel'dbaum	ADJ
ijassa-1367	406	40	-	-	PUNCT
ijassa-1367	406	41	bushaw	bushaw	ADJ
ijassa-1367	406	42	problem	problem	NOUN
ijassa-1367	406	43	car	car	NOUN
ijassa-1367	406	44	motion	motion	NOUN
ijassa-1367	406	45	to	to	ADP
ijassa-1367	406	46	the	the	DET
ijassa-1367	406	47	parking	parking	NOUN
ijassa-1367	406	48	place	place	NOUN
ijassa-1367	406	49	differential	differential	PROPN
ijassa-1367	406	50	games	game	NOUN
ijassa-1367	406	51	simplest	simple	ADJ
ijassa-1367	406	52	pursuit	pursuit	NOUN
ijassa-1367	406	53	game	game	NOUN
ijassa-1367	406	54	homicidal	homicidal	ADJ
ijassa-1367	406	55	chauffeur	chauffeur	NOUN
ijassa-1367	406	56	game	game	NOUN
ijassa-1367	406	57	game	game	NOUN
ijassa-1367	406	58	of	of	ADP
ijassa-1367	406	59	two	two	NUM
ijassa-1367	406	60	cars	car	NOUN
ijassa-1367	406	61	optimization	optimization	NOUN
ijassa-1367	406	62	in	in	ADP
ijassa-1367	406	63	lack	lack	NOUN
ijassa-1367	406	64	of	of	ADP
ijassa-1367	406	65	information	information	NOUN
ijassa-1367	406	66	problem	problem	NOUN
ijassa-1367	406	67	on	on	ADP
ijassa-1367	406	68	plane	plane	NOUN
ijassa-1367	406	69	inverted	invert	VERB
ijassa-1367	406	70	pendulum	pendulum	NOUN
ijassa-1367	406	71	conclusion	conclusion	NOUN