id	sid	tid	token	lemma	pos
ijassa-1364	1	1	adv	adv	PROPN
ijassa-1364	1	2	syst	syst	PROPN
ijassa-1364	1	3	sci	sci	PROPN
ijassa-1364	1	4	appl	appl	PROPN
ijassa-1364	1	5	2023	2023	NUM
ijassa-1364	1	6	;	;	PUNCT
ijassa-1364	1	7	01:61–68	01:61–68	NOUN
ijassa-1364	1	8	published	publish	VERB
ijassa-1364	1	9	online	online	ADV
ijassa-1364	1	10	at	at	ADP
ijassa-1364	1	11	https://ijassa.ipu.ru	https://ijassa.ipu.ru	ADV
ijassa-1364	1	12	.	.	PUNCT
ijassa-1364	2	1	the	the	DET
ijassa-1364	2	2	problem	problem	NOUN
ijassa-1364	2	3	of	of	ADP
ijassa-1364	2	4	controllability	controllability	NOUN
ijassa-1364	2	5	with	with	ADP
ijassa-1364	2	6	the	the	DET
ijassa-1364	2	7	phase	phase	NOUN
ijassa-1364	2	8	space	space	NOUN
ijassa-1364	2	9	change	change	NOUN
ijassa-1364	2	10	irina	irina	PROPN
ijassa-1364	2	11	maximova	maximova	PROPN
ijassa-1364	2	12	peoples	peoples	PROPN
ijassa-1364	2	13	’	’	PART
ijassa-1364	2	14	friendship	friendship	NOUN
ijassa-1364	2	15	university	university	NOUN
ijassa-1364	2	16	of	of	ADP
ijassa-1364	2	17	russia	russia	PROPN
ijassa-1364	2	18	(	(	PUNCT
ijassa-1364	2	19	rudn	rudn	VERB
ijassa-1364	2	20	university	university	NOUN
ijassa-1364	2	21	)	)	PUNCT
ijassa-1364	2	22	,	,	PUNCT
ijassa-1364	2	23	moscow	moscow	PROPN
ijassa-1364	2	24	,	,	PUNCT
ijassa-1364	2	25	russia	russia	PROPN
ijassa-1364	2	26	abstract	abstract	NOUN
ijassa-1364	2	27	:	:	PUNCT
ijassa-1364	2	28	in	in	ADP
ijassa-1364	2	29	this	this	DET
ijassa-1364	2	30	paper	paper	NOUN
ijassa-1364	2	31	,	,	PUNCT
ijassa-1364	2	32	we	we	PRON
ijassa-1364	2	33	consider	consider	VERB
ijassa-1364	2	34	differential	differential	ADJ
ijassa-1364	2	35	systems	system	NOUN
ijassa-1364	2	36	of	of	ADP
ijassa-1364	2	37	the	the	DET
ijassa-1364	2	38	following	follow	VERB
ijassa-1364	2	39	structure	structure	NOUN
ijassa-1364	2	40	:	:	PUNCT
ijassa-1364	2	41	at	at	ADP
ijassa-1364	2	42	two	two	NUM
ijassa-1364	2	43	consecutive	consecutive	ADJ
ijassa-1364	2	44	time	time	NOUN
ijassa-1364	2	45	intervals	interval	NOUN
ijassa-1364	2	46	the	the	DET
ijassa-1364	2	47	motion	motion	NOUN
ijassa-1364	2	48	of	of	ADP
ijassa-1364	2	49	the	the	DET
ijassa-1364	2	50	object	object	NOUN
ijassa-1364	2	51	is	be	AUX
ijassa-1364	2	52	described	describe	VERB
ijassa-1364	2	53	by	by	ADP
ijassa-1364	2	54	two	two	NUM
ijassa-1364	2	55	different	different	ADJ
ijassa-1364	2	56	systems	system	NOUN
ijassa-1364	2	57	of	of	ADP
ijassa-1364	2	58	differential	differential	ADJ
ijassa-1364	2	59	equations	equation	NOUN
ijassa-1364	2	60	.	.	PUNCT
ijassa-1364	3	1	we	we	PRON
ijassa-1364	3	2	study	study	VERB
ijassa-1364	3	3	the	the	DET
ijassa-1364	3	4	controllability	controllability	NOUN
ijassa-1364	3	5	of	of	ADP
ijassa-1364	3	6	the	the	DET
ijassa-1364	3	7	object	object	NOUN
ijassa-1364	3	8	described	describe	VERB
ijassa-1364	3	9	by	by	ADP
ijassa-1364	3	10	such	such	ADJ
ijassa-1364	3	11	system	system	NOUN
ijassa-1364	3	12	from	from	ADP
ijassa-1364	3	13	the	the	DET
ijassa-1364	3	14	initial	initial	ADJ
ijassa-1364	3	15	set	set	NOUN
ijassa-1364	3	16	in	in	ADP
ijassa-1364	3	17	one	one	NUM
ijassa-1364	3	18	space	space	NOUN
ijassa-1364	3	19	to	to	ADP
ijassa-1364	3	20	the	the	DET
ijassa-1364	3	21	given	give	VERB
ijassa-1364	3	22	set	set	NOUN
ijassa-1364	3	23	in	in	ADP
ijassa-1364	3	24	another	another	DET
ijassa-1364	3	25	space	space	NOUN
ijassa-1364	3	26	through	through	ADP
ijassa-1364	3	27	so	so	ADV
ijassa-1364	3	28	-	-	PUNCT
ijassa-1364	3	29	called	call	VERB
ijassa-1364	3	30	”	"	PUNCT
ijassa-1364	3	31	transition	transition	NOUN
ijassa-1364	3	32	hypersurface	hypersurface	NOUN
ijassa-1364	3	33	”	"	PUNCT
ijassa-1364	3	34	.	.	PUNCT
ijassa-1364	4	1	the	the	DET
ijassa-1364	4	2	transition	transition	NOUN
ijassa-1364	4	3	of	of	ADP
ijassa-1364	4	4	an	an	DET
ijassa-1364	4	5	object	object	NOUN
ijassa-1364	4	6	from	from	ADP
ijassa-1364	4	7	one	one	NUM
ijassa-1364	4	8	space	space	NOUN
ijassa-1364	4	9	to	to	ADP
ijassa-1364	4	10	another	another	DET
ijassa-1364	4	11	one	one	NOUN
ijassa-1364	4	12	is	be	AUX
ijassa-1364	4	13	given	give	VERB
ijassa-1364	4	14	by	by	ADP
ijassa-1364	4	15	a	a	DET
ijassa-1364	4	16	certain	certain	ADJ
ijassa-1364	4	17	reflection	reflection	NOUN
ijassa-1364	4	18	.	.	PUNCT
ijassa-1364	5	1	sufficient	sufficient	ADJ
ijassa-1364	5	2	conditions	condition	NOUN
ijassa-1364	5	3	of	of	ADP
ijassa-1364	5	4	the	the	DET
ijassa-1364	5	5	controllability	controllability	NOUN
ijassa-1364	5	6	of	of	ADP
ijassa-1364	5	7	such	such	ADJ
ijassa-1364	5	8	differential	differential	ADJ
ijassa-1364	5	9	systems	system	NOUN
ijassa-1364	5	10	in	in	ADP
ijassa-1364	5	11	the	the	DET
ijassa-1364	5	12	problem	problem	NOUN
ijassa-1364	5	13	with	with	ADP
ijassa-1364	5	14	phase	phase	NOUN
ijassa-1364	5	15	space	space	NOUN
ijassa-1364	5	16	change	change	NOUN
ijassa-1364	5	17	are	be	AUX
ijassa-1364	5	18	obtained	obtain	VERB
ijassa-1364	5	19	.	.	PUNCT
ijassa-1364	6	1	approaches	approach	NOUN
ijassa-1364	6	2	to	to	ADP
ijassa-1364	6	3	the	the	DET
ijassa-1364	6	4	study	study	NOUN
ijassa-1364	6	5	of	of	ADP
ijassa-1364	6	6	both	both	CCONJ
ijassa-1364	6	7	nonlinear	nonlinear	ADJ
ijassa-1364	6	8	and	and	CCONJ
ijassa-1364	6	9	linear	linear	ADJ
ijassa-1364	6	10	systems	system	NOUN
ijassa-1364	6	11	are	be	AUX
ijassa-1364	6	12	considered	consider	VERB
ijassa-1364	6	13	.	.	PUNCT
ijassa-1364	7	1	keywords	keyword	NOUN
ijassa-1364	7	2	:	:	PUNCT
ijassa-1364	7	3	controllability	controllability	NOUN
ijassa-1364	7	4	,	,	PUNCT
ijassa-1364	7	5	reachability	reachability	NOUN
ijassa-1364	7	6	set	set	NOUN
ijassa-1364	7	7	,	,	PUNCT
ijassa-1364	7	8	multiple	multiple	ADV
ijassa-1364	7	9	-	-	PUNCT
ijassa-1364	7	10	valued	value	VERB
ijassa-1364	7	11	mapping	mapping	NOUN
ijassa-1364	7	12	,	,	PUNCT
ijassa-1364	7	13	support	support	NOUN
ijassa-1364	7	14	function	function	NOUN
ijassa-1364	7	15	1	1	NUM
ijassa-1364	7	16	.	.	PUNCT
ijassa-1364	7	17	introduction	introduction	NOUN
ijassa-1364	7	18	problems	problem	NOUN
ijassa-1364	7	19	with	with	ADP
ijassa-1364	7	20	the	the	DET
ijassa-1364	7	21	change	change	NOUN
ijassa-1364	7	22	of	of	ADP
ijassa-1364	7	23	the	the	DET
ijassa-1364	7	24	phase	phase	NOUN
ijassa-1364	7	25	space	space	NOUN
ijassa-1364	7	26	are	be	AUX
ijassa-1364	7	27	an	an	DET
ijassa-1364	7	28	important	important	ADJ
ijassa-1364	7	29	class	class	NOUN
ijassa-1364	7	30	of	of	ADP
ijassa-1364	7	31	so	so	ADV
ijassa-1364	7	32	-	-	PUNCT
ijassa-1364	7	33	called	call	VERB
ijassa-1364	7	34	hybrid	hybrid	NOUN
ijassa-1364	7	35	(	(	PUNCT
ijassa-1364	7	36	composite	composite	ADJ
ijassa-1364	7	37	)	)	PUNCT
ijassa-1364	7	38	systems	system	NOUN
ijassa-1364	7	39	,	,	PUNCT
ijassa-1364	7	40	they	they	PRON
ijassa-1364	7	41	are	be	AUX
ijassa-1364	7	42	characterized	characterize	VERB
ijassa-1364	7	43	by	by	ADP
ijassa-1364	7	44	the	the	DET
ijassa-1364	7	45	condition	condition	NOUN
ijassa-1364	7	46	that	that	SCONJ
ijassa-1364	7	47	at	at	ADP
ijassa-1364	7	48	different	different	ADJ
ijassa-1364	7	49	time	time	NOUN
ijassa-1364	7	50	intervals	interval	NOUN
ijassa-1364	7	51	the	the	DET
ijassa-1364	7	52	motion	motion	NOUN
ijassa-1364	7	53	of	of	ADP
ijassa-1364	7	54	the	the	DET
ijassa-1364	7	55	object	object	NOUN
ijassa-1364	7	56	is	be	AUX
ijassa-1364	7	57	described	describe	VERB
ijassa-1364	7	58	by	by	ADP
ijassa-1364	7	59	different	different	ADJ
ijassa-1364	7	60	differential	differential	ADJ
ijassa-1364	7	61	equations	equation	NOUN
ijassa-1364	7	62	and	and	CCONJ
ijassa-1364	7	63	some	some	DET
ijassa-1364	7	64	links	link	NOUN
ijassa-1364	7	65	for	for	ADP
ijassa-1364	7	66	trajectory	trajectory	NOUN
ijassa-1364	7	67	mating	mating	NOUN
ijassa-1364	7	68	.	.	PUNCT
ijassa-1364	8	1	the	the	DET
ijassa-1364	8	2	initial	initial	ADJ
ijassa-1364	8	3	source	source	NOUN
ijassa-1364	8	4	of	of	ADP
ijassa-1364	8	5	such	such	ADJ
ijassa-1364	8	6	problems	problem	NOUN
ijassa-1364	8	7	was	be	AUX
ijassa-1364	8	8	the	the	DET
ijassa-1364	8	9	multistage	multistage	NOUN
ijassa-1364	8	10	processes	process	NOUN
ijassa-1364	8	11	of	of	ADP
ijassa-1364	8	12	space	space	NOUN
ijassa-1364	8	13	flight	flight	NOUN
ijassa-1364	8	14	(	(	PUNCT
ijassa-1364	8	15	see	see	VERB
ijassa-1364	8	16	[	[	X
ijassa-1364	8	17	16	16	NUM
ijassa-1364	8	18	]	]	SYM
ijassa-1364	8	19	)	)	PUNCT
ijassa-1364	8	20	.	.	PUNCT
ijassa-1364	9	1	problems	problem	NOUN
ijassa-1364	9	2	with	with	ADP
ijassa-1364	9	3	the	the	DET
ijassa-1364	9	4	phase	phase	NOUN
ijassa-1364	9	5	space	space	NOUN
ijassa-1364	9	6	change	change	NOUN
ijassa-1364	9	7	arise	arise	VERB
ijassa-1364	9	8	in	in	ADP
ijassa-1364	9	9	various	various	ADJ
ijassa-1364	9	10	applied	apply	VERB
ijassa-1364	9	11	problems	problem	NOUN
ijassa-1364	9	12	,	,	PUNCT
ijassa-1364	9	13	including	include	VERB
ijassa-1364	9	14	aircraft	aircraft	NOUN
ijassa-1364	9	15	engineering	engineering	NOUN
ijassa-1364	9	16	,	,	PUNCT
ijassa-1364	9	17	robotics	robotic	NOUN
ijassa-1364	9	18	,	,	PUNCT
ijassa-1364	9	19	economics	economic	NOUN
ijassa-1364	9	20	,	,	PUNCT
ijassa-1364	9	21	etc	etc	X
ijassa-1364	9	22	.	.	X
ijassa-1364	9	23	for	for	ADP
ijassa-1364	9	24	example	example	NOUN
ijassa-1364	9	25	,	,	PUNCT
ijassa-1364	9	26	the	the	DET
ijassa-1364	9	27	problem	problem	NOUN
ijassa-1364	9	28	of	of	ADP
ijassa-1364	9	29	launching	launch	VERB
ijassa-1364	9	30	a	a	DET
ijassa-1364	9	31	missile	missile	NOUN
ijassa-1364	9	32	from	from	ADP
ijassa-1364	9	33	an	an	DET
ijassa-1364	9	34	underwater	underwater	ADJ
ijassa-1364	9	35	object	object	NOUN
ijassa-1364	9	36	:	:	PUNCT
ijassa-1364	9	37	in	in	ADP
ijassa-1364	9	38	this	this	DET
ijassa-1364	9	39	case	case	NOUN
ijassa-1364	9	40	the	the	DET
ijassa-1364	9	41	dimension	dimension	NOUN
ijassa-1364	9	42	of	of	ADP
ijassa-1364	9	43	the	the	DET
ijassa-1364	9	44	space	space	NOUN
ijassa-1364	9	45	does	do	AUX
ijassa-1364	9	46	not	not	PART
ijassa-1364	9	47	change	change	VERB
ijassa-1364	9	48	,	,	PUNCT
ijassa-1364	9	49	but	but	CCONJ
ijassa-1364	9	50	the	the	DET
ijassa-1364	9	51	environment	environment	NOUN
ijassa-1364	9	52	and	and	CCONJ
ijassa-1364	9	53	conditions	condition	NOUN
ijassa-1364	9	54	of	of	ADP
ijassa-1364	9	55	the	the	DET
ijassa-1364	9	56	motion	motion	NOUN
ijassa-1364	9	57	do	do	VERB
ijassa-1364	9	58	.	.	PUNCT
ijassa-1364	10	1	the	the	DET
ijassa-1364	10	2	change	change	NOUN
ijassa-1364	10	3	of	of	ADP
ijassa-1364	10	4	the	the	DET
ijassa-1364	10	5	phase	phase	NOUN
ijassa-1364	10	6	spaces	space	NOUN
ijassa-1364	10	7	can	can	AUX
ijassa-1364	10	8	occur	occur	VERB
ijassa-1364	10	9	in	in	ADP
ijassa-1364	10	10	the	the	DET
ijassa-1364	10	11	mathematical	mathematical	ADJ
ijassa-1364	10	12	modeling	modeling	NOUN
ijassa-1364	10	13	of	of	ADP
ijassa-1364	10	14	complex	complex	ADJ
ijassa-1364	10	15	dynamic	dynamic	ADJ
ijassa-1364	10	16	systems	system	NOUN
ijassa-1364	10	17	,	,	PUNCT
ijassa-1364	10	18	for	for	ADP
ijassa-1364	10	19	example	example	NOUN
ijassa-1364	10	20	,	,	PUNCT
ijassa-1364	10	21	large	large	ADJ
ijassa-1364	10	22	production	production	NOUN
ijassa-1364	10	23	complexes	complex	NOUN
ijassa-1364	10	24	,	,	PUNCT
ijassa-1364	10	25	multistage	multistage	NOUN
ijassa-1364	10	26	technological	technological	ADJ
ijassa-1364	10	27	processes	process	NOUN
ijassa-1364	10	28	.	.	PUNCT
ijassa-1364	11	1	the	the	DET
ijassa-1364	11	2	process	process	NOUN
ijassa-1364	11	3	of	of	ADP
ijassa-1364	11	4	controlling	control	VERB
ijassa-1364	11	5	a	a	DET
ijassa-1364	11	6	system	system	NOUN
ijassa-1364	11	7	of	of	ADP
ijassa-1364	11	8	chemical	chemical	ADJ
ijassa-1364	11	9	reactors	reactor	NOUN
ijassa-1364	11	10	,	,	PUNCT
ijassa-1364	11	11	models	model	NOUN
ijassa-1364	11	12	of	of	ADP
ijassa-1364	11	13	the	the	DET
ijassa-1364	11	14	dynamics	dynamic	NOUN
ijassa-1364	11	15	of	of	ADP
ijassa-1364	11	16	metapopulations	metapopulation	NOUN
ijassa-1364	11	17	,	,	PUNCT
ijassa-1364	11	18	and	and	CCONJ
ijassa-1364	11	19	economic	economic	ADJ
ijassa-1364	11	20	systems	system	NOUN
ijassa-1364	11	21	with	with	ADP
ijassa-1364	11	22	a	a	DET
ijassa-1364	11	23	variable	variable	ADJ
ijassa-1364	11	24	structure	structure	NOUN
ijassa-1364	11	25	are	be	AUX
ijassa-1364	11	26	also	also	ADV
ijassa-1364	11	27	characterized	characterize	VERB
ijassa-1364	11	28	by	by	ADP
ijassa-1364	11	29	a	a	DET
ijassa-1364	11	30	sequence	sequence	NOUN
ijassa-1364	11	31	of	of	ADP
ijassa-1364	11	32	consecutive	consecutive	ADJ
ijassa-1364	11	33	stages	stage	NOUN
ijassa-1364	11	34	.	.	PUNCT
ijassa-1364	12	1	the	the	DET
ijassa-1364	12	2	dimensionality	dimensionality	NOUN
ijassa-1364	12	3	of	of	ADP
ijassa-1364	12	4	dynamic	dynamic	ADJ
ijassa-1364	12	5	systems	system	NOUN
ijassa-1364	12	6	used	use	VERB
ijassa-1364	12	7	when	when	SCONJ
ijassa-1364	12	8	modelling	model	VERB
ijassa-1364	12	9	these	these	DET
ijassa-1364	12	10	processes	process	NOUN
ijassa-1364	12	11	depends	depend	VERB
ijassa-1364	12	12	on	on	ADP
ijassa-1364	12	13	their	their	PRON
ijassa-1364	12	14	state	state	NOUN
ijassa-1364	12	15	and	and	CCONJ
ijassa-1364	12	16	can	can	AUX
ijassa-1364	12	17	change	change	VERB
ijassa-1364	12	18	over	over	ADP
ijassa-1364	12	19	time	time	NOUN
ijassa-1364	12	20	,	,	PUNCT
ijassa-1364	12	21	i.e.	i.e.	X
ijassa-1364	12	22	the	the	DET
ijassa-1364	12	23	decomposition	decomposition	NOUN
ijassa-1364	12	24	of	of	ADP
ijassa-1364	12	25	the	the	DET
ijassa-1364	12	26	complex	complex	ADJ
ijassa-1364	12	27	system	system	NOUN
ijassa-1364	12	28	is	be	AUX
ijassa-1364	12	29	taking	take	VERB
ijassa-1364	12	30	place	place	NOUN
ijassa-1364	12	31	.	.	PUNCT
ijassa-1364	13	1	the	the	DET
ijassa-1364	13	2	possibility	possibility	NOUN
ijassa-1364	13	3	of	of	ADP
ijassa-1364	13	4	using	use	VERB
ijassa-1364	13	5	systems	system	NOUN
ijassa-1364	13	6	with	with	ADP
ijassa-1364	13	7	the	the	DET
ijassa-1364	13	8	variable	variable	ADJ
ijassa-1364	13	9	dimensionality	dimensionality	NOUN
ijassa-1364	13	10	in	in	ADP
ijassa-1364	13	11	modeling	model	VERB
ijassa-1364	13	12	the	the	DET
ijassa-1364	13	13	dynamics	dynamic	NOUN
ijassa-1364	13	14	of	of	ADP
ijassa-1364	13	15	biological	biological	ADJ
ijassa-1364	13	16	communities	community	NOUN
ijassa-1364	13	17	was	be	AUX
ijassa-1364	13	18	pointed	point	VERB
ijassa-1364	13	19	out	out	ADP
ijassa-1364	13	20	in	in	ADP
ijassa-1364	13	21	the	the	DET
ijassa-1364	13	22	work	work	NOUN
ijassa-1364	13	23	[	[	X
ijassa-1364	13	24	15	15	NUM
ijassa-1364	13	25	]	]	PUNCT
ijassa-1364	13	26	.	.	PUNCT
ijassa-1364	14	1	during	during	ADP
ijassa-1364	14	2	the	the	DET
ijassa-1364	14	3	construction	construction	NOUN
ijassa-1364	14	4	of	of	ADP
ijassa-1364	14	5	realization	realization	NOUN
ijassa-1364	14	6	theory	theory	NOUN
ijassa-1364	14	7	,	,	PUNCT
ijassa-1364	14	8	r.	r.	PROPN
ijassa-1364	14	9	kalman	kalman	PROPN
ijassa-1364	14	10	proposed	propose	VERB
ijassa-1364	14	11	to	to	PART
ijassa-1364	14	12	generalize	generalize	VERB
ijassa-1364	14	13	the	the	DET
ijassa-1364	14	14	notion	notion	NOUN
ijassa-1364	14	15	of	of	ADP
ijassa-1364	14	16	dynamic	dynamic	ADJ
ijassa-1364	14	17	system	system	NOUN
ijassa-1364	14	18	that	that	PRON
ijassa-1364	14	19	the	the	DET
ijassa-1364	14	20	dimensionality	dimensionality	NOUN
ijassa-1364	14	21	of	of	ADP
ijassa-1364	14	22	its	its	PRON
ijassa-1364	14	23	space	space	NOUN
ijassa-1364	14	24	of	of	ADP
ijassa-1364	14	25	states	state	NOUN
ijassa-1364	14	26	could	could	AUX
ijassa-1364	14	27	change	change	VERB
ijassa-1364	14	28	over	over	ADP
ijassa-1364	14	29	time	time	NOUN
ijassa-1364	14	30	(	(	PUNCT
ijassa-1364	14	31	see	see	VERB
ijassa-1364	14	32	[	[	X
ijassa-1364	14	33	9	9	NUM
ijassa-1364	14	34	]	]	NUM
ijassa-1364	14	35	)	)	PUNCT
ijassa-1364	14	36	.	.	PUNCT
ijassa-1364	15	1	problems	problem	NOUN
ijassa-1364	15	2	of	of	ADP
ijassa-1364	15	3	optimal	optimal	ADJ
ijassa-1364	15	4	control	control	NOUN
ijassa-1364	15	5	of	of	ADP
ijassa-1364	15	6	composite	composite	ADJ
ijassa-1364	15	7	systems	system	NOUN
ijassa-1364	15	8	were	be	AUX
ijassa-1364	15	9	studied	study	VERB
ijassa-1364	15	10	at	at	ADP
ijassa-1364	15	11	different	different	ADJ
ijassa-1364	15	12	times	time	NOUN
ijassa-1364	15	13	by	by	ADP
ijassa-1364	15	14	,	,	PUNCT
ijassa-1364	15	15	for	for	ADP
ijassa-1364	15	16	example	example	NOUN
ijassa-1364	15	17	,	,	PUNCT
ijassa-1364	15	18	v.g	v.g	PROPN
ijassa-1364	15	19	.	.	PROPN
ijassa-1364	15	20	boltyansky	boltyansky	PROPN
ijassa-1364	15	21	,	,	PUNCT
ijassa-1364	15	22	l.t	l.t	PROPN
ijassa-1364	15	23	.	.	PROPN
ijassa-1364	15	24	ashchepkov	ashchepkov	PROPN
ijassa-1364	15	25	,	,	PUNCT
ijassa-1364	15	26	and	and	CCONJ
ijassa-1364	15	27	v.n	v.n	PROPN
ijassa-1364	15	28	.	.	PROPN
ijassa-1364	15	29	rozova	rozova	PROPN
ijassa-1364	15	30	.	.	PUNCT
ijassa-1364	16	1	necessary	necessary	ADJ
ijassa-1364	16	2	optimality	optimality	NOUN
ijassa-1364	16	3	conditions	condition	NOUN
ijassa-1364	16	4	were	be	AUX
ijassa-1364	16	5	derived	derive	VERB
ijassa-1364	16	6	in	in	ADP
ijassa-1364	16	7	the	the	DET
ijassa-1364	16	8	general	general	ADJ
ijassa-1364	16	9	problem	problem	NOUN
ijassa-1364	16	10	of	of	ADP
ijassa-1364	16	11	control	control	NOUN
ijassa-1364	16	12	with	with	ADP
ijassa-1364	16	13	intermediate	intermediate	ADJ
ijassa-1364	16	14	constraints	constraint	NOUN
ijassa-1364	16	15	on	on	ADP
ijassa-1364	16	16	the	the	DET
ijassa-1364	16	17	trajectory	trajectory	NOUN
ijassa-1364	16	18	(	(	PUNCT
ijassa-1364	16	19	see	see	VERB
ijassa-1364	16	20	[	[	X
ijassa-1364	16	21	2	2	NUM
ijassa-1364	16	22	]	]	PUNCT
ijassa-1364	16	23	)	)	PUNCT
ijassa-1364	16	24	.	.	PUNCT
ijassa-1364	17	1	in	in	ADP
ijassa-1364	17	2	the	the	DET
ijassa-1364	17	3	paper	paper	NOUN
ijassa-1364	17	4	[	[	X
ijassa-1364	17	5	7	7	NUM
ijassa-1364	17	6	]	]	PUNCT
ijassa-1364	17	7	,	,	PUNCT
ijassa-1364	17	8	the	the	DET
ijassa-1364	17	9	necessary	necessary	ADJ
ijassa-1364	17	10	optimality	optimality	NOUN
ijassa-1364	17	11	conditions	condition	NOUN
ijassa-1364	17	12	for	for	ADP
ijassa-1364	17	13	the	the	DET
ijassa-1364	17	14	problem	problem	NOUN
ijassa-1364	17	15	with	with	ADP
ijassa-1364	17	16	a	a	DET
ijassa-1364	17	17	phase	phase	NOUN
ijassa-1364	17	18	space	space	NOUN
ijassa-1364	17	19	change	change	NOUN
ijassa-1364	17	20	were	be	AUX
ijassa-1364	17	21	obtained	obtain	VERB
ijassa-1364	17	22	.	.	PUNCT
ijassa-1364	18	1	the	the	DET
ijassa-1364	18	2	paper	paper	NOUN
ijassa-1364	18	3	[	[	X
ijassa-1364	18	4	14	14	NUM
ijassa-1364	18	5	]	]	PUNCT
ijassa-1364	18	6	considers	consider	VERB
ijassa-1364	18	7	the	the	DET
ijassa-1364	18	8	problem	problem	NOUN
ijassa-1364	18	9	of	of	ADP
ijassa-1364	18	10	optimal	optimal	ADJ
ijassa-1364	18	11	control	control	NOUN
ijassa-1364	18	12	of	of	ADP
ijassa-1364	18	13	several	several	ADJ
ijassa-1364	18	14	objects	object	NOUN
ijassa-1364	18	15	with	with	ADP
ijassa-1364	18	16	sequential	sequential	ADJ
ijassa-1364	18	17	mode	mode	NOUN
ijassa-1364	18	18	of	of	ADP
ijassa-1364	18	19	operation	operation	NOUN
ijassa-1364	18	20	.	.	PUNCT
ijassa-1364	19	1	the	the	DET
ijassa-1364	19	2	initial	initial	ADJ
ijassa-1364	19	3	state	state	NOUN
ijassa-1364	19	4	of	of	ADP
ijassa-1364	19	5	each	each	DET
ijassa-1364	19	6	subsequent	subsequent	ADJ
ijassa-1364	19	7	object	object	NOUN
ijassa-1364	19	8	depends	depend	VERB
ijassa-1364	19	9	on	on	ADP
ijassa-1364	19	10	the	the	DET
ijassa-1364	19	11	final	final	ADJ
ijassa-1364	19	12	state	state	NOUN
ijassa-1364	19	13	of	of	ADP
ijassa-1364	19	14	∗corresponding	∗corresponde	VERB
ijassa-1364	19	15	author	author	NOUN
ijassa-1364	19	16	:	:	PUNCT
ijassa-1364	19	17	maximova-is@rudn.ru	maximova-is@rudn.ru	PROPN
ijassa-1364	19	18	62	62	NUM
ijassa-1364	19	19	i.	i.	NOUN
ijassa-1364	19	20	maximova	maximova	NOUN
ijassa-1364	19	21	the	the	DET
ijassa-1364	19	22	previous	previous	ADJ
ijassa-1364	19	23	one	one	NUM
ijassa-1364	19	24	.	.	PUNCT
ijassa-1364	20	1	each	each	DET
ijassa-1364	20	2	object	object	NOUN
ijassa-1364	20	3	is	be	AUX
ijassa-1364	20	4	described	describe	VERB
ijassa-1364	20	5	by	by	ADP
ijassa-1364	20	6	a	a	DET
ijassa-1364	20	7	system	system	NOUN
ijassa-1364	20	8	of	of	ADP
ijassa-1364	20	9	ordinary	ordinary	ADJ
ijassa-1364	20	10	differential	differential	ADJ
ijassa-1364	20	11	equations	equation	NOUN
ijassa-1364	20	12	on	on	ADP
ijassa-1364	20	13	the	the	DET
ijassa-1364	20	14	interval	interval	NOUN
ijassa-1364	20	15	of	of	ADP
ijassa-1364	20	16	its	its	PRON
ijassa-1364	20	17	action	action	NOUN
ijassa-1364	20	18	.	.	PUNCT
ijassa-1364	21	1	necessary	necessary	ADJ
ijassa-1364	21	2	and	and	CCONJ
ijassa-1364	21	3	sufficient	sufficient	ADJ
ijassa-1364	21	4	optimality	optimality	NOUN
ijassa-1364	21	5	conditions	condition	NOUN
ijassa-1364	21	6	were	be	AUX
ijassa-1364	21	7	obtained	obtain	VERB
ijassa-1364	21	8	for	for	ADP
ijassa-1364	21	9	the	the	DET
ijassa-1364	21	10	problem	problem	NOUN
ijassa-1364	21	11	of	of	ADP
ijassa-1364	21	12	optimal	optimal	ADJ
ijassa-1364	21	13	control	control	NOUN
ijassa-1364	21	14	with	with	ADP
ijassa-1364	21	15	a	a	DET
ijassa-1364	21	16	criterion	criterion	NOUN
ijassa-1364	21	17	of	of	ADP
ijassa-1364	21	18	sufficiently	sufficiently	ADV
ijassa-1364	21	19	general	general	ADJ
ijassa-1364	21	20	form	form	NOUN
ijassa-1364	21	21	.	.	PUNCT
ijassa-1364	22	1	necessary	necessary	ADJ
ijassa-1364	22	2	optimality	optimality	NOUN
ijassa-1364	22	3	conditions	condition	NOUN
ijassa-1364	22	4	for	for	ADP
ijassa-1364	22	5	the	the	DET
ijassa-1364	22	6	problem	problem	NOUN
ijassa-1364	22	7	with	with	ADP
ijassa-1364	22	8	a	a	DET
ijassa-1364	22	9	change	change	NOUN
ijassa-1364	22	10	of	of	ADP
ijassa-1364	22	11	phase	phase	NOUN
ijassa-1364	22	12	space	space	NOUN
ijassa-1364	22	13	were	be	AUX
ijassa-1364	22	14	obtained	obtain	VERB
ijassa-1364	22	15	by	by	ADP
ijassa-1364	22	16	maximova	maximova	NOUN
ijassa-1364	22	17	in	in	ADP
ijassa-1364	22	18	[	[	X
ijassa-1364	22	19	11	11	NUM
ijassa-1364	22	20	]	]	PUNCT
ijassa-1364	22	21	.	.	PUNCT
ijassa-1364	23	1	the	the	DET
ijassa-1364	23	2	results	result	NOUN
ijassa-1364	23	3	were	be	AUX
ijassa-1364	23	4	generalized	generalize	VERB
ijassa-1364	23	5	to	to	ADP
ijassa-1364	23	6	the	the	DET
ijassa-1364	23	7	case	case	NOUN
ijassa-1364	23	8	of	of	ADP
ijassa-1364	23	9	several	several	ADJ
ijassa-1364	23	10	spaces	space	NOUN
ijassa-1364	23	11	.	.	PUNCT
ijassa-1364	24	1	in	in	ADP
ijassa-1364	24	2	many	many	ADJ
ijassa-1364	24	3	works	work	NOUN
ijassa-1364	24	4	devoted	devote	VERB
ijassa-1364	24	5	to	to	ADP
ijassa-1364	24	6	problems	problem	NOUN
ijassa-1364	24	7	of	of	ADP
ijassa-1364	24	8	this	this	DET
ijassa-1364	24	9	kind	kind	NOUN
ijassa-1364	24	10	,	,	PUNCT
ijassa-1364	24	11	the	the	DET
ijassa-1364	24	12	optimization	optimization	NOUN
ijassa-1364	24	13	issue	issue	NOUN
ijassa-1364	24	14	is	be	AUX
ijassa-1364	24	15	mainly	mainly	ADV
ijassa-1364	24	16	studied	study	VERB
ijassa-1364	24	17	.	.	PUNCT
ijassa-1364	25	1	meanwhile	meanwhile	ADV
ijassa-1364	25	2	,	,	PUNCT
ijassa-1364	25	3	typical	typical	ADJ
ijassa-1364	25	4	theorems	theorem	NOUN
ijassa-1364	25	5	of	of	ADP
ijassa-1364	25	6	the	the	DET
ijassa-1364	25	7	existence	existence	NOUN
ijassa-1364	25	8	of	of	ADP
ijassa-1364	25	9	optimal	optimal	ADJ
ijassa-1364	25	10	control	control	NOUN
ijassa-1364	25	11	assume	assume	VERB
ijassa-1364	25	12	the	the	DET
ijassa-1364	25	13	existence	existence	NOUN
ijassa-1364	25	14	of	of	ADP
ijassa-1364	25	15	at	at	ADV
ijassa-1364	25	16	least	least	ADV
ijassa-1364	25	17	one	one	NUM
ijassa-1364	25	18	admissible	admissible	ADJ
ijassa-1364	25	19	control	control	NOUN
ijassa-1364	25	20	that	that	PRON
ijassa-1364	25	21	generates	generate	VERB
ijassa-1364	25	22	a	a	DET
ijassa-1364	25	23	trajectory	trajectory	NOUN
ijassa-1364	25	24	that	that	PRON
ijassa-1364	25	25	satisfies	satisfy	VERB
ijassa-1364	25	26	the	the	DET
ijassa-1364	25	27	given	give	VERB
ijassa-1364	25	28	boundary	boundary	ADJ
ijassa-1364	25	29	conditions	condition	NOUN
ijassa-1364	25	30	,	,	PUNCT
ijassa-1364	25	31	for	for	ADP
ijassa-1364	25	32	example	example	NOUN
ijassa-1364	25	33	,	,	PUNCT
ijassa-1364	25	34	a	a	DET
ijassa-1364	25	35	control	control	NOUN
ijassa-1364	25	36	that	that	PRON
ijassa-1364	25	37	translates	translate	VERB
ijassa-1364	25	38	a	a	DET
ijassa-1364	25	39	trajectory	trajectory	NOUN
ijassa-1364	25	40	from	from	ADP
ijassa-1364	25	41	one	one	NUM
ijassa-1364	25	42	given	give	VERB
ijassa-1364	25	43	position	position	NOUN
ijassa-1364	25	44	to	to	ADP
ijassa-1364	25	45	another	another	PRON
ijassa-1364	25	46	.	.	PUNCT
ijassa-1364	26	1	the	the	DET
ijassa-1364	26	2	latter	latter	ADJ
ijassa-1364	26	3	problem	problem	NOUN
ijassa-1364	26	4	is	be	AUX
ijassa-1364	26	5	the	the	DET
ijassa-1364	26	6	essence	essence	NOUN
ijassa-1364	26	7	of	of	ADP
ijassa-1364	26	8	the	the	DET
ijassa-1364	26	9	controllability	controllability	NOUN
ijassa-1364	26	10	problem	problem	NOUN
ijassa-1364	26	11	.	.	PUNCT
ijassa-1364	27	1	thus	thus	ADV
ijassa-1364	27	2	,	,	PUNCT
ijassa-1364	27	3	the	the	DET
ijassa-1364	27	4	problem	problem	NOUN
ijassa-1364	27	5	of	of	ADP
ijassa-1364	27	6	controllability	controllability	NOUN
ijassa-1364	27	7	is	be	AUX
ijassa-1364	27	8	important	important	ADJ
ijassa-1364	27	9	and	and	CCONJ
ijassa-1364	27	10	relevant	relevant	ADJ
ijassa-1364	27	11	in	in	ADP
ijassa-1364	27	12	solving	solve	VERB
ijassa-1364	27	13	optimal	optimal	ADJ
ijassa-1364	27	14	control	control	NOUN
ijassa-1364	27	15	problems	problem	NOUN
ijassa-1364	27	16	.	.	PUNCT
ijassa-1364	28	1	in	in	ADP
ijassa-1364	28	2	the	the	DET
ijassa-1364	28	3	paper	paper	NOUN
ijassa-1364	28	4	[	[	X
ijassa-1364	28	5	3	3	NUM
ijassa-1364	28	6	]	]	PUNCT
ijassa-1364	28	7	,	,	PUNCT
ijassa-1364	28	8	bargsegyan	bargsegyan	PROPN
ijassa-1364	28	9	v.r	v.r	PROPN
ijassa-1364	28	10	.	.	PROPN
ijassa-1364	28	11	considered	consider	VERB
ijassa-1364	28	12	a	a	DET
ijassa-1364	28	13	mathematical	mathematical	ADJ
ijassa-1364	28	14	model	model	NOUN
ijassa-1364	28	15	of	of	ADP
ijassa-1364	28	16	control	control	NOUN
ijassa-1364	28	17	of	of	ADP
ijassa-1364	28	18	linear	linear	ADJ
ijassa-1364	28	19	composite	composite	ADJ
ijassa-1364	28	20	systems	system	NOUN
ijassa-1364	28	21	described	describe	VERB
ijassa-1364	28	22	at	at	ADP
ijassa-1364	28	23	different	different	ADJ
ijassa-1364	28	24	time	time	NOUN
ijassa-1364	28	25	intervals	interval	NOUN
ijassa-1364	28	26	by	by	ADP
ijassa-1364	28	27	different	different	ADJ
ijassa-1364	28	28	differential	differential	ADJ
ijassa-1364	28	29	equations	equation	NOUN
ijassa-1364	28	30	and	and	CCONJ
ijassa-1364	28	31	some	some	DET
ijassa-1364	28	32	finite	finite	ADJ
ijassa-1364	28	33	relations	relation	NOUN
ijassa-1364	28	34	for	for	ADP
ijassa-1364	28	35	continuity	continuity	NOUN
ijassa-1364	28	36	of	of	ADP
ijassa-1364	28	37	motion	motion	NOUN
ijassa-1364	28	38	of	of	ADP
ijassa-1364	28	39	composite	composite	ADJ
ijassa-1364	28	40	systems	system	NOUN
ijassa-1364	28	41	.	.	PUNCT
ijassa-1364	29	1	the	the	DET
ijassa-1364	29	2	analytical	analytical	ADJ
ijassa-1364	29	3	view	view	NOUN
ijassa-1364	29	4	of	of	ADP
ijassa-1364	29	5	motion	motion	NOUN
ijassa-1364	29	6	of	of	ADP
ijassa-1364	29	7	composite	composite	ADJ
ijassa-1364	29	8	systems	system	NOUN
ijassa-1364	29	9	is	be	AUX
ijassa-1364	29	10	constructed	construct	VERB
ijassa-1364	29	11	,	,	PUNCT
ijassa-1364	29	12	the	the	DET
ijassa-1364	29	13	properties	property	NOUN
ijassa-1364	29	14	of	of	ADP
ijassa-1364	29	15	motion	motion	NOUN
ijassa-1364	29	16	and	and	CCONJ
ijassa-1364	29	17	the	the	DET
ijassa-1364	29	18	geometrical	geometrical	ADJ
ijassa-1364	29	19	structure	structure	NOUN
ijassa-1364	29	20	of	of	ADP
ijassa-1364	29	21	the	the	DET
ijassa-1364	29	22	reachability	reachability	NOUN
ijassa-1364	29	23	region	region	NOUN
ijassa-1364	29	24	were	be	AUX
ijassa-1364	29	25	investigated	investigate	VERB
ijassa-1364	29	26	.	.	PUNCT
ijassa-1364	30	1	necessary	necessary	ADJ
ijassa-1364	30	2	and	and	CCONJ
ijassa-1364	30	3	sufficient	sufficient	ADJ
ijassa-1364	30	4	conditions	condition	NOUN
ijassa-1364	30	5	for	for	ADP
ijassa-1364	30	6	the	the	DET
ijassa-1364	30	7	complete	complete	ADJ
ijassa-1364	30	8	controllability	controllability	NOUN
ijassa-1364	30	9	were	be	AUX
ijassa-1364	30	10	formulated	formulate	VERB
ijassa-1364	30	11	.	.	PUNCT
ijassa-1364	31	1	the	the	DET
ijassa-1364	31	2	method	method	NOUN
ijassa-1364	31	3	of	of	ADP
ijassa-1364	31	4	solving	solve	VERB
ijassa-1364	31	5	the	the	DET
ijassa-1364	31	6	problem	problem	NOUN
ijassa-1364	31	7	of	of	ADP
ijassa-1364	31	8	control	control	NOUN
ijassa-1364	31	9	of	of	ADP
ijassa-1364	31	10	composite	composite	ADJ
ijassa-1364	31	11	systems	system	NOUN
ijassa-1364	31	12	and	and	CCONJ
ijassa-1364	31	13	the	the	DET
ijassa-1364	31	14	method	method	NOUN
ijassa-1364	31	15	of	of	ADP
ijassa-1364	31	16	solving	solve	VERB
ijassa-1364	31	17	the	the	DET
ijassa-1364	31	18	problem	problem	NOUN
ijassa-1364	31	19	of	of	ADP
ijassa-1364	31	20	optimal	optimal	ADJ
ijassa-1364	31	21	control	control	NOUN
ijassa-1364	31	22	were	be	AUX
ijassa-1364	31	23	proposed	propose	VERB
ijassa-1364	31	24	.	.	PUNCT
ijassa-1364	32	1	the	the	DET
ijassa-1364	32	2	monograph	monograph	NOUN
ijassa-1364	33	1	[	[	X
ijassa-1364	33	2	4	4	X
ijassa-1364	33	3	]	]	PUNCT
ijassa-1364	33	4	is	be	AUX
ijassa-1364	33	5	devoted	devote	VERB
ijassa-1364	33	6	to	to	ADP
ijassa-1364	33	7	the	the	DET
ijassa-1364	33	8	control	control	NOUN
ijassa-1364	33	9	problems	problem	NOUN
ijassa-1364	33	10	of	of	ADP
ijassa-1364	33	11	composite	composite	ADJ
ijassa-1364	33	12	linear	linear	ADJ
ijassa-1364	33	13	dynamical	dynamical	ADJ
ijassa-1364	33	14	systems	system	NOUN
ijassa-1364	33	15	and	and	CCONJ
ijassa-1364	33	16	systems	system	NOUN
ijassa-1364	33	17	with	with	ADP
ijassa-1364	33	18	multipoint	multipoint	NOUN
ijassa-1364	33	19	intermediate	intermediate	ADJ
ijassa-1364	33	20	conditions	condition	NOUN
ijassa-1364	33	21	.	.	PUNCT
ijassa-1364	34	1	particular	particular	ADJ
ijassa-1364	34	2	attention	attention	NOUN
ijassa-1364	34	3	is	be	AUX
ijassa-1364	34	4	paid	pay	VERB
ijassa-1364	34	5	to	to	PART
ijassa-1364	34	6	necessary	necessary	ADJ
ijassa-1364	34	7	and	and	CCONJ
ijassa-1364	34	8	sufficient	sufficient	ADJ
ijassa-1364	34	9	conditions	condition	NOUN
ijassa-1364	34	10	for	for	ADP
ijassa-1364	34	11	the	the	DET
ijassa-1364	34	12	complete	complete	ADJ
ijassa-1364	34	13	controllability	controllability	NOUN
ijassa-1364	34	14	and	and	CCONJ
ijassa-1364	34	15	observability	observability	NOUN
ijassa-1364	34	16	of	of	ADP
ijassa-1364	34	17	composite	composite	ADJ
ijassa-1364	34	18	linear	linear	NOUN
ijassa-1364	34	19	systems	system	NOUN
ijassa-1364	34	20	,	,	PUNCT
ijassa-1364	34	21	which	which	PRON
ijassa-1364	34	22	in	in	ADP
ijassa-1364	34	23	the	the	DET
ijassa-1364	34	24	stationary	stationary	ADJ
ijassa-1364	34	25	case	case	NOUN
ijassa-1364	34	26	are	be	AUX
ijassa-1364	34	27	comparable	comparable	ADJ
ijassa-1364	34	28	to	to	ADP
ijassa-1364	34	29	the	the	DET
ijassa-1364	34	30	kalman	kalman	NOUN
ijassa-1364	34	31	conditions	condition	NOUN
ijassa-1364	34	32	by	by	ADP
ijassa-1364	34	33	their	their	PRON
ijassa-1364	34	34	completeness	completeness	NOUN
ijassa-1364	34	35	.	.	PUNCT
ijassa-1364	35	1	qualitative	qualitative	ADJ
ijassa-1364	35	2	properties	property	NOUN
ijassa-1364	35	3	of	of	ADP
ijassa-1364	35	4	controllability	controllability	NOUN
ijassa-1364	35	5	and	and	CCONJ
ijassa-1364	35	6	observability	observability	NOUN
ijassa-1364	35	7	of	of	ADP
ijassa-1364	35	8	composite	composite	ADJ
ijassa-1364	35	9	systems	system	NOUN
ijassa-1364	35	10	are	be	AUX
ijassa-1364	35	11	revealed	reveal	VERB
ijassa-1364	35	12	.	.	PUNCT
ijassa-1364	36	1	constructive	constructive	ADJ
ijassa-1364	36	2	methods	method	NOUN
ijassa-1364	36	3	for	for	ADP
ijassa-1364	36	4	solving	solve	VERB
ijassa-1364	36	5	control	control	NOUN
ijassa-1364	36	6	problems	problem	NOUN
ijassa-1364	36	7	of	of	ADP
ijassa-1364	36	8	composite	composite	ADJ
ijassa-1364	36	9	systems	system	NOUN
ijassa-1364	36	10	,	,	PUNCT
ijassa-1364	36	11	systems	system	NOUN
ijassa-1364	36	12	with	with	ADP
ijassa-1364	36	13	undivided	undivided	ADJ
ijassa-1364	36	14	multipoint	multipoint	NOUN
ijassa-1364	36	15	intermediate	intermediate	ADJ
ijassa-1364	36	16	conditions	condition	NOUN
ijassa-1364	36	17	,	,	PUNCT
ijassa-1364	36	18	with	with	ADP
ijassa-1364	36	19	constraints	constraint	NOUN
ijassa-1364	36	20	on	on	ADP
ijassa-1364	36	21	the	the	DET
ijassa-1364	36	22	values	value	NOUN
ijassa-1364	36	23	of	of	ADP
ijassa-1364	36	24	different	different	ADJ
ijassa-1364	36	25	parts	part	NOUN
ijassa-1364	36	26	of	of	ADP
ijassa-1364	36	27	the	the	DET
ijassa-1364	36	28	phase	phase	NOUN
ijassa-1364	36	29	vector	vector	NOUN
ijassa-1364	36	30	coordinates	coordinate	NOUN
ijassa-1364	36	31	at	at	ADP
ijassa-1364	36	32	intermediate	intermediate	ADJ
ijassa-1364	36	33	points	point	NOUN
ijassa-1364	36	34	in	in	ADP
ijassa-1364	36	35	time	time	NOUN
ijassa-1364	36	36	are	be	AUX
ijassa-1364	36	37	proposed	propose	VERB
ijassa-1364	36	38	.	.	PUNCT
ijassa-1364	37	1	the	the	DET
ijassa-1364	37	2	issue	issue	NOUN
ijassa-1364	37	3	of	of	ADP
ijassa-1364	37	4	controllability	controllability	NOUN
ijassa-1364	37	5	for	for	ADP
ijassa-1364	37	6	some	some	DET
ijassa-1364	37	7	classes	class	NOUN
ijassa-1364	37	8	of	of	ADP
ijassa-1364	37	9	nonlinear	nonlinear	ADJ
ijassa-1364	37	10	systems	system	NOUN
ijassa-1364	37	11	with	with	ADP
ijassa-1364	37	12	a	a	DET
ijassa-1364	37	13	phase	phase	NOUN
ijassa-1364	37	14	space	space	NOUN
ijassa-1364	37	15	change	change	NOUN
ijassa-1364	37	16	was	be	AUX
ijassa-1364	37	17	studied	study	VERB
ijassa-1364	37	18	by	by	ADP
ijassa-1364	37	19	the	the	DET
ijassa-1364	37	20	author	author	NOUN
ijassa-1364	37	21	in	in	ADP
ijassa-1364	37	22	[	[	X
ijassa-1364	37	23	12	12	NUM
ijassa-1364	37	24	]	]	PUNCT
ijassa-1364	37	25	.	.	PUNCT
ijassa-1364	38	1	the	the	DET
ijassa-1364	38	2	paper	paper	NOUN
ijassa-1364	38	3	consists	consist	VERB
ijassa-1364	38	4	of	of	ADP
ijassa-1364	38	5	two	two	NUM
ijassa-1364	38	6	sections	section	NOUN
ijassa-1364	38	7	devoted	devote	VERB
ijassa-1364	38	8	to	to	ADP
ijassa-1364	38	9	the	the	DET
ijassa-1364	38	10	cases	case	NOUN
ijassa-1364	38	11	of	of	ADP
ijassa-1364	38	12	nonlinear	nonlinear	ADJ
ijassa-1364	38	13	and	and	CCONJ
ijassa-1364	38	14	linear	linear	PROPN
ijassa-1364	38	15	systems	system	NOUN
ijassa-1364	38	16	,	,	PUNCT
ijassa-1364	38	17	respectively	respectively	ADV
ijassa-1364	38	18	.	.	PUNCT
ijassa-1364	39	1	an	an	DET
ijassa-1364	39	2	example	example	NOUN
ijassa-1364	39	3	illustrating	illustrate	VERB
ijassa-1364	39	4	this	this	DET
ijassa-1364	39	5	approach	approach	NOUN
ijassa-1364	39	6	is	be	AUX
ijassa-1364	39	7	considered	consider	VERB
ijassa-1364	39	8	.	.	PUNCT
ijassa-1364	40	1	2	2	X
ijassa-1364	40	2	.	.	X
ijassa-1364	40	3	nonlinear	nonlinear	ADJ
ijassa-1364	40	4	systems	system	NOUN
ijassa-1364	40	5	let	let	VERB
ijassa-1364	40	6	x	x	PRON
ijassa-1364	40	7	and	and	CCONJ
ijassa-1364	40	8	y	y	PROPN
ijassa-1364	40	9	be	be	VERB
ijassa-1364	40	10	two	two	NUM
ijassa-1364	40	11	phase	phase	NOUN
ijassa-1364	40	12	variables	variable	NOUN
ijassa-1364	40	13	:	:	PUNCT
ijassa-1364	40	14	x	x	SYM
ijassa-1364	40	15	=	=	SYM
ijassa-1364	40	16	(	(	PUNCT
ijassa-1364	40	17	x1	x1	PROPN
ijassa-1364	40	18	,	,	PUNCT
ijassa-1364	40	19	.	.	PUNCT
ijassa-1364	40	20	.	.	PUNCT
ijassa-1364	40	21	.	.	PUNCT
ijassa-1364	41	1	,	,	PUNCT
ijassa-1364	41	2	xn	xn	X
ijassa-1364	41	3	)	)	PUNCT
ijassa-1364	41	4	∈	∈	NOUN
ijassa-1364	41	5	x	x	X
ijassa-1364	41	6	=	=	SYM
ijassa-1364	41	7	rn	rn	PROPN
ijassa-1364	41	8	,	,	PUNCT
ijassa-1364	41	9	y	y	PROPN
ijassa-1364	41	10	=	=	SYM
ijassa-1364	41	11	(	(	PUNCT
ijassa-1364	41	12	y1	y1	INTJ
ijassa-1364	41	13	,	,	PUNCT
ijassa-1364	41	14	.	.	PUNCT
ijassa-1364	41	15	.	.	PUNCT
ijassa-1364	41	16	.	.	PUNCT
ijassa-1364	42	1	,	,	PUNCT
ijassa-1364	42	2	ym	ym	X
ijassa-1364	42	3	)	)	PUNCT
ijassa-1364	42	4	∈	∈	PROPN
ijassa-1364	42	5	y	y	PROPN
ijassa-1364	42	6	=	=	SYM
ijassa-1364	42	7	rm	rm	PROPN
ijassa-1364	42	8	.	.	PUNCT
ijassa-1364	43	1	the	the	DET
ijassa-1364	43	2	motion	motion	NOUN
ijassa-1364	43	3	of	of	ADP
ijassa-1364	43	4	the	the	DET
ijassa-1364	43	5	object	object	NOUN
ijassa-1364	43	6	is	be	AUX
ijassa-1364	43	7	described	describe	VERB
ijassa-1364	43	8	by	by	ADP
ijassa-1364	43	9	the	the	DET
ijassa-1364	43	10	following	follow	VERB
ijassa-1364	43	11	non	non	ADJ
ijassa-1364	43	12	-	-	ADJ
ijassa-1364	43	13	linear	linear	ADJ
ijassa-1364	43	14	systems	system	NOUN
ijassa-1364	43	15	of	of	ADP
ijassa-1364	43	16	differential	differential	ADJ
ijassa-1364	43	17	equations	equation	NOUN
ijassa-1364	43	18	:	:	PUNCT
ijassa-1364	43	19	ẋ	ẋ	PROPN
ijassa-1364	43	20	=	=	PUNCT
ijassa-1364	44	1	f(t	f(t	PROPN
ijassa-1364	44	2	,	,	PUNCT
ijassa-1364	44	3	x(t	x(t	PROPN
ijassa-1364	44	4	)	)	PUNCT
ijassa-1364	44	5	,	,	PUNCT
ijassa-1364	44	6	u(t	u(t	NOUN
ijassa-1364	44	7	)	)	PUNCT
ijassa-1364	44	8	)	)	PUNCT
ijassa-1364	44	9	,	,	PUNCT
ijassa-1364	44	10	u(t	u(t	NOUN
ijassa-1364	44	11	)	)	PUNCT
ijassa-1364	44	12	∈	∈	PROPN
ijassa-1364	44	13	u	u	NOUN
ijassa-1364	44	14	,	,	PUNCT
ijassa-1364	44	15	t	t	PROPN
ijassa-1364	44	16	∈	∈	PROPN
ijassa-1364	45	1	[	[	X
ijassa-1364	45	2	0	0	NUM
ijassa-1364	45	3	,	,	PUNCT
ijassa-1364	45	4	τ	τ	X
ijassa-1364	45	5	]	]	X
ijassa-1364	45	6	,	,	PUNCT
ijassa-1364	45	7	x	x	SYM
ijassa-1364	45	8	∈	∈	PROPN
ijassa-1364	45	9	x	x	X
ijassa-1364	45	10	,	,	PUNCT
ijassa-1364	45	11	(	(	PUNCT
ijassa-1364	45	12	2.1	2.1	NUM
ijassa-1364	45	13	)	)	PUNCT
ijassa-1364	45	14	ẏ	ẏ	PROPN
ijassa-1364	45	15	=	=	SYM
ijassa-1364	45	16	g(t	g(t	PROPN
ijassa-1364	45	17	,	,	PUNCT
ijassa-1364	45	18	y(t	y(t	PROPN
ijassa-1364	45	19	)	)	PUNCT
ijassa-1364	45	20	,	,	PUNCT
ijassa-1364	45	21	v(t	v(t	NOUN
ijassa-1364	45	22	)	)	PUNCT
ijassa-1364	45	23	)	)	PUNCT
ijassa-1364	45	24	,	,	PUNCT
ijassa-1364	45	25	v(t	v(t	NOUN
ijassa-1364	45	26	)	)	PUNCT
ijassa-1364	45	27	∈	∈	PROPN
ijassa-1364	45	28	v	v	NOUN
ijassa-1364	45	29	,	,	PUNCT
ijassa-1364	45	30	t	t	PROPN
ijassa-1364	45	31	∈	∈	PROPN
ijassa-1364	46	1	[	[	X
ijassa-1364	46	2	τ	τ	PROPN
ijassa-1364	46	3	,	,	PUNCT
ijassa-1364	46	4	t	t	X
ijassa-1364	46	5	]	]	PUNCT
ijassa-1364	46	6	,	,	PUNCT
ijassa-1364	46	7	y	y	PROPN
ijassa-1364	46	8	∈	∈	PROPN
ijassa-1364	46	9	y.	y.	NOUN
ijassa-1364	46	10	(	(	PUNCT
ijassa-1364	46	11	2.2	2.2	NUM
ijassa-1364	46	12	)	)	PUNCT
ijassa-1364	46	13	the	the	DET
ijassa-1364	46	14	class	class	NOUN
ijassa-1364	46	15	of	of	ADP
ijassa-1364	46	16	admissible	admissible	ADJ
ijassa-1364	46	17	controls	control	NOUN
ijassa-1364	46	18	consists	consist	VERB
ijassa-1364	46	19	of	of	ADP
ijassa-1364	46	20	all	all	DET
ijassa-1364	46	21	functions	function	NOUN
ijassa-1364	46	22	u	u	NOUN
ijassa-1364	46	23	(	(	PUNCT
ijassa-1364	46	24	·	·	PUNCT
ijassa-1364	46	25	)	)	PUNCT
ijassa-1364	46	26	∈	∈	PROPN
ijassa-1364	46	27	u	u	NOUN
ijassa-1364	46	28	=	=	NOUN
ijassa-1364	46	29	{	{	PUNCT
ijassa-1364	46	30	u(t	u(t	PROPN
ijassa-1364	46	31	)	)	PUNCT
ijassa-1364	46	32	∈	∈	PROPN
ijassa-1364	46	33	rn	rn	PROPN
ijassa-1364	46	34	|	|	ADV
ijassa-1364	46	35	u	u	NOUN
ijassa-1364	46	36	(	(	PUNCT
ijassa-1364	46	37	·	·	PUNCT
ijassa-1364	46	38	)	)	PUNCT
ijassa-1364	46	39	∈	∈	NOUN
ijassa-1364	46	40	l∞[0	l∞[0	NOUN
ijassa-1364	46	41	,	,	PUNCT
ijassa-1364	46	42	τ	τ	X
ijassa-1364	46	43	]	]	X
ijassa-1364	46	44	;	;	PUNCT
ijassa-1364	46	45	u(t	u(t	NOUN
ijassa-1364	46	46	)	)	PUNCT
ijassa-1364	46	47	∈	∈	PROPN
ijassa-1364	46	48	u1	u1	NOUN
ijassa-1364	46	49	⊂	⊂	PROPN
ijassa-1364	46	50	rn	rn	PROPN
ijassa-1364	46	51	,	,	PUNCT
ijassa-1364	46	52	t	t	PROPN
ijassa-1364	46	53	∈	∈	PROPN
ijassa-1364	47	1	[	[	X
ijassa-1364	47	2	0	0	NUM
ijassa-1364	47	3	,	,	PUNCT
ijassa-1364	47	4	τ	τ	X
ijassa-1364	47	5	]	]	PUNCT
ijassa-1364	47	6	}	}	PUNCT
ijassa-1364	47	7	,	,	PUNCT
ijassa-1364	47	8	v	v	NOUN
ijassa-1364	47	9	(	(	PUNCT
ijassa-1364	47	10	·	·	PUNCT
ijassa-1364	47	11	)	)	PUNCT
ijassa-1364	47	12	∈	∈	NOUN
ijassa-1364	47	13	v	v	NOUN
ijassa-1364	47	14	=	=	SYM
ijassa-1364	47	15	{	{	PUNCT
ijassa-1364	47	16	v(t	v(t	NOUN
ijassa-1364	47	17	)	)	PUNCT
ijassa-1364	47	18	∈	∈	PROPN
ijassa-1364	47	19	rm	rm	NOUN
ijassa-1364	47	20	|	|	ADV
ijassa-1364	47	21	v	v	PROPN
ijassa-1364	47	22	(	(	PUNCT
ijassa-1364	47	23	·	·	PUNCT
ijassa-1364	47	24	)	)	PUNCT
ijassa-1364	47	25	∈	∈	PROPN
ijassa-1364	47	26	l∞[τ	l∞[τ	NOUN
ijassa-1364	47	27	,	,	PUNCT
ijassa-1364	47	28	t	t	X
ijassa-1364	47	29	]	]	PUNCT
ijassa-1364	47	30	;	;	PUNCT
ijassa-1364	47	31	v(t	v(t	X
ijassa-1364	47	32	)	)	PUNCT
ijassa-1364	47	33	∈	∈	PROPN
ijassa-1364	47	34	v1	v1	PROPN
ijassa-1364	47	35	⊂	⊂	PROPN
ijassa-1364	47	36	rm	rm	PROPN
ijassa-1364	47	37	,	,	PUNCT
ijassa-1364	47	38	t	t	PROPN
ijassa-1364	47	39	∈	∈	PROPN
ijassa-1364	48	1	[	[	X
ijassa-1364	48	2	τ	τ	PROPN
ijassa-1364	48	3	,	,	PUNCT
ijassa-1364	48	4	t	t	X
ijassa-1364	48	5	]	]	PUNCT
ijassa-1364	48	6	}	}	PUNCT
ijassa-1364	48	7	,	,	PUNCT
ijassa-1364	48	8	whereu1	whereu1	NOUN
ijassa-1364	48	9	∈	∈	NOUN
ijassa-1364	48	10	ω(rn	ω(rn	NUM
ijassa-1364	48	11	)	)	PUNCT
ijassa-1364	48	12	,	,	PUNCT
ijassa-1364	48	13	v1	v1	VERB
ijassa-1364	48	14	∈	∈	PROPN
ijassa-1364	48	15	ω(rm	ω(rm	NUM
ijassa-1364	48	16	)	)	PUNCT
ijassa-1364	48	17	.	.	PUNCT
ijassa-1364	49	1	here	here	ADV
ijassa-1364	49	2	ω(rn	ω(rn	NUM
ijassa-1364	49	3	)	)	PUNCT
ijassa-1364	49	4	and	and	CCONJ
ijassa-1364	49	5	ω(rm	ω(rm	NOUN
ijassa-1364	49	6	)	)	PUNCT
ijassa-1364	49	7	are	be	AUX
ijassa-1364	49	8	the	the	DET
ijassa-1364	49	9	sets	set	NOUN
ijassa-1364	49	10	of	of	ADP
ijassa-1364	49	11	all	all	DET
ijassa-1364	49	12	nonempty	nonempty	X
ijassa-1364	49	13	convex	convex	ADJ
ijassa-1364	49	14	compact	compact	ADJ
ijassa-1364	49	15	subsets	subset	NOUN
ijassa-1364	49	16	of	of	ADP
ijassa-1364	49	17	the	the	DET
ijassa-1364	49	18	spaces	space	NOUN
ijassa-1364	49	19	rn	rn	PROPN
ijassa-1364	49	20	and	and	CCONJ
ijassa-1364	49	21	rm	rm	PROPN
ijassa-1364	49	22	,	,	PUNCT
ijassa-1364	49	23	respectively	respectively	ADV
ijassa-1364	49	24	.	.	PUNCT
ijassa-1364	50	1	the	the	DET
ijassa-1364	50	2	functions	function	NOUN
ijassa-1364	50	3	f(t	f(t	PROPN
ijassa-1364	50	4	,	,	PUNCT
ijassa-1364	50	5	x(t	x(t	PROPN
ijassa-1364	50	6	)	)	PUNCT
ijassa-1364	50	7	,	,	PUNCT
ijassa-1364	50	8	u(t	u(t	NOUN
ijassa-1364	50	9	)	)	PUNCT
ijassa-1364	50	10	)	)	PUNCT
ijassa-1364	50	11	,	,	PUNCT
ijassa-1364	50	12	g(t	g(t	PROPN
ijassa-1364	50	13	,	,	PUNCT
ijassa-1364	50	14	y(t	y(t	PROPN
ijassa-1364	50	15	)	)	PUNCT
ijassa-1364	50	16	,	,	PUNCT
ijassa-1364	50	17	v(t	v(t	NOUN
ijassa-1364	50	18	)	)	PUNCT
ijassa-1364	50	19	)	)	PUNCT
ijassa-1364	50	20	are	be	AUX
ijassa-1364	50	21	such	such	ADJ
ijassa-1364	50	22	that	that	SCONJ
ijassa-1364	50	23	for	for	ADP
ijassa-1364	50	24	systems	system	NOUN
ijassa-1364	50	25	(	(	PUNCT
ijassa-1364	50	26	2.1	2.1	NUM
ijassa-1364	50	27	)	)	PUNCT
ijassa-1364	50	28	and	and	CCONJ
ijassa-1364	50	29	(	(	PUNCT
ijassa-1364	50	30	2.2	2.2	NUM
ijassa-1364	50	31	)	)	PUNCT
ijassa-1364	50	32	the	the	DET
ijassa-1364	50	33	existence	existence	NOUN
ijassa-1364	50	34	and	and	CCONJ
ijassa-1364	50	35	uniqueness	uniqueness	NOUN
ijassa-1364	50	36	theorem	theorem	NOUN
ijassa-1364	50	37	of	of	ADP
ijassa-1364	50	38	the	the	DET
ijassa-1364	50	39	cauchy	cauchy	ADJ
ijassa-1364	50	40	problem	problem	NOUN
ijassa-1364	50	41	is	be	AUX
ijassa-1364	50	42	satisfied	satisfied	ADJ
ijassa-1364	50	43	.	.	PUNCT
ijassa-1364	51	1	solutions	solution	NOUN
ijassa-1364	51	2	of	of	ADP
ijassa-1364	51	3	systems	system	NOUN
ijassa-1364	51	4	(	(	PUNCT
ijassa-1364	51	5	2.1	2.1	NUM
ijassa-1364	51	6	)	)	PUNCT
ijassa-1364	51	7	and	and	CCONJ
ijassa-1364	51	8	(	(	PUNCT
ijassa-1364	51	9	2.2	2.2	NUM
ijassa-1364	51	10	)	)	PUNCT
ijassa-1364	51	11	at	at	ADP
ijassa-1364	51	12	t	t	PROPN
ijassa-1364	51	13	∈	∈	PROPN
ijassa-1364	52	1	[	[	X
ijassa-1364	52	2	0	0	NUM
ijassa-1364	52	3	,	,	PUNCT
ijassa-1364	52	4	τ	τ	X
ijassa-1364	52	5	]	]	PUNCT
ijassa-1364	52	6	and	and	CCONJ
ijassa-1364	52	7	t	t	PROPN
ijassa-1364	52	8	∈	∈	PROPN
ijassa-1364	53	1	[	[	X
ijassa-1364	53	2	τ	τ	PROPN
ijassa-1364	53	3	,	,	PUNCT
ijassa-1364	53	4	t	t	PROPN
ijassa-1364	53	5	]	]	PUNCT
ijassa-1364	53	6	are	be	AUX
ijassa-1364	53	7	absolutely	absolutely	ADV
ijassa-1364	53	8	continuous	continuous	ADJ
ijassa-1364	53	9	functions	function	NOUN
ijassa-1364	53	10	that	that	PRON
ijassa-1364	53	11	satisfy	satisfy	VERB
ijassa-1364	53	12	systems	system	NOUN
ijassa-1364	53	13	(	(	PUNCT
ijassa-1364	53	14	2.1	2.1	NUM
ijassa-1364	53	15	)	)	PUNCT
ijassa-1364	53	16	and	and	CCONJ
ijassa-1364	53	17	(	(	PUNCT
ijassa-1364	53	18	2.2	2.2	NUM
ijassa-1364	53	19	)	)	PUNCT
ijassa-1364	53	20	almost	almost	ADV
ijassa-1364	53	21	everywhere	everywhere	ADV
ijassa-1364	53	22	on	on	ADP
ijassa-1364	53	23	[	[	X
ijassa-1364	53	24	0	0	NUM
ijassa-1364	53	25	,	,	PUNCT
ijassa-1364	53	26	τ	τ	X
ijassa-1364	53	27	]	]	PUNCT
ijassa-1364	53	28	and	and	CCONJ
ijassa-1364	53	29	[	[	X
ijassa-1364	53	30	τ	τ	X
ijassa-1364	53	31	,	,	PUNCT
ijassa-1364	53	32	t	t	X
ijassa-1364	53	33	]	]	PUNCT
ijassa-1364	53	34	,	,	PUNCT
ijassa-1364	53	35	respectively	respectively	ADV
ijassa-1364	53	36	.	.	PUNCT
ijassa-1364	54	1	copyright	copyright	NOUN
ijassa-1364	54	2	©	©	PROPN
ijassa-1364	54	3	2023	2023	NUM
ijassa-1364	54	4	assa	assa	NOUN
ijassa-1364	54	5	.	.	PUNCT
ijassa-1364	55	1	adv	adv	PROPN
ijassa-1364	55	2	syst	syst	PROPN
ijassa-1364	55	3	sci	sci	PROPN
ijassa-1364	55	4	appl	appl	PROPN
ijassa-1364	55	5	(	(	PUNCT
ijassa-1364	55	6	2023	2023	NUM
ijassa-1364	55	7	)	)	PUNCT
ijassa-1364	55	8	the	the	DET
ijassa-1364	55	9	problem	problem	NOUN
ijassa-1364	55	10	of	of	ADP
ijassa-1364	55	11	controllability	controllability	NOUN
ijassa-1364	55	12	63	63	NUM
ijassa-1364	55	13	there	there	PRON
ijassa-1364	55	14	is	be	VERB
ijassa-1364	55	15	an	an	DET
ijassa-1364	55	16	initial	initial	ADJ
ijassa-1364	55	17	set	set	VERB
ijassa-1364	55	18	m0	m0	NOUN
ijassa-1364	55	19	∈	∈	PROPN
ijassa-1364	55	20	ω(rn	ω(rn	NUM
ijassa-1364	55	21	)	)	PUNCT
ijassa-1364	55	22	and	and	CCONJ
ijassa-1364	55	23	a	a	DET
ijassa-1364	55	24	nonintersecting	nonintersecte	VERB
ijassa-1364	55	25	convex	convex	NOUN
ijassa-1364	55	26	”	"	PUNCT
ijassa-1364	55	27	transition	transition	NOUN
ijassa-1364	55	28	hypersurface	hypersurface	NOUN
ijassa-1364	55	29	”	"	PUNCT
ijassa-1364	55	30	in	in	ADP
ijassa-1364	55	31	the	the	DET
ijassa-1364	55	32	space	space	NOUN
ijassa-1364	55	33	x	x	X
ijassa-1364	55	34	γ	γ	X
ijassa-1364	55	35	.	.	PUNCT
ijassa-1364	55	36	let	let	VERB
ijassa-1364	55	37	’s	’s	NOUN
ijassa-1364	55	38	suppose	suppose	VERB
ijassa-1364	55	39	that	that	SCONJ
ijassa-1364	55	40	τ	τ	PROPN
ijassa-1364	55	41	is	be	AUX
ijassa-1364	55	42	the	the	DET
ijassa-1364	55	43	smallest	small	ADJ
ijassa-1364	55	44	time	time	NOUN
ijassa-1364	55	45	moment	moment	NOUN
ijassa-1364	55	46	at	at	ADP
ijassa-1364	55	47	which	which	PRON
ijassa-1364	55	48	the	the	DET
ijassa-1364	55	49	object	object	NOUN
ijassa-1364	55	50	reaches	reach	VERB
ijassa-1364	55	51	the	the	DET
ijassa-1364	55	52	hypersurface	hypersurface	NOUN
ijassa-1364	55	53	γ	γ	X
ijassa-1364	55	54	.	.	PROPN
ijassa-1364	55	55	when	when	SCONJ
ijassa-1364	55	56	an	an	DET
ijassa-1364	55	57	object	object	NOUN
ijassa-1364	55	58	moving	move	VERB
ijassa-1364	55	59	according	accord	VERB
ijassa-1364	55	60	to	to	ADP
ijassa-1364	55	61	the	the	DET
ijassa-1364	55	62	law	law	NOUN
ijassa-1364	55	63	(	(	PUNCT
ijassa-1364	55	64	2.1	2.1	NUM
ijassa-1364	55	65	)	)	PUNCT
ijassa-1364	55	66	reaches	reach	VERB
ijassa-1364	55	67	the	the	DET
ijassa-1364	55	68	hypersurface	hypersurface	NOUN
ijassa-1364	55	69	γ	γ	X
ijassa-1364	55	70	,	,	PUNCT
ijassa-1364	55	71	it	it	PRON
ijassa-1364	55	72	moves	move	VERB
ijassa-1364	55	73	to	to	ADP
ijassa-1364	55	74	the	the	DET
ijassa-1364	55	75	space	space	NOUN
ijassa-1364	55	76	y	y	NOUN
ijassa-1364	55	77	given	give	VERB
ijassa-1364	55	78	by	by	ADP
ijassa-1364	55	79	the	the	DET
ijassa-1364	55	80	mapping	mapping	NOUN
ijassa-1364	55	81	q	q	NOUN
ijassa-1364	55	82	:	:	PUNCT
ijassa-1364	55	83	x	x	X
ijassa-1364	55	84	→	→	SYM
ijassa-1364	55	85	y	y	PROPN
ijassa-1364	55	86	(	(	PUNCT
ijassa-1364	55	87	it	it	PRON
ijassa-1364	55	88	is	be	AUX
ijassa-1364	55	89	assumed	assume	VERB
ijassa-1364	55	90	that	that	SCONJ
ijassa-1364	55	91	this	this	DET
ijassa-1364	55	92	mapping	mapping	NOUN
ijassa-1364	55	93	translates	translate	VERB
ijassa-1364	55	94	the	the	DET
ijassa-1364	55	95	convex	convex	NOUN
ijassa-1364	55	96	set	set	VERB
ijassa-1364	55	97	into	into	ADP
ijassa-1364	55	98	the	the	DET
ijassa-1364	55	99	convex	convex	NOUN
ijassa-1364	55	100	one	one	NUM
ijassa-1364	55	101	)	)	PUNCT
ijassa-1364	55	102	,	,	PUNCT
ijassa-1364	55	103	and	and	CCONJ
ijassa-1364	55	104	further	further	ADJ
ijassa-1364	55	105	motion	motion	NOUN
ijassa-1364	55	106	is	be	AUX
ijassa-1364	55	107	performed	perform	VERB
ijassa-1364	55	108	in	in	ADP
ijassa-1364	55	109	the	the	DET
ijassa-1364	55	110	space	space	NOUN
ijassa-1364	55	111	y	y	NOUN
ijassa-1364	55	112	according	accord	VERB
ijassa-1364	55	113	to	to	ADP
ijassa-1364	55	114	the	the	DET
ijassa-1364	55	115	law	law	NOUN
ijassa-1364	55	116	(	(	PUNCT
ijassa-1364	55	117	2.2	2.2	NUM
ijassa-1364	55	118	)	)	PUNCT
ijassa-1364	55	119	.	.	PUNCT
ijassa-1364	56	1	finally	finally	ADV
ijassa-1364	56	2	,	,	PUNCT
ijassa-1364	56	3	the	the	DET
ijassa-1364	56	4	terminal	terminal	NOUN
ijassa-1364	56	5	set	set	VERB
ijassa-1364	56	6	m1	m1	PROPN
ijassa-1364	56	7	∈	∈	PROPN
ijassa-1364	56	8	ω(rm	ω(rm	NUM
ijassa-1364	56	9	)	)	PUNCT
ijassa-1364	56	10	(	(	PUNCT
ijassa-1364	56	11	not	not	PART
ijassa-1364	56	12	overlapping	overlap	VERB
ijassa-1364	56	13	with	with	ADP
ijassa-1364	56	14	the	the	DET
ijassa-1364	56	15	set	set	NOUN
ijassa-1364	56	16	q(γ	q(γ	PROPN
ijassa-1364	56	17	)	)	PUNCT
ijassa-1364	56	18	)	)	PUNCT
ijassa-1364	56	19	is	be	AUX
ijassa-1364	56	20	given	give	VERB
ijassa-1364	56	21	in	in	ADP
ijassa-1364	56	22	y	y	PROPN
ijassa-1364	56	23	.	.	PUNCT
ijassa-1364	57	1	a	a	DET
ijassa-1364	57	2	similar	similar	ADJ
ijassa-1364	57	3	scheme	scheme	NOUN
ijassa-1364	57	4	of	of	ADP
ijassa-1364	57	5	motion	motion	NOUN
ijassa-1364	57	6	of	of	ADP
ijassa-1364	57	7	an	an	DET
ijassa-1364	57	8	object	object	NOUN
ijassa-1364	57	9	was	be	AUX
ijassa-1364	57	10	considered	consider	VERB
ijassa-1364	57	11	in	in	ADP
ijassa-1364	57	12	[	[	X
ijassa-1364	57	13	7	7	NUM
ijassa-1364	57	14	]	]	PUNCT
ijassa-1364	57	15	.	.	PUNCT
ijassa-1364	58	1	the	the	DET
ijassa-1364	58	2	problem	problem	NOUN
ijassa-1364	58	3	is	be	AUX
ijassa-1364	58	4	to	to	PART
ijassa-1364	58	5	find	find	VERB
ijassa-1364	58	6	the	the	DET
ijassa-1364	58	7	conditions	condition	NOUN
ijassa-1364	58	8	under	under	ADP
ijassa-1364	58	9	which	which	PRON
ijassa-1364	58	10	the	the	DET
ijassa-1364	58	11	object	object	NOUN
ijassa-1364	58	12	described	describe	VERB
ijassa-1364	58	13	by	by	ADP
ijassa-1364	58	14	the	the	DET
ijassa-1364	58	15	systems	system	NOUN
ijassa-1364	58	16	(	(	PUNCT
ijassa-1364	58	17	2.1	2.1	NUM
ijassa-1364	58	18	)	)	PUNCT
ijassa-1364	58	19	and	and	CCONJ
ijassa-1364	58	20	(	(	PUNCT
ijassa-1364	58	21	2.2	2.2	NUM
ijassa-1364	58	22	)	)	PUNCT
ijassa-1364	58	23	will	will	AUX
ijassa-1364	58	24	be	be	AUX
ijassa-1364	58	25	controllable	controllable	ADJ
ijassa-1364	58	26	from	from	ADP
ijassa-1364	58	27	m0	m0	PROPN
ijassa-1364	58	28	to	to	ADP
ijassa-1364	58	29	m1	m1	PROPN
ijassa-1364	58	30	.	.	PUNCT
ijassa-1364	59	1	definition	definition	NOUN
ijassa-1364	59	2	2.1	2.1	NUM
ijassa-1364	59	3	:	:	PUNCT
ijassa-1364	59	4	an	an	DET
ijassa-1364	59	5	object	object	NOUN
ijassa-1364	59	6	described	describe	VERB
ijassa-1364	59	7	by	by	ADP
ijassa-1364	59	8	systems	system	NOUN
ijassa-1364	59	9	(	(	PUNCT
ijassa-1364	59	10	2.1	2.1	NUM
ijassa-1364	59	11	)	)	PUNCT
ijassa-1364	59	12	and	and	CCONJ
ijassa-1364	59	13	(	(	PUNCT
ijassa-1364	59	14	2.2	2.2	NUM
ijassa-1364	59	15	)	)	PUNCT
ijassa-1364	59	16	is	be	AUX
ijassa-1364	59	17	called	call	VERB
ijassa-1364	59	18	controllable	controllable	ADJ
ijassa-1364	59	19	from	from	ADP
ijassa-1364	59	20	m0	m0	PROPN
ijassa-1364	59	21	to	to	ADP
ijassa-1364	59	22	m1	m1	PROPN
ijassa-1364	59	23	,	,	PUNCT
ijassa-1364	59	24	if	if	SCONJ
ijassa-1364	59	25	there	there	PRON
ijassa-1364	59	26	exist	exist	VERB
ijassa-1364	59	27	allowable	allowable	ADJ
ijassa-1364	59	28	controls	control	NOUN
ijassa-1364	59	29	u	u	NOUN
ijassa-1364	59	30	(	(	PUNCT
ijassa-1364	59	31	·	·	PUNCT
ijassa-1364	59	32	)	)	PUNCT
ijassa-1364	59	33	and	and	CCONJ
ijassa-1364	59	34	v	v	NOUN
ijassa-1364	59	35	(	(	PUNCT
ijassa-1364	59	36	·	·	PUNCT
ijassa-1364	59	37	)	)	PUNCT
ijassa-1364	59	38	such	such	ADJ
ijassa-1364	59	39	that	that	SCONJ
ijassa-1364	59	40	the	the	DET
ijassa-1364	59	41	corresponding	correspond	VERB
ijassa-1364	59	42	solutions	solution	NOUN
ijassa-1364	59	43	of	of	ADP
ijassa-1364	59	44	the	the	DET
ijassa-1364	59	45	systems	system	NOUN
ijassa-1364	59	46	satisfy	satisfy	VERB
ijassa-1364	59	47	the	the	DET
ijassa-1364	59	48	boundary	boundary	ADJ
ijassa-1364	59	49	conditions	condition	NOUN
ijassa-1364	59	50	x(0	x(0	PROPN
ijassa-1364	59	51	)	)	PUNCT
ijassa-1364	59	52	∈m0	∈m0	NOUN
ijassa-1364	59	53	,	,	PUNCT
ijassa-1364	59	54	x(τ	x(τ	PROPN
ijassa-1364	59	55	)	)	PUNCT
ijassa-1364	59	56	∈	∈	PROPN
ijassa-1364	59	57	γ	γ	NOUN
ijassa-1364	59	58	and	and	CCONJ
ijassa-1364	59	59	y(τ	y(τ	PROPN
ijassa-1364	59	60	)	)	PUNCT
ijassa-1364	59	61	=	=	PUNCT
ijassa-1364	59	62	q(x(τ	q(x(τ	PROPN
ijassa-1364	59	63	)	)	PUNCT
ijassa-1364	59	64	)	)	PUNCT
ijassa-1364	60	1	,	,	PUNCT
ijassa-1364	60	2	y(t	y(t	NOUN
ijassa-1364	60	3	)	)	PUNCT
ijassa-1364	60	4	∈m1	∈m1	PROPN
ijassa-1364	60	5	.	.	PUNCT
ijassa-1364	60	6	remark	remark	VERB
ijassa-1364	60	7	2.1	2.1	NUM
ijassa-1364	60	8	:	:	PUNCT
ijassa-1364	60	9	for	for	ADP
ijassa-1364	60	10	system	system	NOUN
ijassa-1364	60	11	(	(	PUNCT
ijassa-1364	60	12	2.1	2.1	NUM
ijassa-1364	60	13	)	)	PUNCT
ijassa-1364	60	14	,	,	PUNCT
ijassa-1364	60	15	consider	consider	VERB
ijassa-1364	60	16	the	the	DET
ijassa-1364	60	17	set	set	ADJ
ijassa-1364	60	18	f(t	f(t	NOUN
ijassa-1364	60	19	,	,	PUNCT
ijassa-1364	60	20	x(t	x(t	PROPN
ijassa-1364	60	21	)	)	PUNCT
ijassa-1364	60	22	,	,	PUNCT
ijassa-1364	60	23	u	u	NOUN
ijassa-1364	60	24	)	)	PUNCT
ijassa-1364	60	25	consisting	consist	VERB
ijassa-1364	60	26	of	of	ADP
ijassa-1364	60	27	all	all	DET
ijassa-1364	60	28	vectors	vector	NOUN
ijassa-1364	60	29	f(t	f(t	NOUN
ijassa-1364	60	30	,	,	PUNCT
ijassa-1364	60	31	x(t	x(t	PROPN
ijassa-1364	60	32	)	)	PUNCT
ijassa-1364	60	33	,	,	PUNCT
ijassa-1364	60	34	u(t	u(t	NOUN
ijassa-1364	60	35	)	)	PUNCT
ijassa-1364	60	36	)	)	PUNCT
ijassa-1364	60	37	,	,	PUNCT
ijassa-1364	60	38	where	where	SCONJ
ijassa-1364	60	39	u(t	u(t	NOUN
ijassa-1364	60	40	)	)	PUNCT
ijassa-1364	60	41	∈	∈	PROPN
ijassa-1364	60	42	u	u	NOUN
ijassa-1364	60	43	.	.	PUNCT
ijassa-1364	61	1	if	if	SCONJ
ijassa-1364	61	2	x(t	x(t	PROPN
ijassa-1364	61	3	)	)	PUNCT
ijassa-1364	61	4	is	be	AUX
ijassa-1364	61	5	a	a	DET
ijassa-1364	61	6	trajectory	trajectory	NOUN
ijassa-1364	61	7	of	of	ADP
ijassa-1364	61	8	system	system	NOUN
ijassa-1364	61	9	(	(	PUNCT
ijassa-1364	61	10	2.1	2.1	NUM
ijassa-1364	61	11	)	)	PUNCT
ijassa-1364	61	12	corresponding	correspond	VERB
ijassa-1364	61	13	to	to	ADP
ijassa-1364	61	14	an	an	DET
ijassa-1364	61	15	admissible	admissible	ADJ
ijassa-1364	61	16	control	control	NOUN
ijassa-1364	61	17	u(t	u(t	NOUN
ijassa-1364	61	18	)	)	PUNCT
ijassa-1364	61	19	,	,	PUNCT
ijassa-1364	61	20	then	then	ADV
ijassa-1364	61	21	for	for	ADP
ijassa-1364	61	22	almost	almost	ADV
ijassa-1364	61	23	all	all	PRON
ijassa-1364	61	24	t	t	NOUN
ijassa-1364	61	25	∈	∈	PROPN
ijassa-1364	62	1	[	[	X
ijassa-1364	62	2	0	0	NUM
ijassa-1364	62	3	,	,	PUNCT
ijassa-1364	62	4	τ	τ	PROPN
ijassa-1364	62	5	]	]	PUNCT
ijassa-1364	62	6	the	the	DET
ijassa-1364	62	7	inclusion	inclusion	NOUN
ijassa-1364	62	8	ẋ(t	ẋ(t	NOUN
ijassa-1364	62	9	)	)	PUNCT
ijassa-1364	62	10	∈	∈	PROPN
ijassa-1364	62	11	f(t	f(t	NOUN
ijassa-1364	62	12	,	,	PUNCT
ijassa-1364	62	13	x(t	x(t	PROPN
ijassa-1364	62	14	)	)	PUNCT
ijassa-1364	62	15	,	,	PUNCT
ijassa-1364	62	16	u	u	NOUN
ijassa-1364	62	17	)	)	PUNCT
ijassa-1364	62	18	(	(	PUNCT
ijassa-1364	62	19	2.3	2.3	NUM
ijassa-1364	62	20	)	)	PUNCT
ijassa-1364	62	21	holds	hold	VERB
ijassa-1364	62	22	true	true	ADJ
ijassa-1364	62	23	.	.	PUNCT
ijassa-1364	63	1	this	this	PRON
ijassa-1364	63	2	leads	lead	VERB
ijassa-1364	63	3	us	we	PRON
ijassa-1364	63	4	to	to	ADP
ijassa-1364	63	5	the	the	DET
ijassa-1364	63	6	differential	differential	ADJ
ijassa-1364	63	7	inclusion	inclusion	NOUN
ijassa-1364	63	8	of	of	ADP
ijassa-1364	63	9	ẋ	ẋ	PROPN
ijassa-1364	63	10	∈	∈	PROPN
ijassa-1364	63	11	f(t	f(t	PROPN
ijassa-1364	63	12	,	,	PUNCT
ijassa-1364	63	13	x	x	NOUN
ijassa-1364	63	14	,	,	PUNCT
ijassa-1364	63	15	u	u	NOUN
ijassa-1364	63	16	)	)	PUNCT
ijassa-1364	63	17	.	.	PUNCT
ijassa-1364	64	1	(	(	PUNCT
ijassa-1364	64	2	2.4	2.4	NUM
ijassa-1364	64	3	)	)	PUNCT
ijassa-1364	64	4	solutions	solution	NOUN
ijassa-1364	64	5	of	of	ADP
ijassa-1364	64	6	the	the	DET
ijassa-1364	64	7	differential	differential	ADJ
ijassa-1364	64	8	inclusion	inclusion	NOUN
ijassa-1364	64	9	(	(	PUNCT
ijassa-1364	64	10	2.4	2.4	NUM
ijassa-1364	64	11	)	)	PUNCT
ijassa-1364	64	12	are	be	AUX
ijassa-1364	64	13	absolutely	absolutely	ADV
ijassa-1364	64	14	continuous	continuous	ADJ
ijassa-1364	64	15	functions	function	NOUN
ijassa-1364	64	16	x(t	x(t	PROPN
ijassa-1364	64	17	)	)	PUNCT
ijassa-1364	64	18	defined	define	VERB
ijassa-1364	64	19	on	on	ADP
ijassa-1364	64	20	the	the	DET
ijassa-1364	64	21	interval	interval	NOUN
ijassa-1364	64	22	[	[	X
ijassa-1364	64	23	0	0	NUM
ijassa-1364	64	24	,	,	PUNCT
ijassa-1364	64	25	τ	τ	PROPN
ijassa-1364	64	26	]	]	PUNCT
ijassa-1364	64	27	that	that	PRON
ijassa-1364	64	28	satisfy	satisfy	VERB
ijassa-1364	64	29	the	the	DET
ijassa-1364	64	30	inclusion	inclusion	NOUN
ijassa-1364	64	31	(	(	PUNCT
ijassa-1364	64	32	2.3	2.3	NUM
ijassa-1364	64	33	)	)	PUNCT
ijassa-1364	64	34	for	for	ADP
ijassa-1364	64	35	almost	almost	ADV
ijassa-1364	64	36	all	all	PRON
ijassa-1364	64	37	t	t	NOUN
ijassa-1364	64	38	∈	∈	PROPN
ijassa-1364	65	1	[	[	X
ijassa-1364	65	2	0	0	NUM
ijassa-1364	65	3	,	,	PUNCT
ijassa-1364	65	4	τ	τ	X
ijassa-1364	65	5	]	]	X
ijassa-1364	65	6	.	.	PUNCT
ijassa-1364	66	1	so	so	ADV
ijassa-1364	66	2	,	,	PUNCT
ijassa-1364	66	3	under	under	ADP
ijassa-1364	66	4	rather	rather	ADV
ijassa-1364	66	5	general	general	ADJ
ijassa-1364	66	6	assumptions	assumption	NOUN
ijassa-1364	66	7	,	,	PUNCT
ijassa-1364	66	8	system	system	NOUN
ijassa-1364	66	9	(	(	PUNCT
ijassa-1364	66	10	2.1	2.1	NUM
ijassa-1364	66	11	)	)	PUNCT
ijassa-1364	66	12	is	be	AUX
ijassa-1364	66	13	equivalent	equivalent	ADJ
ijassa-1364	66	14	to	to	ADP
ijassa-1364	66	15	a	a	DET
ijassa-1364	66	16	differential	differential	ADJ
ijassa-1364	66	17	inclusion	inclusion	NOUN
ijassa-1364	66	18	(	(	PUNCT
ijassa-1364	66	19	2.4	2.4	NUM
ijassa-1364	66	20	)	)	PUNCT
ijassa-1364	66	21	,	,	PUNCT
ijassa-1364	66	22	i.e.	i.e.	X
ijassa-1364	66	23	for	for	ADP
ijassa-1364	66	24	any	any	DET
ijassa-1364	66	25	solution	solution	NOUN
ijassa-1364	66	26	x	x	X
ijassa-1364	66	27	(	(	PUNCT
ijassa-1364	66	28	·	·	PUNCT
ijassa-1364	66	29	)	)	PUNCT
ijassa-1364	66	30	of	of	ADP
ijassa-1364	66	31	the	the	DET
ijassa-1364	66	32	inclusion	inclusion	NOUN
ijassa-1364	66	33	(	(	PUNCT
ijassa-1364	66	34	2.4	2.4	NUM
ijassa-1364	66	35	)	)	PUNCT
ijassa-1364	66	36	there	there	PRON
ijassa-1364	66	37	exists	exist	VERB
ijassa-1364	66	38	a	a	DET
ijassa-1364	66	39	valid	valid	ADJ
ijassa-1364	66	40	control	control	NOUN
ijassa-1364	66	41	u	u	NOUN
ijassa-1364	66	42	(	(	PUNCT
ijassa-1364	66	43	·	·	PUNCT
ijassa-1364	66	44	)	)	PUNCT
ijassa-1364	66	45	such	such	ADJ
ijassa-1364	66	46	that	that	SCONJ
ijassa-1364	66	47	the	the	DET
ijassa-1364	66	48	function	function	NOUN
ijassa-1364	66	49	x	x	X
ijassa-1364	66	50	(	(	PUNCT
ijassa-1364	66	51	·	·	PUNCT
ijassa-1364	66	52	)	)	PUNCT
ijassa-1364	66	53	is	be	AUX
ijassa-1364	66	54	the	the	DET
ijassa-1364	66	55	path	path	NOUN
ijassa-1364	66	56	of	of	ADP
ijassa-1364	66	57	system	system	NOUN
ijassa-1364	66	58	(	(	PUNCT
ijassa-1364	66	59	2.1	2.1	NUM
ijassa-1364	66	60	)	)	PUNCT
ijassa-1364	66	61	with	with	ADP
ijassa-1364	66	62	the	the	DET
ijassa-1364	66	63	control	control	NOUN
ijassa-1364	66	64	u	u	NOUN
ijassa-1364	66	65	(	(	PUNCT
ijassa-1364	66	66	·	·	PUNCT
ijassa-1364	66	67	)	)	PUNCT
ijassa-1364	66	68	.	.	PUNCT
ijassa-1364	67	1	this	this	DET
ijassa-1364	67	2	question	question	NOUN
ijassa-1364	67	3	is	be	AUX
ijassa-1364	67	4	discussed	discuss	VERB
ijassa-1364	67	5	in	in	ADP
ijassa-1364	67	6	detail	detail	NOUN
ijassa-1364	67	7	in	in	ADP
ijassa-1364	67	8	[	[	X
ijassa-1364	67	9	8	8	NUM
ijassa-1364	67	10	]	]	PUNCT
ijassa-1364	67	11	.	.	PUNCT
ijassa-1364	68	1	taking	take	VERB
ijassa-1364	68	2	into	into	ADP
ijassa-1364	68	3	account	account	NOUN
ijassa-1364	68	4	previous	previous	ADJ
ijassa-1364	68	5	remarks	remark	NOUN
ijassa-1364	68	6	,	,	PUNCT
ijassa-1364	68	7	we	we	PRON
ijassa-1364	68	8	shall	shall	AUX
ijassa-1364	68	9	consider	consider	VERB
ijassa-1364	68	10	differential	differential	ADJ
ijassa-1364	68	11	inclusion	inclusion	NOUN
ijassa-1364	68	12	(	(	PUNCT
ijassa-1364	68	13	2.4	2.4	NUM
ijassa-1364	68	14	)	)	PUNCT
ijassa-1364	68	15	instead	instead	ADV
ijassa-1364	68	16	of	of	ADP
ijassa-1364	68	17	nonlinear	nonlinear	ADJ
ijassa-1364	68	18	system	system	NOUN
ijassa-1364	68	19	(	(	PUNCT
ijassa-1364	68	20	2.1	2.1	NUM
ijassa-1364	68	21	)	)	PUNCT
ijassa-1364	68	22	.	.	PUNCT
ijassa-1364	69	1	let	let	VERB
ijassa-1364	69	2	us	we	PRON
ijassa-1364	69	3	denote	denote	VERB
ijassa-1364	69	4	f(t	f(t	PROPN
ijassa-1364	69	5	,	,	PUNCT
ijassa-1364	69	6	x	x	NOUN
ijassa-1364	69	7	,	,	PUNCT
ijassa-1364	69	8	u	u	NOUN
ijassa-1364	69	9	)	)	PUNCT
ijassa-1364	69	10	by	by	ADP
ijassa-1364	69	11	f	f	PROPN
ijassa-1364	69	12	(	(	PUNCT
ijassa-1364	69	13	t	t	PROPN
ijassa-1364	69	14	,	,	PUNCT
ijassa-1364	69	15	x	x	NOUN
ijassa-1364	69	16	)	)	PUNCT
ijassa-1364	69	17	,	,	PUNCT
ijassa-1364	69	18	then	then	ADV
ijassa-1364	69	19	the	the	DET
ijassa-1364	69	20	motion	motion	NOUN
ijassa-1364	69	21	of	of	ADP
ijassa-1364	69	22	the	the	DET
ijassa-1364	69	23	controlled	control	VERB
ijassa-1364	69	24	object	object	NOUN
ijassa-1364	69	25	is	be	AUX
ijassa-1364	69	26	described	describe	VERB
ijassa-1364	69	27	by	by	ADP
ijassa-1364	69	28	the	the	DET
ijassa-1364	69	29	differential	differential	ADJ
ijassa-1364	69	30	inclusion	inclusion	NOUN
ijassa-1364	69	31	ẋ	ẋ	PROPN
ijassa-1364	69	32	∈	∈	PROPN
ijassa-1364	70	1	f	f	X
ijassa-1364	70	2	(	(	PUNCT
ijassa-1364	70	3	t	t	PROPN
ijassa-1364	70	4	,	,	PUNCT
ijassa-1364	70	5	x	x	NOUN
ijassa-1364	70	6	)	)	PUNCT
ijassa-1364	70	7	,	,	PUNCT
ijassa-1364	70	8	t	t	PROPN
ijassa-1364	70	9	∈	∈	PROPN
ijassa-1364	71	1	[	[	X
ijassa-1364	71	2	0	0	NUM
ijassa-1364	71	3	,	,	PUNCT
ijassa-1364	71	4	τ	τ	X
ijassa-1364	71	5	]	]	X
ijassa-1364	71	6	.	.	PUNCT
ijassa-1364	72	1	(	(	PUNCT
ijassa-1364	72	2	2.5	2.5	NUM
ijassa-1364	72	3	)	)	PUNCT
ijassa-1364	72	4	similarly	similarly	ADV
ijassa-1364	72	5	,	,	PUNCT
ijassa-1364	72	6	the	the	DET
ijassa-1364	72	7	motion	motion	NOUN
ijassa-1364	72	8	of	of	ADP
ijassa-1364	72	9	the	the	DET
ijassa-1364	72	10	controlled	control	VERB
ijassa-1364	72	11	object	object	NOUN
ijassa-1364	72	12	in	in	ADP
ijassa-1364	72	13	the	the	DET
ijassa-1364	72	14	space	space	NOUN
ijassa-1364	72	15	y	y	PROPN
ijassa-1364	72	16	=	=	PUNCT
ijassa-1364	72	17	rm	rm	PROPN
ijassa-1364	72	18	is	be	AUX
ijassa-1364	72	19	described	describe	VERB
ijassa-1364	72	20	by	by	ADP
ijassa-1364	72	21	the	the	DET
ijassa-1364	72	22	differential	differential	ADJ
ijassa-1364	72	23	inclusion	inclusion	NOUN
ijassa-1364	72	24	ẏ	ẏ	PROPN
ijassa-1364	72	25	∈	∈	PROPN
ijassa-1364	72	26	g(t	g(t	PROPN
ijassa-1364	72	27	,	,	PUNCT
ijassa-1364	72	28	y	y	PROPN
ijassa-1364	72	29	)	)	PUNCT
ijassa-1364	72	30	,	,	PUNCT
ijassa-1364	72	31	t	t	PROPN
ijassa-1364	72	32	∈	∈	PROPN
ijassa-1364	73	1	[	[	X
ijassa-1364	73	2	τ	τ	PROPN
ijassa-1364	73	3	,	,	PUNCT
ijassa-1364	73	4	t	t	X
ijassa-1364	73	5	]	]	PUNCT
ijassa-1364	73	6	.	.	PUNCT
ijassa-1364	74	1	(	(	PUNCT
ijassa-1364	74	2	2.6	2.6	NUM
ijassa-1364	74	3	)	)	PUNCT
ijassa-1364	74	4	the	the	DET
ijassa-1364	74	5	motion	motion	NOUN
ijassa-1364	74	6	of	of	ADP
ijassa-1364	74	7	an	an	DET
ijassa-1364	74	8	object	object	NOUN
ijassa-1364	74	9	from	from	ADP
ijassa-1364	74	10	the	the	DET
ijassa-1364	74	11	space	space	NOUN
ijassa-1364	74	12	x	x	PART
ijassa-1364	74	13	to	to	ADP
ijassa-1364	74	14	the	the	DET
ijassa-1364	74	15	space	space	NOUN
ijassa-1364	74	16	y	y	PROPN
ijassa-1364	74	17	is	be	AUX
ijassa-1364	74	18	described	describe	VERB
ijassa-1364	74	19	above	above	ADV
ijassa-1364	74	20	.	.	PUNCT
ijassa-1364	75	1	definition	definition	NOUN
ijassa-1364	75	2	2.2	2.2	NUM
ijassa-1364	75	3	(	(	PUNCT
ijassa-1364	75	4	[	[	X
ijassa-1364	75	5	6	6	NUM
ijassa-1364	75	6	]	]	PUNCT
ijassa-1364	75	7	):	):	PUNCT
ijassa-1364	75	8	a	a	DET
ijassa-1364	75	9	multi	multi	ADJ
ijassa-1364	75	10	-	-	ADJ
ijassa-1364	75	11	valued	value	VERB
ijassa-1364	75	12	mapping	mapping	NOUN
ijassa-1364	75	13	f	f	X
ijassa-1364	75	14	(	(	PUNCT
ijassa-1364	75	15	t	t	PROPN
ijassa-1364	75	16	,	,	PUNCT
ijassa-1364	75	17	x	x	X
ijassa-1364	75	18	)	)	PUNCT
ijassa-1364	75	19	is	be	AUX
ijassa-1364	75	20	called	call	VERB
ijassa-1364	75	21	concave	concave	VERB
ijassa-1364	75	22	by	by	ADP
ijassa-1364	75	23	x	x	PUNCT
ijassa-1364	75	24	on	on	ADP
ijassa-1364	75	25	a	a	DET
ijassa-1364	75	26	set	set	NOUN
ijassa-1364	75	27	m	m	VERB
ijassa-1364	75	28	⊂	⊂	X
ijassa-1364	75	29	x	x	X
ijassa-1364	76	1	if	if	SCONJ
ijassa-1364	76	2	for	for	ADP
ijassa-1364	76	3	any	any	DET
ijassa-1364	76	4	points	point	NOUN
ijassa-1364	76	5	x1	x1	PROPN
ijassa-1364	76	6	,	,	PUNCT
ijassa-1364	76	7	x2	x2	PROPN
ijassa-1364	76	8	∈m	∈m	NOUN
ijassa-1364	76	9	and	and	CCONJ
ijassa-1364	76	10	any	any	DET
ijassa-1364	76	11	λ	λ	X
ijassa-1364	76	12	∈	∈	PROPN
ijassa-1364	77	1	[	[	X
ijassa-1364	77	2	0	0	NUM
ijassa-1364	77	3	,	,	PUNCT
ijassa-1364	77	4	1	1	NUM
ijassa-1364	77	5	]	]	PUNCT
ijassa-1364	77	6	the	the	DET
ijassa-1364	77	7	condition	condition	NOUN
ijassa-1364	77	8	λf	λf	X
ijassa-1364	77	9	(	(	PUNCT
ijassa-1364	77	10	t	t	PROPN
ijassa-1364	77	11	,	,	PUNCT
ijassa-1364	77	12	x1	x1	PROPN
ijassa-1364	77	13	)	)	PUNCT
ijassa-1364	78	1	+	+	CCONJ
ijassa-1364	78	2	(	(	PUNCT
ijassa-1364	78	3	1−	1−	NUM
ijassa-1364	78	4	λ)f	λ)f	X
ijassa-1364	78	5	(	(	PUNCT
ijassa-1364	78	6	t	t	PROPN
ijassa-1364	78	7	,	,	PUNCT
ijassa-1364	78	8	x2	x2	PROPN
ijassa-1364	78	9	)	)	PUNCT
ijassa-1364	79	1	⊂	⊂	PROPN
ijassa-1364	79	2	f	f	X
ijassa-1364	79	3	(	(	PUNCT
ijassa-1364	79	4	t	t	PROPN
ijassa-1364	79	5	,	,	PUNCT
ijassa-1364	79	6	λx1	λx1	X
ijassa-1364	79	7	+	+	CCONJ
ijassa-1364	79	8	(	(	PUNCT
ijassa-1364	79	9	1−	1−	NUM
ijassa-1364	79	10	λ)x2	λ)x2	NOUN
ijassa-1364	79	11	)	)	PUNCT
ijassa-1364	79	12	holds	hold	VERB
ijassa-1364	79	13	true	true	ADJ
ijassa-1364	79	14	.	.	PUNCT
ijassa-1364	80	1	we	we	PRON
ijassa-1364	80	2	note	note	VERB
ijassa-1364	80	3	that	that	SCONJ
ijassa-1364	80	4	the	the	DET
ijassa-1364	80	5	above	above	ADJ
ijassa-1364	80	6	condition	condition	NOUN
ijassa-1364	80	7	implies	imply	VERB
ijassa-1364	80	8	the	the	DET
ijassa-1364	80	9	set	set	ADJ
ijassa-1364	80	10	f	f	PROPN
ijassa-1364	80	11	(	(	PUNCT
ijassa-1364	80	12	t	t	PROPN
ijassa-1364	80	13	,	,	PUNCT
ijassa-1364	80	14	x	x	PRON
ijassa-1364	80	15	)	)	PUNCT
ijassa-1364	80	16	is	be	AUX
ijassa-1364	80	17	convex	convex	ADJ
ijassa-1364	80	18	for	for	ADP
ijassa-1364	80	19	every	every	DET
ijassa-1364	80	20	x	x	SYM
ijassa-1364	80	21	∈m	∈m	NOUN
ijassa-1364	80	22	(	(	PUNCT
ijassa-1364	80	23	see	see	VERB
ijassa-1364	80	24	[	[	X
ijassa-1364	80	25	6	6	NUM
ijassa-1364	80	26	]	]	NUM
ijassa-1364	80	27	)	)	PUNCT
ijassa-1364	80	28	.	.	PUNCT
ijassa-1364	81	1	the	the	DET
ijassa-1364	81	2	reachability	reachability	NOUN
ijassa-1364	81	3	set	set	VERB
ijassa-1364	81	4	k(t	k(t	PROPN
ijassa-1364	81	5	)	)	PUNCT
ijassa-1364	81	6	for	for	ADP
ijassa-1364	81	7	each	each	DET
ijassa-1364	81	8	t	t	NOUN
ijassa-1364	81	9	∈	∈	PROPN
ijassa-1364	82	1	[	[	X
ijassa-1364	82	2	0	0	NUM
ijassa-1364	82	3	,	,	PUNCT
ijassa-1364	82	4	τ	τ	PROPN
ijassa-1364	82	5	]	]	PUNCT
ijassa-1364	82	6	consists	consist	VERB
ijassa-1364	82	7	of	of	ADP
ijassa-1364	82	8	all	all	DET
ijassa-1364	82	9	points	point	NOUN
ijassa-1364	82	10	x(t	x(t	PROPN
ijassa-1364	82	11	)	)	PUNCT
ijassa-1364	82	12	∈	∈	PROPN
ijassa-1364	82	13	rn	rn	PROPN
ijassa-1364	82	14	,	,	PUNCT
ijassa-1364	82	15	where	where	SCONJ
ijassa-1364	82	16	x(t	x(t	PROPN
ijassa-1364	82	17	)	)	PUNCT
ijassa-1364	82	18	is	be	AUX
ijassa-1364	82	19	the	the	DET
ijassa-1364	82	20	solution	solution	NOUN
ijassa-1364	82	21	of	of	ADP
ijassa-1364	82	22	the	the	DET
ijassa-1364	82	23	inclusion	inclusion	NOUN
ijassa-1364	82	24	(	(	PUNCT
ijassa-1364	82	25	2.5	2.5	NUM
ijassa-1364	82	26	)	)	PUNCT
ijassa-1364	82	27	with	with	ADP
ijassa-1364	82	28	initial	initial	ADJ
ijassa-1364	82	29	condition	condition	NOUN
ijassa-1364	82	30	x(0	x(0	PROPN
ijassa-1364	82	31	)	)	PUNCT
ijassa-1364	82	32	∈m0	∈m0	NOUN
ijassa-1364	82	33	.	.	PUNCT
ijassa-1364	83	1	consider	consider	VERB
ijassa-1364	83	2	the	the	DET
ijassa-1364	83	3	motion	motion	NOUN
ijassa-1364	83	4	of	of	ADP
ijassa-1364	83	5	an	an	DET
ijassa-1364	83	6	object	object	NOUN
ijassa-1364	83	7	in	in	ADP
ijassa-1364	83	8	the	the	DET
ijassa-1364	83	9	space	space	NOUN
ijassa-1364	83	10	x	x	NOUN
ijassa-1364	83	11	from	from	ADP
ijassa-1364	83	12	the	the	DET
ijassa-1364	83	13	initial	initial	ADJ
ijassa-1364	83	14	set	set	VERB
ijassa-1364	83	15	m0	m0	NOUN
ijassa-1364	83	16	to	to	ADP
ijassa-1364	83	17	the	the	DET
ijassa-1364	83	18	transition	transition	NOUN
ijassa-1364	83	19	hypersurface	hypersurface	NOUN
ijassa-1364	83	20	γ	γ	X
ijassa-1364	83	21	.	.	PUNCT
ijassa-1364	83	22	let	let	VERB
ijassa-1364	83	23	us	we	PRON
ijassa-1364	83	24	suppose	suppose	VERB
ijassa-1364	83	25	that	that	SCONJ
ijassa-1364	83	26	the	the	DET
ijassa-1364	83	27	mapping	mapping	NOUN
ijassa-1364	83	28	f	f	X
ijassa-1364	83	29	(	(	PUNCT
ijassa-1364	83	30	t	t	PROPN
ijassa-1364	83	31	,	,	PUNCT
ijassa-1364	83	32	x	x	PRON
ijassa-1364	83	33	)	)	PUNCT
ijassa-1364	83	34	is	be	AUX
ijassa-1364	83	35	concave	concave	VERB
ijassa-1364	83	36	by	by	ADP
ijassa-1364	83	37	x	x	PUNCT
ijassa-1364	83	38	on	on	ADP
ijassa-1364	83	39	the	the	DET
ijassa-1364	83	40	reachability	reachability	NOUN
ijassa-1364	83	41	copyright	copyright	NOUN
ijassa-1364	83	42	©	©	ADP
ijassa-1364	83	43	2023	2023	NUM
ijassa-1364	83	44	assa	assa	NOUN
ijassa-1364	83	45	.	.	PUNCT
ijassa-1364	84	1	adv	adv	PROPN
ijassa-1364	84	2	syst	syst	PROPN
ijassa-1364	84	3	sci	sci	PROPN
ijassa-1364	84	4	appl	appl	PROPN
ijassa-1364	84	5	(	(	PUNCT
ijassa-1364	84	6	2023	2023	NUM
ijassa-1364	84	7	)	)	PUNCT
ijassa-1364	84	8	64	64	NUM
ijassa-1364	84	9	i.	i.	NOUN
ijassa-1364	84	10	maximova	maximova	PROPN
ijassa-1364	84	11	set	set	PROPN
ijassa-1364	84	12	k(τ	k(τ	PROPN
ijassa-1364	84	13	)	)	PUNCT
ijassa-1364	84	14	for	for	ADP
ijassa-1364	84	15	all	all	DET
ijassa-1364	84	16	t	t	NOUN
ijassa-1364	84	17	∈	∈	PROPN
ijassa-1364	85	1	[	[	X
ijassa-1364	85	2	0	0	NUM
ijassa-1364	85	3	,	,	PUNCT
ijassa-1364	85	4	τ	τ	X
ijassa-1364	85	5	]	]	PUNCT
ijassa-1364	85	6	.	.	PUNCT
ijassa-1364	86	1	it	it	PRON
ijassa-1364	86	2	is	be	AUX
ijassa-1364	86	3	known	know	VERB
ijassa-1364	86	4	(	(	PUNCT
ijassa-1364	86	5	see	see	VERB
ijassa-1364	86	6	[	[	X
ijassa-1364	86	7	6	6	NUM
ijassa-1364	86	8	]	]	PUNCT
ijassa-1364	86	9	)	)	PUNCT
ijassa-1364	86	10	that	that	SCONJ
ijassa-1364	86	11	in	in	ADP
ijassa-1364	86	12	this	this	DET
ijassa-1364	86	13	case	case	NOUN
ijassa-1364	86	14	the	the	DET
ijassa-1364	86	15	family	family	NOUN
ijassa-1364	86	16	of	of	ADP
ijassa-1364	86	17	all	all	DET
ijassa-1364	86	18	solutions	solution	NOUN
ijassa-1364	86	19	on	on	ADP
ijassa-1364	86	20	the	the	DET
ijassa-1364	86	21	interval	interval	NOUN
ijassa-1364	86	22	[	[	X
ijassa-1364	86	23	0	0	NUM
ijassa-1364	86	24	,	,	PUNCT
ijassa-1364	86	25	τ	τ	X
ijassa-1364	86	26	]	]	PUNCT
ijassa-1364	86	27	with	with	ADP
ijassa-1364	86	28	initial	initial	ADJ
ijassa-1364	86	29	condition	condition	NOUN
ijassa-1364	86	30	x(0	x(0	PROPN
ijassa-1364	86	31	)	)	PUNCT
ijassa-1364	86	32	∈m0	∈m0	NOUN
ijassa-1364	86	33	is	be	AUX
ijassa-1364	86	34	a	a	DET
ijassa-1364	86	35	convex	convex	NOUN
ijassa-1364	86	36	set	set	VERB
ijassa-1364	86	37	in	in	ADP
ijassa-1364	86	38	the	the	DET
ijassa-1364	86	39	space	space	NOUN
ijassa-1364	86	40	c[0	c[0	PROPN
ijassa-1364	86	41	,	,	PUNCT
ijassa-1364	86	42	τ	τ	X
ijassa-1364	86	43	]	]	PUNCT
ijassa-1364	86	44	.	.	PUNCT
ijassa-1364	87	1	the	the	DET
ijassa-1364	87	2	convexity	convexity	NOUN
ijassa-1364	87	3	of	of	ADP
ijassa-1364	87	4	the	the	DET
ijassa-1364	87	5	solution	solution	NOUN
ijassa-1364	87	6	family	family	NOUN
ijassa-1364	87	7	implies	imply	VERB
ijassa-1364	87	8	that	that	SCONJ
ijassa-1364	87	9	the	the	DET
ijassa-1364	87	10	reachability	reachability	NOUN
ijassa-1364	87	11	set	set	VERB
ijassa-1364	87	12	k(τ	k(τ	PROPN
ijassa-1364	87	13	)	)	PUNCT
ijassa-1364	87	14	is	be	AUX
ijassa-1364	87	15	convex	convex	ADJ
ijassa-1364	87	16	(	(	PUNCT
ijassa-1364	87	17	the	the	DET
ijassa-1364	87	18	reverse	reverse	NOUN
ijassa-1364	87	19	is	be	AUX
ijassa-1364	87	20	not	not	PART
ijassa-1364	87	21	true	true	ADJ
ijassa-1364	87	22	)	)	PUNCT
ijassa-1364	87	23	.	.	PUNCT
ijassa-1364	88	1	so	so	ADV
ijassa-1364	88	2	,	,	PUNCT
ijassa-1364	88	3	under	under	ADP
ijassa-1364	88	4	the	the	DET
ijassa-1364	88	5	above	above	ADJ
ijassa-1364	88	6	assumptions	assumption	NOUN
ijassa-1364	88	7	,	,	PUNCT
ijassa-1364	88	8	the	the	DET
ijassa-1364	88	9	reachability	reachability	NOUN
ijassa-1364	88	10	set	set	VERB
ijassa-1364	88	11	k(τ	k(τ	PROPN
ijassa-1364	88	12	)	)	PUNCT
ijassa-1364	88	13	is	be	AUX
ijassa-1364	88	14	convex	convex	PROPN
ijassa-1364	88	15	.	.	PUNCT
ijassa-1364	89	1	the	the	DET
ijassa-1364	89	2	intersection	intersection	NOUN
ijassa-1364	89	3	of	of	ADP
ijassa-1364	89	4	k(τ	k(τ	PROPN
ijassa-1364	89	5	)	)	PUNCT
ijassa-1364	89	6	with	with	ADP
ijassa-1364	89	7	the	the	DET
ijassa-1364	89	8	transition	transition	NOUN
ijassa-1364	89	9	hypersurface	hypersurface	NOUN
ijassa-1364	89	10	γ	γ	PROPN
ijassa-1364	89	11	,	,	PUNCT
ijassa-1364	89	12	we	we	PRON
ijassa-1364	89	13	obtain	obtain	VERB
ijassa-1364	89	14	the	the	DET
ijassa-1364	89	15	set	set	NOUN
ijassa-1364	89	16	k1(τ	k1(τ	PROPN
ijassa-1364	89	17	)	)	PUNCT
ijassa-1364	89	18	=	=	SYM
ijassa-1364	89	19	k(τ	k(τ	PROPN
ijassa-1364	89	20	)	)	PUNCT
ijassa-1364	89	21	∩	∩	PROPN
ijassa-1364	89	22	γ	γ	X
ijassa-1364	89	23	.	.	PROPN
ijassa-1364	89	24	suppose	suppose	VERB
ijassa-1364	89	25	that	that	SCONJ
ijassa-1364	89	26	there	there	PRON
ijassa-1364	89	27	exists	exist	VERB
ijassa-1364	89	28	τ	τ	X
ijassa-1364	89	29	:	:	PUNCT
ijassa-1364	89	30	k1(τ	k1(τ	PROPN
ijassa-1364	89	31	)	)	PUNCT
ijassa-1364	89	32	̸=	̸=	PROPN
ijassa-1364	89	33	∅.	∅.	PRON
ijassa-1364	89	34	then	then	ADV
ijassa-1364	89	35	k1(τ	k1(τ	PROPN
ijassa-1364	89	36	)	)	PUNCT
ijassa-1364	89	37	is	be	AUX
ijassa-1364	89	38	convex	convex	ADJ
ijassa-1364	89	39	as	as	ADP
ijassa-1364	89	40	intersection	intersection	NOUN
ijassa-1364	89	41	of	of	ADP
ijassa-1364	89	42	two	two	NUM
ijassa-1364	89	43	convex	convex	NOUN
ijassa-1364	89	44	sets	set	NOUN
ijassa-1364	89	45	.	.	PUNCT
ijassa-1364	90	1	let	let	VERB
ijassa-1364	90	2	us	we	PRON
ijassa-1364	90	3	transform	transform	VERB
ijassa-1364	90	4	the	the	DET
ijassa-1364	90	5	set	set	NOUN
ijassa-1364	90	6	k1(τ	k1(τ	PROPN
ijassa-1364	90	7	)	)	PUNCT
ijassa-1364	90	8	as	as	SCONJ
ijassa-1364	90	9	follows	follow	VERB
ijassa-1364	90	10	:	:	PUNCT
ijassa-1364	90	11	k2(τ	k2(τ	X
ijassa-1364	90	12	)	)	PUNCT
ijassa-1364	90	13	=	=	SYM
ijassa-1364	90	14	q(k1(τ	q(k1(τ	PROPN
ijassa-1364	90	15	)	)	PUNCT
ijassa-1364	90	16	)	)	PUNCT
ijassa-1364	90	17	,	,	PUNCT
ijassa-1364	90	18	where	where	SCONJ
ijassa-1364	90	19	q	q	X
ijassa-1364	90	20	:	:	PUNCT
ijassa-1364	90	21	x	x	X
ijassa-1364	90	22	→	→	PUNCT
ijassa-1364	90	23	y.	y.	NOUN
ijassa-1364	90	24	the	the	DET
ijassa-1364	90	25	resulting	result	VERB
ijassa-1364	90	26	set	set	VERB
ijassa-1364	90	27	k2(τ	k2(τ	PROPN
ijassa-1364	90	28	)	)	PUNCT
ijassa-1364	90	29	is	be	AUX
ijassa-1364	90	30	convex	convex	ADJ
ijassa-1364	90	31	due	due	ADP
ijassa-1364	90	32	to	to	ADP
ijassa-1364	90	33	the	the	DET
ijassa-1364	90	34	properties	property	NOUN
ijassa-1364	90	35	of	of	ADP
ijassa-1364	90	36	mapping	map	VERB
ijassa-1364	90	37	q.	q.	NOUN
ijassa-1364	90	38	the	the	DET
ijassa-1364	90	39	set	set	NOUN
ijassa-1364	90	40	k2(τ	k2(τ	PROPN
ijassa-1364	90	41	)	)	PUNCT
ijassa-1364	90	42	is	be	AUX
ijassa-1364	90	43	the	the	DET
ijassa-1364	90	44	initial	initial	ADJ
ijassa-1364	90	45	set	set	NOUN
ijassa-1364	90	46	when	when	SCONJ
ijassa-1364	90	47	the	the	DET
ijassa-1364	90	48	object	object	NOUN
ijassa-1364	90	49	moves	move	VERB
ijassa-1364	90	50	in	in	ADP
ijassa-1364	90	51	the	the	DET
ijassa-1364	90	52	space	space	NOUN
ijassa-1364	90	53	y	y	NOUN
ijassa-1364	90	54	into	into	ADP
ijassa-1364	90	55	the	the	DET
ijassa-1364	90	56	set	set	NOUN
ijassa-1364	90	57	m1	m1	NOUN
ijassa-1364	90	58	.	.	PUNCT
ijassa-1364	91	1	in	in	ADP
ijassa-1364	91	2	the	the	DET
ijassa-1364	91	3	space	space	NOUN
ijassa-1364	91	4	y	y	NOUN
ijassa-1364	91	5	we	we	PRON
ijassa-1364	91	6	obtain	obtain	VERB
ijassa-1364	91	7	the	the	DET
ijassa-1364	91	8	following	follow	VERB
ijassa-1364	91	9	controllability	controllability	NOUN
ijassa-1364	91	10	problem	problem	NOUN
ijassa-1364	91	11	:	:	PUNCT
ijassa-1364	91	12	whether	whether	SCONJ
ijassa-1364	91	13	the	the	DET
ijassa-1364	91	14	system	system	NOUN
ijassa-1364	91	15	(	(	PUNCT
ijassa-1364	91	16	2.2	2.2	NUM
ijassa-1364	91	17	)	)	PUNCT
ijassa-1364	91	18	is	be	AUX
ijassa-1364	91	19	controllable	controllable	ADJ
ijassa-1364	91	20	from	from	ADP
ijassa-1364	91	21	the	the	DET
ijassa-1364	91	22	set	set	NOUN
ijassa-1364	91	23	k2(τ	k2(τ	PROPN
ijassa-1364	91	24	)	)	PUNCT
ijassa-1364	91	25	to	to	ADP
ijassa-1364	91	26	the	the	DET
ijassa-1364	91	27	set	set	VERB
ijassa-1364	91	28	m1	m1	PROPN
ijassa-1364	91	29	at	at	ADP
ijassa-1364	91	30	the	the	DET
ijassa-1364	91	31	time	time	NOUN
ijassa-1364	91	32	interval	interval	NOUN
ijassa-1364	91	33	[	[	X
ijassa-1364	91	34	τ	τ	PROPN
ijassa-1364	91	35	,	,	PUNCT
ijassa-1364	91	36	t	t	X
ijassa-1364	91	37	]	]	PUNCT
ijassa-1364	91	38	.	.	PUNCT
ijassa-1364	92	1	let	let	VERB
ijassa-1364	92	2	us	we	PRON
ijassa-1364	92	3	denote	denote	VERB
ijassa-1364	92	4	the	the	DET
ijassa-1364	92	5	system	system	NOUN
ijassa-1364	92	6	reachability	reachability	NOUN
ijassa-1364	92	7	set	set	NOUN
ijassa-1364	92	8	(	(	PUNCT
ijassa-1364	92	9	2.2	2.2	NUM
ijassa-1364	92	10	)	)	PUNCT
ijassa-1364	92	11	from	from	ADP
ijassa-1364	92	12	k2(τ	k2(τ	PROPN
ijassa-1364	92	13	)	)	PUNCT
ijassa-1364	92	14	at	at	ADP
ijassa-1364	92	15	time	time	NOUN
ijassa-1364	92	16	t	t	NOUN
ijassa-1364	92	17	by	by	ADP
ijassa-1364	92	18	k3(t	k3(t	PROPN
ijassa-1364	92	19	)	)	PUNCT
ijassa-1364	92	20	.	.	PUNCT
ijassa-1364	93	1	let	let	VERB
ijassa-1364	93	2	us	we	PRON
ijassa-1364	93	3	suppose	suppose	VERB
ijassa-1364	93	4	that	that	SCONJ
ijassa-1364	93	5	the	the	DET
ijassa-1364	93	6	mapping	mapping	PROPN
ijassa-1364	93	7	g(t	g(t	PROPN
ijassa-1364	93	8	,	,	PUNCT
ijassa-1364	93	9	y	y	PROPN
ijassa-1364	93	10	)	)	PUNCT
ijassa-1364	93	11	is	be	AUX
ijassa-1364	93	12	concave	concave	VERB
ijassa-1364	93	13	on	on	ADP
ijassa-1364	93	14	y	y	PROPN
ijassa-1364	93	15	on	on	ADP
ijassa-1364	93	16	the	the	DET
ijassa-1364	93	17	reachability	reachability	NOUN
ijassa-1364	93	18	set	set	VERB
ijassa-1364	93	19	k3(t	k3(t	PROPN
ijassa-1364	93	20	)	)	PUNCT
ijassa-1364	93	21	and	and	CCONJ
ijassa-1364	93	22	k3(t	k3(t	PROPN
ijassa-1364	93	23	)	)	PUNCT
ijassa-1364	93	24	is	be	AUX
ijassa-1364	93	25	compact	compact	ADJ
ijassa-1364	93	26	.	.	PUNCT
ijassa-1364	94	1	then	then	ADV
ijassa-1364	94	2	,	,	PUNCT
ijassa-1364	94	3	for	for	ADP
ijassa-1364	94	4	the	the	DET
ijassa-1364	94	5	controllability	controllability	NOUN
ijassa-1364	94	6	of	of	ADP
ijassa-1364	94	7	the	the	DET
ijassa-1364	94	8	system	system	NOUN
ijassa-1364	94	9	(	(	PUNCT
ijassa-1364	94	10	2.2	2.2	NUM
ijassa-1364	94	11	)	)	PUNCT
ijassa-1364	94	12	it	it	PRON
ijassa-1364	94	13	is	be	AUX
ijassa-1364	94	14	sufficient	sufficient	ADJ
ijassa-1364	94	15	that	that	SCONJ
ijassa-1364	94	16	k3(t	k3(t	PROPN
ijassa-1364	94	17	)	)	PUNCT
ijassa-1364	94	18	∩m1	∩m1	PROPN
ijassa-1364	94	19	̸=	̸=	PROPN
ijassa-1364	94	20	∅	∅	NOUN
ijassa-1364	94	21	or	or	CCONJ
ijassa-1364	94	22	,	,	PUNCT
ijassa-1364	94	23	in	in	ADP
ijassa-1364	94	24	the	the	DET
ijassa-1364	94	25	terms	term	NOUN
ijassa-1364	94	26	of	of	ADP
ijassa-1364	94	27	support	support	NOUN
ijassa-1364	94	28	functions	function	NOUN
ijassa-1364	94	29	,	,	PUNCT
ijassa-1364	94	30	the	the	DET
ijassa-1364	94	31	inequality	inequality	NOUN
ijassa-1364	94	32	c(k3(t	c(k3(t	NOUN
ijassa-1364	94	33	)	)	PUNCT
ijassa-1364	94	34	,	,	PUNCT
ijassa-1364	94	35	ψ	ψ	X
ijassa-1364	94	36	)	)	PUNCT
ijassa-1364	94	37	+	+	CCONJ
ijassa-1364	94	38	c(m1,−ψ	c(m1,−ψ	NOUN
ijassa-1364	94	39	)	)	PUNCT
ijassa-1364	94	40	≥	≥	X
ijassa-1364	94	41	0	0	NUM
ijassa-1364	94	42	holds	hold	VERB
ijassa-1364	94	43	true	true	ADJ
ijassa-1364	94	44	for	for	SCONJ
ijassa-1364	94	45	any	any	DET
ijassa-1364	94	46	ψ	ψ	NOUN
ijassa-1364	94	47	∈	∈	PROPN
ijassa-1364	94	48	rm	rm	NOUN
ijassa-1364	94	49	(	(	PUNCT
ijassa-1364	94	50	see	see	VERB
ijassa-1364	94	51	[	[	X
ijassa-1364	94	52	5	5	NUM
ijassa-1364	94	53	]	]	NUM
ijassa-1364	94	54	)	)	PUNCT
ijassa-1364	94	55	.	.	PUNCT
ijassa-1364	95	1	thus	thus	ADV
ijassa-1364	95	2	,	,	PUNCT
ijassa-1364	95	3	the	the	DET
ijassa-1364	95	4	controllability	controllability	NOUN
ijassa-1364	95	5	conditions	condition	NOUN
ijassa-1364	95	6	from	from	ADP
ijassa-1364	95	7	the	the	DET
ijassa-1364	95	8	set	set	NOUN
ijassa-1364	95	9	m0	m0	NOUN
ijassa-1364	95	10	⊂	⊂	PROPN
ijassa-1364	95	11	x	x	PUNCT
ijassa-1364	95	12	to	to	ADP
ijassa-1364	95	13	the	the	DET
ijassa-1364	95	14	set	set	NOUN
ijassa-1364	95	15	m1	m1	PROPN
ijassa-1364	95	16	⊂	⊂	PROPN
ijassa-1364	95	17	y	y	PROPN
ijassa-1364	95	18	for	for	ADP
ijassa-1364	95	19	systems	system	NOUN
ijassa-1364	95	20	(	(	PUNCT
ijassa-1364	95	21	2.1	2.1	NUM
ijassa-1364	95	22	)	)	PUNCT
ijassa-1364	95	23	and	and	CCONJ
ijassa-1364	95	24	(	(	PUNCT
ijassa-1364	95	25	2.2	2.2	NUM
ijassa-1364	95	26	)	)	PUNCT
ijassa-1364	95	27	can	can	AUX
ijassa-1364	95	28	be	be	AUX
ijassa-1364	95	29	expressed	express	VERB
ijassa-1364	95	30	as	as	ADP
ijassa-1364	95	31	the	the	DET
ijassa-1364	95	32	following	follow	VERB
ijassa-1364	95	33	statement	statement	NOUN
ijassa-1364	95	34	:	:	PUNCT
ijassa-1364	95	35	theorem	theorem	VERB
ijassa-1364	95	36	2.1	2.1	NUM
ijassa-1364	95	37	:	:	PUNCT
ijassa-1364	95	38	under	under	ADP
ijassa-1364	95	39	the	the	DET
ijassa-1364	95	40	above	above	ADJ
ijassa-1364	95	41	assumptions	assumption	NOUN
ijassa-1364	95	42	,	,	PUNCT
ijassa-1364	95	43	for	for	ADP
ijassa-1364	95	44	the	the	DET
ijassa-1364	95	45	controllability	controllability	NOUN
ijassa-1364	95	46	of	of	ADP
ijassa-1364	95	47	an	an	DET
ijassa-1364	95	48	object	object	NOUN
ijassa-1364	95	49	described	describe	VERB
ijassa-1364	95	50	by	by	ADP
ijassa-1364	95	51	systems	system	NOUN
ijassa-1364	95	52	(	(	PUNCT
ijassa-1364	95	53	2.1	2.1	NUM
ijassa-1364	95	54	)	)	PUNCT
ijassa-1364	95	55	and	and	CCONJ
ijassa-1364	95	56	(	(	PUNCT
ijassa-1364	95	57	2.2	2.2	NUM
ijassa-1364	95	58	)	)	PUNCT
ijassa-1364	95	59	on	on	ADP
ijassa-1364	95	60	the	the	DET
ijassa-1364	95	61	time	time	NOUN
ijassa-1364	95	62	interval	interval	NOUN
ijassa-1364	95	63	[	[	X
ijassa-1364	95	64	0	0	NUM
ijassa-1364	95	65	,	,	PUNCT
ijassa-1364	95	66	t	t	X
ijassa-1364	95	67	]	]	PUNCT
ijassa-1364	95	68	it	it	PRON
ijassa-1364	95	69	is	be	AUX
ijassa-1364	95	70	sufficient	sufficient	ADJ
ijassa-1364	95	71	that	that	SCONJ
ijassa-1364	95	72	c(k3(t	c(k3(t	NOUN
ijassa-1364	95	73	)	)	PUNCT
ijassa-1364	95	74	,	,	PUNCT
ijassa-1364	95	75	ψ	ψ	X
ijassa-1364	95	76	)	)	PUNCT
ijassa-1364	95	77	+	+	CCONJ
ijassa-1364	95	78	c(m1,−ψ	c(m1,−ψ	NOUN
ijassa-1364	95	79	)	)	PUNCT
ijassa-1364	95	80	≥	≥	NOUN
ijassa-1364	95	81	0	0	NUM
ijassa-1364	95	82	,	,	PUNCT
ijassa-1364	95	83	for	for	ADP
ijassa-1364	95	84	any	any	DET
ijassa-1364	95	85	ψ	ψ	NOUN
ijassa-1364	95	86	∈	∈	PROPN
ijassa-1364	95	87	rm	rm	PROPN
ijassa-1364	95	88	.	.	PROPN
ijassa-1364	95	89	remark	remark	PROPN
ijassa-1364	95	90	2.2	2.2	NUM
ijassa-1364	95	91	:	:	PUNCT
ijassa-1364	95	92	for	for	ADP
ijassa-1364	95	93	autonomous	autonomous	ADJ
ijassa-1364	95	94	system	system	NOUN
ijassa-1364	95	95	(	(	PUNCT
ijassa-1364	95	96	2.2	2.2	NUM
ijassa-1364	95	97	)	)	PUNCT
ijassa-1364	95	98	,	,	PUNCT
ijassa-1364	95	99	one	one	PRON
ijassa-1364	95	100	can	can	AUX
ijassa-1364	95	101	consider	consider	VERB
ijassa-1364	95	102	the	the	DET
ijassa-1364	95	103	motion	motion	NOUN
ijassa-1364	95	104	of	of	ADP
ijassa-1364	95	105	an	an	DET
ijassa-1364	95	106	object	object	NOUN
ijassa-1364	95	107	in	in	ADP
ijassa-1364	95	108	y	y	PROPN
ijassa-1364	95	109	space	space	NOUN
ijassa-1364	95	110	in	in	ADP
ijassa-1364	95	111	backward	backward	ADJ
ijassa-1364	95	112	time	time	NOUN
ijassa-1364	95	113	and	and	CCONJ
ijassa-1364	95	114	get	get	VERB
ijassa-1364	95	115	the	the	DET
ijassa-1364	95	116	reachability	reachability	NOUN
ijassa-1364	95	117	set	set	VERB
ijassa-1364	95	118	k4(t	k4(t	PROPN
ijassa-1364	95	119	)	)	PUNCT
ijassa-1364	95	120	from	from	ADP
ijassa-1364	95	121	the	the	DET
ijassa-1364	95	122	set	set	ADJ
ijassa-1364	95	123	m1	m1	PROPN
ijassa-1364	95	124	on	on	ADP
ijassa-1364	95	125	the	the	PRON
ijassa-1364	95	126	of	of	ADP
ijassa-1364	95	127	the	the	DET
ijassa-1364	95	128	transition	transition	NOUN
ijassa-1364	95	129	hypersurface	hypersurface	NOUN
ijassa-1364	95	130	γ	γ	PROPN
ijassa-1364	95	131	.	.	PROPN
ijassa-1364	96	1	then	then	ADV
ijassa-1364	96	2	the	the	DET
ijassa-1364	96	3	controllability	controllability	NOUN
ijassa-1364	96	4	condition	condition	NOUN
ijassa-1364	96	5	for	for	ADP
ijassa-1364	96	6	the	the	DET
ijassa-1364	96	7	systems	system	NOUN
ijassa-1364	96	8	(	(	PUNCT
ijassa-1364	96	9	2.1	2.1	NUM
ijassa-1364	96	10	)	)	PUNCT
ijassa-1364	96	11	and	and	CCONJ
ijassa-1364	96	12	(	(	PUNCT
ijassa-1364	96	13	2.2	2.2	NUM
ijassa-1364	96	14	)	)	PUNCT
ijassa-1364	96	15	on	on	ADP
ijassa-1364	96	16	the	the	DET
ijassa-1364	96	17	time	time	NOUN
ijassa-1364	96	18	interval	interval	NOUN
ijassa-1364	96	19	[	[	X
ijassa-1364	96	20	0	0	NUM
ijassa-1364	96	21	,	,	PUNCT
ijassa-1364	96	22	t	t	PROPN
ijassa-1364	96	23	]	]	PUNCT
ijassa-1364	96	24	is	be	AUX
ijassa-1364	96	25	a	a	DET
ijassa-1364	96	26	non	non	ADJ
ijassa-1364	96	27	-	-	ADJ
ijassa-1364	96	28	empty	empty	ADJ
ijassa-1364	96	29	intersection	intersection	NOUN
ijassa-1364	96	30	of	of	ADP
ijassa-1364	96	31	the	the	DET
ijassa-1364	96	32	sets	set	NOUN
ijassa-1364	96	33	k4(t	k4(t	PROPN
ijassa-1364	96	34	)	)	PUNCT
ijassa-1364	96	35	and	and	CCONJ
ijassa-1364	96	36	k2(τ	k2(τ	PROPN
ijassa-1364	96	37	)	)	PUNCT
ijassa-1364	96	38	.	.	PUNCT
ijassa-1364	97	1	3	3	X
ijassa-1364	97	2	.	.	X
ijassa-1364	97	3	linear	linear	PROPN
ijassa-1364	97	4	systems	system	NOUN
ijassa-1364	97	5	in	in	ADP
ijassa-1364	97	6	this	this	DET
ijassa-1364	97	7	part	part	NOUN
ijassa-1364	97	8	of	of	ADP
ijassa-1364	97	9	the	the	DET
ijassa-1364	97	10	paper	paper	NOUN
ijassa-1364	97	11	we	we	PRON
ijassa-1364	97	12	consider	consider	VERB
ijassa-1364	97	13	the	the	DET
ijassa-1364	97	14	case	case	NOUN
ijassa-1364	97	15	where	where	SCONJ
ijassa-1364	97	16	the	the	DET
ijassa-1364	97	17	motion	motion	NOUN
ijassa-1364	97	18	of	of	ADP
ijassa-1364	97	19	the	the	DET
ijassa-1364	97	20	controlled	control	VERB
ijassa-1364	97	21	object	object	NOUN
ijassa-1364	97	22	is	be	AUX
ijassa-1364	97	23	described	describe	VERB
ijassa-1364	97	24	by	by	ADP
ijassa-1364	97	25	a	a	DET
ijassa-1364	97	26	linear	linear	ADJ
ijassa-1364	97	27	system	system	NOUN
ijassa-1364	97	28	of	of	ADP
ijassa-1364	97	29	differential	differential	ADJ
ijassa-1364	97	30	equations	equation	NOUN
ijassa-1364	97	31	.	.	PUNCT
ijassa-1364	98	1	let	let	VERB
ijassa-1364	98	2	us	we	PRON
ijassa-1364	98	3	suppose	suppose	VERB
ijassa-1364	98	4	that	that	SCONJ
ijassa-1364	98	5	systems	system	NOUN
ijassa-1364	98	6	(	(	PUNCT
ijassa-1364	98	7	2.1	2.1	NUM
ijassa-1364	98	8	)	)	PUNCT
ijassa-1364	98	9	and	and	CCONJ
ijassa-1364	98	10	(	(	PUNCT
ijassa-1364	98	11	2.2	2.2	NUM
ijassa-1364	98	12	)	)	PUNCT
ijassa-1364	98	13	are	be	AUX
ijassa-1364	98	14	linear	linear	ADJ
ijassa-1364	98	15	,	,	PUNCT
ijassa-1364	98	16	then	then	ADV
ijassa-1364	98	17	we	we	PRON
ijassa-1364	98	18	obtain	obtain	VERB
ijassa-1364	98	19	the	the	DET
ijassa-1364	98	20	following	follow	VERB
ijassa-1364	98	21	problem	problem	NOUN
ijassa-1364	98	22	.	.	PUNCT
ijassa-1364	99	1	3.1	3.1	NUM
ijassa-1364	99	2	.	.	PUNCT
ijassa-1364	99	3	problem	problem	NOUN
ijassa-1364	99	4	statement	statement	NOUN
ijassa-1364	99	5	let	let	VERB
ijassa-1364	99	6	x	x	PRON
ijassa-1364	99	7	and	and	CCONJ
ijassa-1364	99	8	y	y	PROPN
ijassa-1364	99	9	be	be	VERB
ijassa-1364	99	10	two	two	NUM
ijassa-1364	99	11	phase	phase	NOUN
ijassa-1364	99	12	variables	variable	NOUN
ijassa-1364	99	13	:	:	PUNCT
ijassa-1364	99	14	x	x	SYM
ijassa-1364	99	15	=	=	SYM
ijassa-1364	99	16	(	(	PUNCT
ijassa-1364	99	17	x1	x1	PROPN
ijassa-1364	99	18	,	,	PUNCT
ijassa-1364	99	19	.	.	PUNCT
ijassa-1364	99	20	.	.	PUNCT
ijassa-1364	100	1	.	.	PUNCT
ijassa-1364	101	1	,	,	PUNCT
ijassa-1364	101	2	xn	xn	X
ijassa-1364	101	3	)	)	PUNCT
ijassa-1364	101	4	∈	∈	NOUN
ijassa-1364	101	5	x	x	X
ijassa-1364	101	6	=	=	SYM
ijassa-1364	101	7	rn	rn	PROPN
ijassa-1364	101	8	,	,	PUNCT
ijassa-1364	101	9	y	y	PROPN
ijassa-1364	101	10	=	=	SYM
ijassa-1364	101	11	(	(	PUNCT
ijassa-1364	101	12	y1	y1	INTJ
ijassa-1364	101	13	,	,	PUNCT
ijassa-1364	101	14	.	.	PUNCT
ijassa-1364	101	15	.	.	PUNCT
ijassa-1364	101	16	.	.	PUNCT
ijassa-1364	102	1	,	,	PUNCT
ijassa-1364	102	2	ym	ym	X
ijassa-1364	102	3	)	)	PUNCT
ijassa-1364	102	4	∈	∈	PROPN
ijassa-1364	102	5	y	y	PROPN
ijassa-1364	102	6	=	=	SYM
ijassa-1364	102	7	rm	rm	PROPN
ijassa-1364	102	8	.	.	PUNCT
ijassa-1364	103	1	the	the	DET
ijassa-1364	103	2	motion	motion	NOUN
ijassa-1364	103	3	of	of	ADP
ijassa-1364	103	4	the	the	DET
ijassa-1364	103	5	object	object	NOUN
ijassa-1364	103	6	is	be	AUX
ijassa-1364	103	7	described	describe	VERB
ijassa-1364	103	8	by	by	ADP
ijassa-1364	103	9	the	the	DET
ijassa-1364	103	10	following	follow	VERB
ijassa-1364	103	11	linear	linear	PROPN
ijassa-1364	103	12	systems	system	NOUN
ijassa-1364	103	13	of	of	ADP
ijassa-1364	103	14	differential	differential	ADJ
ijassa-1364	103	15	equations	equation	NOUN
ijassa-1364	103	16	:	:	PUNCT
ijassa-1364	103	17	ẋ	ẋ	PROPN
ijassa-1364	104	1	=	=	PUNCT
ijassa-1364	105	1	ax+	ax+	PROPN
ijassa-1364	105	2	u	u	NOUN
ijassa-1364	105	3	,	,	PUNCT
ijassa-1364	105	4	u(t	u(t	NOUN
ijassa-1364	105	5	)	)	PUNCT
ijassa-1364	105	6	∈	∈	PROPN
ijassa-1364	105	7	u	u	NOUN
ijassa-1364	105	8	,	,	PUNCT
ijassa-1364	105	9	t	t	PROPN
ijassa-1364	105	10	∈	∈	PROPN
ijassa-1364	106	1	[	[	X
ijassa-1364	106	2	0	0	NUM
ijassa-1364	106	3	,	,	PUNCT
ijassa-1364	106	4	τ	τ	X
ijassa-1364	106	5	]	]	X
ijassa-1364	106	6	,	,	PUNCT
ijassa-1364	106	7	x	x	SYM
ijassa-1364	106	8	∈	∈	NOUN
ijassa-1364	106	9	x.	x.	NOUN
ijassa-1364	106	10	(	(	PUNCT
ijassa-1364	106	11	3.7	3.7	NUM
ijassa-1364	106	12	)	)	PUNCT
ijassa-1364	106	13	ẏ	ẏ	NOUN
ijassa-1364	106	14	=	=	PUNCT
ijassa-1364	106	15	by	by	ADP
ijassa-1364	106	16	+	+	PROPN
ijassa-1364	106	17	v	v	NOUN
ijassa-1364	106	18	,	,	PUNCT
ijassa-1364	106	19	v(t	v(t	NOUN
ijassa-1364	106	20	)	)	PUNCT
ijassa-1364	106	21	∈	∈	PROPN
ijassa-1364	106	22	v	v	NOUN
ijassa-1364	106	23	,	,	PUNCT
ijassa-1364	106	24	t	t	PROPN
ijassa-1364	106	25	∈	∈	PROPN
ijassa-1364	107	1	[	[	X
ijassa-1364	107	2	τ	τ	PROPN
ijassa-1364	107	3	,	,	PUNCT
ijassa-1364	107	4	t	t	X
ijassa-1364	107	5	]	]	PUNCT
ijassa-1364	107	6	,	,	PUNCT
ijassa-1364	107	7	y	y	PROPN
ijassa-1364	107	8	∈	∈	PROPN
ijassa-1364	107	9	y.	y.	NOUN
ijassa-1364	107	10	(	(	PUNCT
ijassa-1364	107	11	3.8	3.8	NUM
ijassa-1364	107	12	)	)	PUNCT
ijassa-1364	107	13	copyright	copyright	NOUN
ijassa-1364	107	14	©	©	PROPN
ijassa-1364	107	15	2023	2023	NUM
ijassa-1364	107	16	assa	assa	NOUN
ijassa-1364	107	17	.	.	PUNCT
ijassa-1364	108	1	adv	adv	PROPN
ijassa-1364	108	2	syst	syst	PROPN
ijassa-1364	108	3	sci	sci	PROPN
ijassa-1364	108	4	appl	appl	PROPN
ijassa-1364	108	5	(	(	PUNCT
ijassa-1364	108	6	2023	2023	NUM
ijassa-1364	108	7	)	)	PUNCT
ijassa-1364	108	8	the	the	DET
ijassa-1364	108	9	problem	problem	NOUN
ijassa-1364	108	10	of	of	ADP
ijassa-1364	108	11	controllability	controllability	NOUN
ijassa-1364	108	12	65	65	NUM
ijassa-1364	108	13	the	the	DET
ijassa-1364	108	14	class	class	NOUN
ijassa-1364	108	15	of	of	ADP
ijassa-1364	108	16	admissible	admissible	ADJ
ijassa-1364	108	17	controls	control	NOUN
ijassa-1364	108	18	is	be	AUX
ijassa-1364	108	19	the	the	DET
ijassa-1364	108	20	sets	set	NOUN
ijassa-1364	108	21	of	of	ADP
ijassa-1364	108	22	functions	function	NOUN
ijassa-1364	108	23	{	{	PUNCT
ijassa-1364	108	24	u	u	NOUN
ijassa-1364	108	25	(	(	PUNCT
ijassa-1364	108	26	·	·	PUNCT
ijassa-1364	108	27	)	)	PUNCT
ijassa-1364	108	28	∈	∈	PROPN
ijassa-1364	108	29	l∞([0	l∞([0	PROPN
ijassa-1364	108	30	,	,	PUNCT
ijassa-1364	108	31	τ	τ	X
ijassa-1364	108	32	]	]	X
ijassa-1364	108	33	,	,	PUNCT
ijassa-1364	108	34	rn	rn	PROPN
ijassa-1364	108	35	)	)	PUNCT
ijassa-1364	108	36	|	|	ADV
ijassa-1364	108	37	u(t	u(t	NOUN
ijassa-1364	108	38	)	)	PUNCT
ijassa-1364	108	39	∈	∈	PROPN
ijassa-1364	108	40	u	u	NOUN
ijassa-1364	108	41	,	,	PUNCT
ijassa-1364	108	42	t	t	PROPN
ijassa-1364	108	43	∈	∈	PROPN
ijassa-1364	109	1	[	[	X
ijassa-1364	109	2	0	0	NUM
ijassa-1364	109	3	,	,	PUNCT
ijassa-1364	109	4	τ	τ	X
ijassa-1364	109	5	]	]	X
ijassa-1364	109	6	}	}	PUNCT
ijassa-1364	109	7	,	,	PUNCT
ijassa-1364	109	8	{	{	PUNCT
ijassa-1364	109	9	v	v	NOUN
ijassa-1364	109	10	(	(	PUNCT
ijassa-1364	109	11	·	·	PUNCT
ijassa-1364	109	12	)	)	PUNCT
ijassa-1364	109	13	∈	∈	PROPN
ijassa-1364	109	14	l∞([τ	l∞([τ	PROPN
ijassa-1364	109	15	,	,	PUNCT
ijassa-1364	109	16	t	t	X
ijassa-1364	109	17	]	]	PUNCT
ijassa-1364	109	18	,	,	PUNCT
ijassa-1364	109	19	rm	rm	PROPN
ijassa-1364	109	20	)	)	PUNCT
ijassa-1364	109	21	|	|	ADV
ijassa-1364	109	22	v(t	v(t	NOUN
ijassa-1364	109	23	)	)	PUNCT
ijassa-1364	109	24	∈	∈	PROPN
ijassa-1364	109	25	v	v	NOUN
ijassa-1364	109	26	,	,	PUNCT
ijassa-1364	109	27	t	t	PROPN
ijassa-1364	109	28	∈	∈	PROPN
ijassa-1364	109	29	[	[	X
ijassa-1364	109	30	τ	τ	PROPN
ijassa-1364	109	31	,	,	PUNCT
ijassa-1364	109	32	t	t	X
ijassa-1364	109	33	]	]	PUNCT
ijassa-1364	109	34	}	}	PUNCT
ijassa-1364	109	35	.	.	PUNCT
ijassa-1364	110	1	in	in	ADP
ijassa-1364	110	2	the	the	DET
ijassa-1364	110	3	space	space	NOUN
ijassa-1364	110	4	x	x	PUNCT
ijassa-1364	110	5	there	there	PRON
ijassa-1364	110	6	is	be	VERB
ijassa-1364	110	7	an	an	DET
ijassa-1364	110	8	initial	initial	ADJ
ijassa-1364	110	9	set	set	VERB
ijassa-1364	110	10	m0	m0	NOUN
ijassa-1364	110	11	∈	∈	PROPN
ijassa-1364	110	12	ω(rn	ω(rn	NUM
ijassa-1364	110	13	)	)	PUNCT
ijassa-1364	110	14	and	and	CCONJ
ijassa-1364	110	15	a	a	DET
ijassa-1364	110	16	non	non	ADJ
ijassa-1364	110	17	-	-	ADJ
ijassa-1364	110	18	overlapping	overlapping	ADJ
ijassa-1364	110	19	convex	convex	NOUN
ijassa-1364	110	20	the	the	DET
ijassa-1364	110	21	transition	transition	NOUN
ijassa-1364	110	22	hypersurface	hypersurface	NOUN
ijassa-1364	110	23	γ	γ	X
ijassa-1364	110	24	.	.	PUNCT
ijassa-1364	111	1	let	let	VERB
ijassa-1364	111	2	τ	τ	PROPN
ijassa-1364	111	3	be	be	AUX
ijassa-1364	111	4	the	the	DET
ijassa-1364	111	5	smallest	small	ADJ
ijassa-1364	111	6	time	time	NOUN
ijassa-1364	111	7	moment	moment	NOUN
ijassa-1364	111	8	at	at	ADP
ijassa-1364	111	9	which	which	PRON
ijassa-1364	111	10	the	the	DET
ijassa-1364	111	11	object	object	NOUN
ijassa-1364	111	12	reaches	reach	VERB
ijassa-1364	111	13	the	the	DET
ijassa-1364	111	14	hypersurface	hypersurface	NOUN
ijassa-1364	111	15	γ	γ	X
ijassa-1364	111	16	.	.	PUNCT
ijassa-1364	112	1	the	the	DET
ijassa-1364	112	2	motion	motion	NOUN
ijassa-1364	112	3	of	of	ADP
ijassa-1364	112	4	the	the	DET
ijassa-1364	112	5	object	object	NOUN
ijassa-1364	112	6	from	from	ADP
ijassa-1364	112	7	one	one	NUM
ijassa-1364	112	8	space	space	NOUN
ijassa-1364	112	9	to	to	ADP
ijassa-1364	112	10	another	another	DET
ijassa-1364	112	11	one	one	NOUN
ijassa-1364	112	12	occurs	occur	VERB
ijassa-1364	112	13	in	in	ADP
ijassa-1364	112	14	the	the	DET
ijassa-1364	112	15	same	same	ADJ
ijassa-1364	112	16	way	way	NOUN
ijassa-1364	112	17	as	as	ADP
ijassa-1364	112	18	in	in	ADP
ijassa-1364	112	19	the	the	DET
ijassa-1364	112	20	first	first	ADJ
ijassa-1364	112	21	part	part	NOUN
ijassa-1364	112	22	of	of	ADP
ijassa-1364	112	23	the	the	DET
ijassa-1364	112	24	paper	paper	NOUN
ijassa-1364	112	25	.	.	PUNCT
ijassa-1364	113	1	the	the	DET
ijassa-1364	113	2	problem	problem	NOUN
ijassa-1364	113	3	is	be	AUX
ijassa-1364	113	4	to	to	PART
ijassa-1364	113	5	find	find	VERB
ijassa-1364	113	6	the	the	DET
ijassa-1364	113	7	conditions	condition	NOUN
ijassa-1364	113	8	under	under	ADP
ijassa-1364	113	9	which	which	PRON
ijassa-1364	113	10	the	the	DET
ijassa-1364	113	11	object	object	NOUN
ijassa-1364	113	12	described	describe	VERB
ijassa-1364	113	13	by	by	ADP
ijassa-1364	113	14	systems	system	NOUN
ijassa-1364	113	15	(	(	PUNCT
ijassa-1364	113	16	3.7	3.7	NUM
ijassa-1364	113	17	)	)	PUNCT
ijassa-1364	113	18	and	and	CCONJ
ijassa-1364	113	19	(	(	PUNCT
ijassa-1364	113	20	3.8	3.8	NUM
ijassa-1364	113	21	)	)	PUNCT
ijassa-1364	113	22	is	be	AUX
ijassa-1364	113	23	controllable	controllable	ADJ
ijassa-1364	113	24	from	from	ADP
ijassa-1364	113	25	m0	m0	PROPN
ijassa-1364	113	26	to	to	ADP
ijassa-1364	113	27	m1	m1	PROPN
ijassa-1364	113	28	.	.	PUNCT
ijassa-1364	114	1	3.2	3.2	NUM
ijassa-1364	114	2	.	.	PUNCT
ijassa-1364	114	3	main	main	ADJ
ijassa-1364	114	4	result	result	NOUN
ijassa-1364	114	5	the	the	DET
ijassa-1364	114	6	reachability	reachability	NOUN
ijassa-1364	114	7	set	set	VERB
ijassa-1364	114	8	k(τ	k(τ	PROPN
ijassa-1364	114	9	)	)	PUNCT
ijassa-1364	114	10	for	for	ADP
ijassa-1364	114	11	system	system	NOUN
ijassa-1364	114	12	(	(	PUNCT
ijassa-1364	114	13	3.7	3.7	NUM
ijassa-1364	114	14	)	)	PUNCT
ijassa-1364	114	15	is	be	AUX
ijassa-1364	114	16	the	the	DET
ijassa-1364	114	17	set	set	NOUN
ijassa-1364	114	18	of	of	ADP
ijassa-1364	114	19	endpoints	endpoint	NOUN
ijassa-1364	114	20	of	of	ADP
ijassa-1364	114	21	trajectories	trajectory	NOUN
ijassa-1364	114	22	of	of	ADP
ijassa-1364	114	23	system	system	NOUN
ijassa-1364	114	24	(	(	PUNCT
ijassa-1364	114	25	3.7	3.7	NUM
ijassa-1364	114	26	)	)	PUNCT
ijassa-1364	114	27	with	with	ADP
ijassa-1364	114	28	initial	initial	ADJ
ijassa-1364	114	29	set	set	VERB
ijassa-1364	114	30	m0	m0	NOUN
ijassa-1364	114	31	,	,	PUNCT
ijassa-1364	114	32	corresponding	correspond	VERB
ijassa-1364	114	33	to	to	ADP
ijassa-1364	114	34	all	all	DET
ijassa-1364	114	35	possible	possible	ADJ
ijassa-1364	114	36	admissible	admissible	ADJ
ijassa-1364	114	37	controls	control	NOUN
ijassa-1364	114	38	u	u	NOUN
ijassa-1364	114	39	(	(	PUNCT
ijassa-1364	114	40	·	·	PUNCT
ijassa-1364	114	41	)	)	PUNCT
ijassa-1364	114	42	∈	∈	PROPN
ijassa-1364	114	43	u	u	NOUN
ijassa-1364	114	44	and	and	CCONJ
ijassa-1364	114	45	considered	consider	VERB
ijassa-1364	114	46	at	at	ADP
ijassa-1364	114	47	time	time	NOUN
ijassa-1364	114	48	τ	τ	X
ijassa-1364	114	49	.	.	PROPN
ijassa-1364	115	1	due	due	ADP
ijassa-1364	115	2	to	to	ADP
ijassa-1364	115	3	linearity	linearity	NOUN
ijassa-1364	115	4	of	of	ADP
ijassa-1364	115	5	system	system	NOUN
ijassa-1364	115	6	(	(	PUNCT
ijassa-1364	115	7	3.7	3.7	NUM
ijassa-1364	115	8	)	)	PUNCT
ijassa-1364	115	9	,	,	PUNCT
ijassa-1364	115	10	the	the	DET
ijassa-1364	115	11	reachability	reachability	NOUN
ijassa-1364	115	12	set	set	NOUN
ijassa-1364	115	13	can	can	AUX
ijassa-1364	115	14	be	be	AUX
ijassa-1364	115	15	presented	present	VERB
ijassa-1364	115	16	in	in	ADP
ijassa-1364	115	17	the	the	DET
ijassa-1364	115	18	explicit	explicit	ADJ
ijassa-1364	115	19	form	form	NOUN
ijassa-1364	115	20	:	:	PUNCT
ijassa-1364	115	21	k(τ	k(τ	PROPN
ijassa-1364	115	22	)	)	PUNCT
ijassa-1364	116	1	=	=	PUNCT
ijassa-1364	117	1	eτam0	eτam0	PROPN
ijassa-1364	117	2	+	+	CCONJ
ijassa-1364	117	3	τ∫	τ∫	PROPN
ijassa-1364	117	4	0	0	NUM
ijassa-1364	117	5	e(τ−s)auds	e(τ−s)auds	PROPN
ijassa-1364	117	6	,	,	PUNCT
ijassa-1364	117	7	(	(	PUNCT
ijassa-1364	117	8	3.9	3.9	NUM
ijassa-1364	117	9	)	)	PUNCT
ijassa-1364	117	10	here	here	ADV
ijassa-1364	117	11	eτam0	eτam0	NOUN
ijassa-1364	117	12	is	be	AUX
ijassa-1364	117	13	the	the	DET
ijassa-1364	117	14	image	image	NOUN
ijassa-1364	117	15	of	of	ADP
ijassa-1364	117	16	the	the	DET
ijassa-1364	117	17	set	set	ADJ
ijassa-1364	117	18	m0	m0	NOUN
ijassa-1364	117	19	under	under	ADP
ijassa-1364	117	20	the	the	DET
ijassa-1364	117	21	linear	linear	PROPN
ijassa-1364	117	22	transformation	transformation	NOUN
ijassa-1364	117	23	eτa	eτa	NOUN
ijassa-1364	117	24	,	,	PUNCT
ijassa-1364	117	25	and	and	CCONJ
ijassa-1364	117	26	the	the	DET
ijassa-1364	117	27	integrand	integrand	NOUN
ijassa-1364	117	28	is	be	AUX
ijassa-1364	117	29	a	a	DET
ijassa-1364	117	30	multivalued	multivalue	VERB
ijassa-1364	117	31	mapping	mapping	NOUN
ijassa-1364	117	32	obtained	obtain	VERB
ijassa-1364	117	33	for	for	ADP
ijassa-1364	117	34	all	all	DET
ijassa-1364	117	35	s	s	PART
ijassa-1364	117	36	∈	∈	NOUN
ijassa-1364	118	1	[	[	X
ijassa-1364	118	2	0	0	NUM
ijassa-1364	118	3	,	,	PUNCT
ijassa-1364	118	4	τ	τ	X
ijassa-1364	118	5	]	]	PUNCT
ijassa-1364	118	6	as	as	ADP
ijassa-1364	118	7	the	the	DET
ijassa-1364	118	8	image	image	NOUN
ijassa-1364	118	9	of	of	ADP
ijassa-1364	118	10	the	the	DET
ijassa-1364	118	11	set	set	NOUN
ijassa-1364	118	12	u	u	NOUN
ijassa-1364	118	13	under	under	ADP
ijassa-1364	118	14	the	the	DET
ijassa-1364	118	15	linear	linear	PROPN
ijassa-1364	118	16	transformation	transformation	NOUN
ijassa-1364	118	17	e(τ−s)a	e(τ−s)a	NOUN
ijassa-1364	118	18	.	.	PUNCT
ijassa-1364	119	1	to	to	PART
ijassa-1364	119	2	find	find	VERB
ijassa-1364	119	3	the	the	DET
ijassa-1364	119	4	reachability	reachability	NOUN
ijassa-1364	119	5	set	set	VERB
ijassa-1364	119	6	with	with	ADP
ijassa-1364	119	7	the	the	DET
ijassa-1364	119	8	initial	initial	ADJ
ijassa-1364	119	9	convex	convex	NOUN
ijassa-1364	119	10	set	set	VERB
ijassa-1364	119	11	m0	m0	NOUN
ijassa-1364	119	12	,	,	PUNCT
ijassa-1364	119	13	let	let	VERB
ijassa-1364	119	14	us	we	PRON
ijassa-1364	119	15	first	first	ADV
ijassa-1364	119	16	calculate	calculate	VERB
ijassa-1364	119	17	its	its	PRON
ijassa-1364	119	18	support	support	NOUN
ijassa-1364	119	19	function	function	NOUN
ijassa-1364	119	20	and	and	CCONJ
ijassa-1364	119	21	then	then	ADV
ijassa-1364	119	22	reconstruct	reconstruct	VERB
ijassa-1364	119	23	the	the	DET
ijassa-1364	119	24	set	set	PROPN
ijassa-1364	119	25	k(τ	k(τ	PROPN
ijassa-1364	119	26	)	)	PUNCT
ijassa-1364	119	27	by	by	ADP
ijassa-1364	119	28	its	its	PRON
ijassa-1364	119	29	support	support	NOUN
ijassa-1364	119	30	function	function	NOUN
ijassa-1364	119	31	.	.	PUNCT
ijassa-1364	120	1	thus	thus	ADV
ijassa-1364	120	2	,	,	PUNCT
ijassa-1364	120	3	the	the	DET
ijassa-1364	120	4	support	support	NOUN
ijassa-1364	120	5	function	function	NOUN
ijassa-1364	120	6	of	of	ADP
ijassa-1364	120	7	the	the	DET
ijassa-1364	120	8	reachability	reachability	NOUN
ijassa-1364	120	9	set	set	NOUN
ijassa-1364	120	10	has	have	VERB
ijassa-1364	120	11	the	the	DET
ijassa-1364	120	12	form	form	NOUN
ijassa-1364	120	13	c(k(τ	c(k(τ	NOUN
ijassa-1364	120	14	)	)	PUNCT
ijassa-1364	120	15	,	,	PUNCT
ijassa-1364	120	16	ψ	ψ	X
ijassa-1364	120	17	)	)	PUNCT
ijassa-1364	120	18	=	=	SYM
ijassa-1364	120	19	c(m0	c(m0	NOUN
ijassa-1364	120	20	,	,	PUNCT
ijassa-1364	120	21	e	e	NOUN
ijassa-1364	120	22	τa∗	τa∗	NOUN
ijassa-1364	120	23	ψ	ψ	X
ijassa-1364	120	24	)	)	PUNCT
ijassa-1364	120	25	+	+	CCONJ
ijassa-1364	120	26	τ∫	τ∫	PROPN
ijassa-1364	120	27	0	0	NUM
ijassa-1364	120	28	c(u	c(u	PROPN
ijassa-1364	120	29	,	,	PUNCT
ijassa-1364	120	30	esa	esa	PROPN
ijassa-1364	120	31	∗	∗	PROPN
ijassa-1364	120	32	ψ)ds	ψ)ds	PROPN
ijassa-1364	120	33	.	.	PUNCT
ijassa-1364	121	1	(	(	PUNCT
ijassa-1364	121	2	3.10	3.10	NUM
ijassa-1364	121	3	)	)	PUNCT
ijassa-1364	121	4	since	since	SCONJ
ijassa-1364	121	5	the	the	DET
ijassa-1364	121	6	initial	initial	ADJ
ijassa-1364	121	7	set	set	NOUN
ijassa-1364	121	8	is	be	AUX
ijassa-1364	121	9	convex	convex	PROPN
ijassa-1364	121	10	,	,	PUNCT
ijassa-1364	121	11	the	the	DET
ijassa-1364	121	12	reachability	reachability	NOUN
ijassa-1364	121	13	set	set	NOUN
ijassa-1364	121	14	is	be	AUX
ijassa-1364	121	15	also	also	ADV
ijassa-1364	121	16	convex	convex	ADJ
ijassa-1364	121	17	(	(	PUNCT
ijassa-1364	121	18	see	see	VERB
ijassa-1364	121	19	[	[	X
ijassa-1364	121	20	5	5	NUM
ijassa-1364	121	21	]	]	NUM
ijassa-1364	121	22	)	)	PUNCT
ijassa-1364	121	23	.	.	PUNCT
ijassa-1364	122	1	then	then	ADV
ijassa-1364	122	2	the	the	DET
ijassa-1364	122	3	set	set	PROPN
ijassa-1364	122	4	k(τ	k(τ	PROPN
ijassa-1364	122	5	)	)	PUNCT
ijassa-1364	122	6	reconstructed	reconstruct	VERB
ijassa-1364	122	7	from	from	ADP
ijassa-1364	122	8	the	the	DET
ijassa-1364	122	9	support	support	NOUN
ijassa-1364	122	10	function	function	NOUN
ijassa-1364	122	11	is	be	AUX
ijassa-1364	122	12	intersected	intersect	VERB
ijassa-1364	122	13	at	at	ADP
ijassa-1364	122	14	the	the	DET
ijassa-1364	122	15	time	time	NOUN
ijassa-1364	122	16	τ	τ	PROPN
ijassa-1364	122	17	with	with	ADP
ijassa-1364	122	18	the	the	DET
ijassa-1364	122	19	the	the	DET
ijassa-1364	122	20	transition	transition	NOUN
ijassa-1364	122	21	hypersurface	hypersurface	NOUN
ijassa-1364	122	22	γ	γ	X
ijassa-1364	122	23	.	.	PROPN
ijassa-1364	122	24	by	by	ADP
ijassa-1364	122	25	assumption	assumption	NOUN
ijassa-1364	122	26	,	,	PUNCT
ijassa-1364	122	27	this	this	PRON
ijassa-1364	122	28	yields	yield	VERB
ijassa-1364	122	29	the	the	DET
ijassa-1364	122	30	convex	convex	PROPN
ijassa-1364	122	31	set	set	VERB
ijassa-1364	122	32	k1(τ	k1(τ	PROPN
ijassa-1364	122	33	)	)	PUNCT
ijassa-1364	122	34	=	=	SYM
ijassa-1364	122	35	k(τ	k(τ	PROPN
ijassa-1364	122	36	)	)	PUNCT
ijassa-1364	122	37	∩	∩	PROPN
ijassa-1364	122	38	γ	γ	PROPN
ijassa-1364	122	39	.	.	PROPN
ijassa-1364	122	40	assume	assume	VERB
ijassa-1364	122	41	that	that	SCONJ
ijassa-1364	122	42	there	there	PRON
ijassa-1364	122	43	exists	exist	VERB
ijassa-1364	122	44	τ	τ	PROPN
ijassa-1364	122	45	such	such	ADJ
ijassa-1364	122	46	thatk1(τ	thatk1(τ	NOUN
ijassa-1364	122	47	)	)	PUNCT
ijassa-1364	122	48	̸=	̸=	PROPN
ijassa-1364	122	49	∅.	∅.	ADV
ijassa-1364	122	50	let	let	VERB
ijassa-1364	122	51	us	we	PRON
ijassa-1364	122	52	transform	transform	VERB
ijassa-1364	122	53	the	the	DET
ijassa-1364	122	54	setk1(τ	setk1(τ	NOUN
ijassa-1364	122	55	)	)	PUNCT
ijassa-1364	122	56	as	as	SCONJ
ijassa-1364	122	57	follows	follow	VERB
ijassa-1364	122	58	:	:	PUNCT
ijassa-1364	122	59	k2(τ	k2(τ	X
ijassa-1364	122	60	)	)	PUNCT
ijassa-1364	122	61	=	=	SYM
ijassa-1364	122	62	q(k1(τ	q(k1(τ	PROPN
ijassa-1364	122	63	)	)	PUNCT
ijassa-1364	122	64	)	)	PUNCT
ijassa-1364	122	65	,	,	PUNCT
ijassa-1364	122	66	where	where	SCONJ
ijassa-1364	122	67	q	q	X
ijassa-1364	122	68	:	:	PUNCT
ijassa-1364	122	69	x	x	X
ijassa-1364	122	70	→	→	PUNCT
ijassa-1364	122	71	y.	y.	NOUN
ijassa-1364	122	72	then	then	ADV
ijassa-1364	122	73	the	the	DET
ijassa-1364	122	74	set	set	NOUN
ijassa-1364	122	75	k2(τ	k2(τ	X
ijassa-1364	122	76	)	)	PUNCT
ijassa-1364	122	77	is	be	AUX
ijassa-1364	122	78	convex	convex	ADJ
ijassa-1364	122	79	due	due	ADP
ijassa-1364	122	80	to	to	ADP
ijassa-1364	122	81	properties	property	NOUN
ijassa-1364	122	82	of	of	ADP
ijassa-1364	122	83	q.	q.	NOUN
ijassa-1364	122	84	the	the	DET
ijassa-1364	122	85	set	set	NOUN
ijassa-1364	122	86	k2(τ	k2(τ	PROPN
ijassa-1364	122	87	)	)	PUNCT
ijassa-1364	122	88	is	be	AUX
ijassa-1364	122	89	the	the	DET
ijassa-1364	122	90	initial	initial	ADJ
ijassa-1364	122	91	set	set	NOUN
ijassa-1364	122	92	for	for	ADP
ijassa-1364	122	93	the	the	DET
ijassa-1364	122	94	system	system	NOUN
ijassa-1364	122	95	(	(	PUNCT
ijassa-1364	122	96	3.8	3.8	NUM
ijassa-1364	122	97	)	)	PUNCT
ijassa-1364	122	98	when	when	SCONJ
ijassa-1364	122	99	the	the	DET
ijassa-1364	122	100	object	object	NOUN
ijassa-1364	122	101	moves	move	VERB
ijassa-1364	122	102	in	in	ADP
ijassa-1364	122	103	space	space	NOUN
ijassa-1364	122	104	y	y	PROPN
ijassa-1364	122	105	to	to	ADP
ijassa-1364	122	106	the	the	DET
ijassa-1364	122	107	set	set	ADJ
ijassa-1364	122	108	m1	m1	NOUN
ijassa-1364	122	109	.	.	PUNCT
ijassa-1364	123	1	so	so	ADV
ijassa-1364	123	2	,	,	PUNCT
ijassa-1364	123	3	we	we	PRON
ijassa-1364	123	4	have	have	AUX
ijassa-1364	123	5	formulated	formulate	VERB
ijassa-1364	123	6	the	the	DET
ijassa-1364	123	7	following	follow	VERB
ijassa-1364	123	8	controllability	controllability	NOUN
ijassa-1364	123	9	problem	problem	NOUN
ijassa-1364	123	10	in	in	ADP
ijassa-1364	123	11	the	the	DET
ijassa-1364	123	12	space	space	NOUN
ijassa-1364	123	13	y	y	NOUN
ijassa-1364	123	14	:	:	PUNCT
ijassa-1364	123	15	whether	whether	SCONJ
ijassa-1364	123	16	system	system	NOUN
ijassa-1364	123	17	(	(	PUNCT
ijassa-1364	123	18	3.8	3.8	NUM
ijassa-1364	123	19	)	)	PUNCT
ijassa-1364	123	20	is	be	AUX
ijassa-1364	123	21	controllable	controllable	ADJ
ijassa-1364	123	22	from	from	ADP
ijassa-1364	123	23	the	the	DET
ijassa-1364	123	24	set	set	NOUN
ijassa-1364	123	25	k2(τ	k2(τ	PROPN
ijassa-1364	123	26	)	)	PUNCT
ijassa-1364	123	27	to	to	ADP
ijassa-1364	123	28	the	the	DET
ijassa-1364	123	29	set	set	ADJ
ijassa-1364	123	30	m1	m1	PROPN
ijassa-1364	123	31	on	on	ADP
ijassa-1364	123	32	the	the	DET
ijassa-1364	123	33	time	time	NOUN
ijassa-1364	123	34	interval	interval	NOUN
ijassa-1364	124	1	[	[	X
ijassa-1364	124	2	τ	τ	PROPN
ijassa-1364	124	3	,	,	PUNCT
ijassa-1364	124	4	t	t	X
ijassa-1364	124	5	]	]	PUNCT
ijassa-1364	124	6	.	.	PUNCT
ijassa-1364	125	1	let	let	VERB
ijassa-1364	125	2	us	we	PRON
ijassa-1364	125	3	define	define	VERB
ijassa-1364	125	4	the	the	DET
ijassa-1364	125	5	controllability	controllability	NOUN
ijassa-1364	125	6	function	function	NOUN
ijassa-1364	125	7	φ	φ	PROPN
ijassa-1364	125	8	:	:	PUNCT
ijassa-1364	125	9	rm	rm	PROPN
ijassa-1364	125	10	→	→	SYM
ijassa-1364	125	11	r1	r1	PROPN
ijassa-1364	125	12	by	by	ADP
ijassa-1364	125	13	the	the	DET
ijassa-1364	125	14	relation	relation	NOUN
ijassa-1364	125	15	φ(ψ	φ(ψ	PROPN
ijassa-1364	125	16	)	)	PUNCT
ijassa-1364	126	1	=	=	SYM
ijassa-1364	126	2	c(k2(τ	c(k2(τ	PROPN
ijassa-1364	126	3	)	)	PUNCT
ijassa-1364	126	4	,	,	PUNCT
ijassa-1364	126	5	e	e	X
ijassa-1364	126	6	(	(	PUNCT
ijassa-1364	126	7	t−τ)b∗	t−τ)b∗	NOUN
ijassa-1364	126	8	ψ	ψ	X
ijassa-1364	126	9	)	)	PUNCT
ijassa-1364	127	1	+	+	CCONJ
ijassa-1364	127	2	c(m1,−ψ	c(m1,−ψ	X
ijassa-1364	127	3	)	)	PUNCT
ijassa-1364	127	4	+	+	CCONJ
ijassa-1364	127	5	t−τ∫	t−τ∫	NOUN
ijassa-1364	127	6	0	0	NUM
ijassa-1364	127	7	c(v	c(v	PROPN
ijassa-1364	127	8	,	,	PUNCT
ijassa-1364	127	9	esb	esb	NOUN
ijassa-1364	127	10	∗	∗	NOUN
ijassa-1364	127	11	ψ)ds	ψ)ds	PROPN
ijassa-1364	127	12	,	,	PUNCT
ijassa-1364	127	13	(	(	PUNCT
ijassa-1364	127	14	3.11	3.11	NUM
ijassa-1364	127	15	)	)	PUNCT
ijassa-1364	127	16	see	see	VERB
ijassa-1364	127	17	[	[	X
ijassa-1364	127	18	5	5	NUM
ijassa-1364	127	19	]	]	PUNCT
ijassa-1364	127	20	)	)	PUNCT
ijassa-1364	127	21	.	.	PUNCT
ijassa-1364	128	1	according	accord	VERB
ijassa-1364	128	2	to	to	ADP
ijassa-1364	128	3	the	the	DET
ijassa-1364	128	4	controllability	controllability	NOUN
ijassa-1364	128	5	theorem	theorem	ADJ
ijassa-1364	128	6	[	[	X
ijassa-1364	128	7	5	5	NUM
ijassa-1364	128	8	]	]	PUNCT
ijassa-1364	128	9	,	,	PUNCT
ijassa-1364	128	10	an	an	DET
ijassa-1364	128	11	object	object	NOUN
ijassa-1364	128	12	is	be	AUX
ijassa-1364	128	13	controllable	controllable	ADJ
ijassa-1364	128	14	on	on	ADP
ijassa-1364	128	15	the	the	DET
ijassa-1364	128	16	time	time	NOUN
ijassa-1364	128	17	segment	segment	NOUN
ijassa-1364	128	18	[	[	X
ijassa-1364	128	19	τ	τ	PROPN
ijassa-1364	128	20	,	,	PUNCT
ijassa-1364	128	21	t	t	X
ijassa-1364	128	22	]	]	PUNCT
ijassa-1364	128	23	from	from	ADP
ijassa-1364	128	24	the	the	DET
ijassa-1364	128	25	set	set	NOUN
ijassa-1364	128	26	k2(τ	k2(τ	PROPN
ijassa-1364	128	27	)	)	PUNCT
ijassa-1364	128	28	to	to	ADP
ijassa-1364	128	29	the	the	DET
ijassa-1364	128	30	set	set	NOUN
ijassa-1364	128	31	m1	m1	PROPN
ijassa-1364	128	32	if	if	SCONJ
ijassa-1364	128	33	and	and	CCONJ
ijassa-1364	128	34	only	only	ADV
ijassa-1364	128	35	if	if	SCONJ
ijassa-1364	128	36	for	for	ADP
ijassa-1364	128	37	the	the	DET
ijassa-1364	128	38	controllability	controllability	NOUN
ijassa-1364	128	39	function	function	NOUN
ijassa-1364	128	40	is	be	AUX
ijassa-1364	128	41	non	non	ADJ
ijassa-1364	128	42	-	-	ADJ
ijassa-1364	128	43	negative	negative	ADJ
ijassa-1364	128	44	,	,	PUNCT
ijassa-1364	128	45	i.e.	i.e.	X
ijassa-1364	128	46	φ(ψ	φ(ψ	NOUN
ijassa-1364	128	47	)	)	PUNCT
ijassa-1364	128	48	≥	≥	NOUN
ijassa-1364	128	49	0	0	NUM
ijassa-1364	128	50	∀ψ	∀ψ	NOUN
ijassa-1364	128	51	∈	∈	PROPN
ijassa-1364	128	52	s	s	NOUN
ijassa-1364	128	53	,	,	PUNCT
ijassa-1364	128	54	copyright	copyright	NOUN
ijassa-1364	128	55	©	©	PROPN
ijassa-1364	128	56	2023	2023	NUM
ijassa-1364	128	57	assa	assa	NOUN
ijassa-1364	128	58	.	.	PUNCT
ijassa-1364	129	1	adv	adv	PROPN
ijassa-1364	129	2	syst	syst	PROPN
ijassa-1364	129	3	sci	sci	PROPN
ijassa-1364	129	4	appl	appl	PROPN
ijassa-1364	129	5	(	(	PUNCT
ijassa-1364	129	6	2023	2023	NUM
ijassa-1364	129	7	)	)	PUNCT
ijassa-1364	129	8	66	66	NUM
ijassa-1364	129	9	i.	i.	NOUN
ijassa-1364	129	10	maximova	maximova	PROPN
ijassa-1364	129	11	where	where	SCONJ
ijassa-1364	129	12	s	s	NOUN
ijassa-1364	129	13	is	be	AUX
ijassa-1364	129	14	the	the	DET
ijassa-1364	129	15	unit	unit	NOUN
ijassa-1364	129	16	sphere	sphere	ADV
ijassa-1364	129	17	in	in	ADP
ijassa-1364	129	18	rn	rn	PROPN
ijassa-1364	129	19	.	.	PUNCT
ijassa-1364	130	1	in	in	ADP
ijassa-1364	130	2	turn	turn	NOUN
ijassa-1364	130	3	,	,	PUNCT
ijassa-1364	130	4	this	this	PRON
ijassa-1364	130	5	is	be	AUX
ijassa-1364	130	6	equivalent	equivalent	ADJ
ijassa-1364	130	7	to	to	ADP
ijassa-1364	130	8	the	the	DET
ijassa-1364	130	9	condition	condition	NOUN
ijassa-1364	130	10	φ0	φ0	PROPN
ijassa-1364	130	11	=	=	PUNCT
ijassa-1364	130	12	min	min	PROPN
ijassa-1364	130	13	ψ∈s	ψ∈s	NOUN
ijassa-1364	130	14	φ(ψ	φ(ψ	PROPN
ijassa-1364	130	15	)	)	PUNCT
ijassa-1364	130	16	≥	≥	NOUN
ijassa-1364	130	17	0	0	NUM
ijassa-1364	130	18	.	.	PUNCT
ijassa-1364	131	1	applying	apply	VERB
ijassa-1364	131	2	this	this	DET
ijassa-1364	131	3	theorem	theorem	NOUN
ijassa-1364	131	4	,	,	PUNCT
ijassa-1364	131	5	we	we	PRON
ijassa-1364	131	6	obtain	obtain	VERB
ijassa-1364	131	7	the	the	DET
ijassa-1364	131	8	following	following	ADJ
ijassa-1364	131	9	result	result	NOUN
ijassa-1364	131	10	:	:	PUNCT
ijassa-1364	131	11	theorem	theorem	VERB
ijassa-1364	131	12	3.1	3.1	NUM
ijassa-1364	131	13	:	:	PUNCT
ijassa-1364	131	14	under	under	ADP
ijassa-1364	131	15	the	the	DET
ijassa-1364	131	16	above	above	ADJ
ijassa-1364	131	17	assumptions	assumption	NOUN
ijassa-1364	131	18	,	,	PUNCT
ijassa-1364	131	19	for	for	ADP
ijassa-1364	131	20	the	the	DET
ijassa-1364	131	21	controllability	controllability	NOUN
ijassa-1364	131	22	of	of	ADP
ijassa-1364	131	23	an	an	DET
ijassa-1364	131	24	object	object	NOUN
ijassa-1364	131	25	described	describe	VERB
ijassa-1364	131	26	by	by	ADP
ijassa-1364	131	27	systems	system	NOUN
ijassa-1364	131	28	(	(	PUNCT
ijassa-1364	131	29	3.7	3.7	NUM
ijassa-1364	131	30	)	)	PUNCT
ijassa-1364	131	31	and	and	CCONJ
ijassa-1364	131	32	(	(	PUNCT
ijassa-1364	131	33	3.8	3.8	NUM
ijassa-1364	131	34	)	)	PUNCT
ijassa-1364	131	35	on	on	ADP
ijassa-1364	131	36	the	the	DET
ijassa-1364	131	37	interval	interval	NOUN
ijassa-1364	131	38	[	[	X
ijassa-1364	131	39	0	0	NUM
ijassa-1364	131	40	,	,	PUNCT
ijassa-1364	131	41	t	t	X
ijassa-1364	131	42	]	]	PUNCT
ijassa-1364	131	43	,	,	PUNCT
ijassa-1364	131	44	it	it	PRON
ijassa-1364	131	45	is	be	AUX
ijassa-1364	131	46	sufficient	sufficient	ADJ
ijassa-1364	131	47	that	that	SCONJ
ijassa-1364	131	48	the	the	DET
ijassa-1364	131	49	controllability	controllability	NOUN
ijassa-1364	131	50	function	function	NOUN
ijassa-1364	131	51	φ(ψ	φ(ψ	PROPN
ijassa-1364	131	52	)	)	PUNCT
ijassa-1364	131	53	=	=	SYM
ijassa-1364	131	54	c(k2(τ	c(k2(τ	PROPN
ijassa-1364	131	55	)	)	PUNCT
ijassa-1364	131	56	,	,	PUNCT
ijassa-1364	131	57	e	e	X
ijassa-1364	131	58	(	(	PUNCT
ijassa-1364	131	59	t−τ)b∗	t−τ)b∗	NOUN
ijassa-1364	131	60	ψ	ψ	X
ijassa-1364	131	61	)	)	PUNCT
ijassa-1364	131	62	+	+	CCONJ
ijassa-1364	131	63	c(m1,−ψ	c(m1,−ψ	X
ijassa-1364	131	64	)	)	PUNCT
ijassa-1364	131	65	+	+	CCONJ
ijassa-1364	131	66	t−τ∫	t−τ∫	NOUN
ijassa-1364	131	67	0	0	NUM
ijassa-1364	131	68	c(v	c(v	PROPN
ijassa-1364	131	69	,	,	PUNCT
ijassa-1364	131	70	esb	esb	NOUN
ijassa-1364	131	71	∗	∗	NOUN
ijassa-1364	131	72	ψ	ψ	NOUN
ijassa-1364	131	73	)	)	PUNCT
ijassa-1364	131	74	ds	ds	X
ijassa-1364	131	75	is	be	AUX
ijassa-1364	131	76	non	non	ADJ
ijassa-1364	131	77	-	-	ADJ
ijassa-1364	131	78	negative	negative	ADJ
ijassa-1364	131	79	for	for	ADP
ijassa-1364	131	80	any	any	DET
ijassa-1364	131	81	ψ	ψ	NOUN
ijassa-1364	131	82	∈	∈	PROPN
ijassa-1364	131	83	s.	s.	PROPN
ijassa-1364	131	84	3.3	3.3	NUM
ijassa-1364	131	85	.	.	PUNCT
ijassa-1364	132	1	example	example	NOUN
ijassa-1364	132	2	let	let	VERB
ijassa-1364	132	3	x	x	SYM
ijassa-1364	132	4	=	=	PUNCT
ijassa-1364	132	5	r3	r3	PROPN
ijassa-1364	132	6	and	and	CCONJ
ijassa-1364	132	7	y	y	NOUN
ijassa-1364	132	8	=	=	PROPN
ijassa-1364	132	9	r2	r2	PROPN
ijassa-1364	132	10	and	and	CCONJ
ijassa-1364	132	11	the	the	DET
ijassa-1364	132	12	motion	motion	NOUN
ijassa-1364	132	13	of	of	ADP
ijassa-1364	132	14	an	an	DET
ijassa-1364	132	15	object	object	NOUN
ijassa-1364	132	16	is	be	AUX
ijassa-1364	132	17	described	describe	VERB
ijassa-1364	132	18	by	by	ADP
ijassa-1364	132	19	the	the	DET
ijassa-1364	132	20	following	follow	VERB
ijassa-1364	132	21	systems	system	NOUN
ijassa-1364	132	22	of	of	ADP
ijassa-1364	132	23	equations	equation	NOUN
ijassa-1364	132	24	:	:	PUNCT
ijassa-1364	132	25	ẋ1	ẋ1	NOUN
ijassa-1364	132	26	=	=	PUNCT
ijassa-1364	133	1	x2	x2	PROPN
ijassa-1364	134	1	+	+	NUM
ijassa-1364	134	2	u1	u1	NOUN
ijassa-1364	134	3	,	,	PUNCT
ijassa-1364	134	4	ẋ2	ẋ2	PROPN
ijassa-1364	134	5	=	=	PROPN
ijassa-1364	135	1	−x1	−x1	PROPN
ijassa-1364	135	2	+	+	CCONJ
ijassa-1364	135	3	u2	u2	PROPN
ijassa-1364	135	4	,	,	PUNCT
ijassa-1364	135	5	|u|	|u|	ADV
ijassa-1364	135	6	≤	≤	NUM
ijassa-1364	135	7	1	1	NUM
ijassa-1364	135	8	,	,	PUNCT
ijassa-1364	135	9	u	u	NOUN
ijassa-1364	135	10	=	=	PUNCT
ijassa-1364	135	11	(	(	PUNCT
ijassa-1364	135	12	u1	u1	PROPN
ijassa-1364	135	13	,	,	PUNCT
ijassa-1364	135	14	u2	u2	NOUN
ijassa-1364	135	15	,	,	PUNCT
ijassa-1364	135	16	u3	u3	NOUN
ijassa-1364	135	17	)	)	PUNCT
ijassa-1364	135	18	∈	∈	PROPN
ijassa-1364	135	19	r3	r3	PROPN
ijassa-1364	135	20	,	,	PUNCT
ijassa-1364	135	21	ẋ3	ẋ3	PROPN
ijassa-1364	135	22	=	=	SYM
ijassa-1364	135	23	u3	u3	PROPN
ijassa-1364	135	24	,	,	PUNCT
ijassa-1364	135	25	t	t	PROPN
ijassa-1364	135	26	∈	∈	PROPN
ijassa-1364	136	1	[	[	X
ijassa-1364	136	2	0	0	NUM
ijassa-1364	136	3	,	,	PUNCT
ijassa-1364	136	4	τ	τ	PROPN
ijassa-1364	136	5	]	]	X
ijassa-1364	136	6	,	,	PUNCT
ijassa-1364	136	7	(	(	PUNCT
ijassa-1364	136	8	3.12	3.12	NUM
ijassa-1364	136	9	)	)	PUNCT
ijassa-1364	136	10	{	{	PUNCT
ijassa-1364	136	11	ẏ1	ẏ1	PROPN
ijassa-1364	136	12	=	=	SYM
ijassa-1364	136	13	y1	y1	PROPN
ijassa-1364	136	14	+	+	CCONJ
ijassa-1364	136	15	v1	v1	NOUN
ijassa-1364	136	16	,	,	PUNCT
ijassa-1364	136	17	|v|	|v|	NOUN
ijassa-1364	136	18	≤	≤	NUM
ijassa-1364	136	19	1	1	NUM
ijassa-1364	136	20	,	,	PUNCT
ijassa-1364	136	21	v	v	NOUN
ijassa-1364	136	22	=	=	SYM
ijassa-1364	136	23	(	(	PUNCT
ijassa-1364	136	24	v1	v1	NOUN
ijassa-1364	136	25	,	,	PUNCT
ijassa-1364	136	26	v2	v2	NOUN
ijassa-1364	136	27	)	)	PUNCT
ijassa-1364	136	28	∈	∈	NOUN
ijassa-1364	136	29	r2	r2	NOUN
ijassa-1364	136	30	,	,	PUNCT
ijassa-1364	136	31	ẏ2	ẏ2	PROPN
ijassa-1364	136	32	=	=	SYM
ijassa-1364	136	33	v2	v2	PROPN
ijassa-1364	136	34	,	,	PUNCT
ijassa-1364	136	35	t	t	PROPN
ijassa-1364	136	36	∈	∈	PROPN
ijassa-1364	137	1	[	[	X
ijassa-1364	137	2	τ	τ	PROPN
ijassa-1364	137	3	,	,	PUNCT
ijassa-1364	137	4	t	t	X
ijassa-1364	137	5	]	]	PUNCT
ijassa-1364	137	6	.	.	PUNCT
ijassa-1364	138	1	(	(	PUNCT
ijassa-1364	138	2	3.13	3.13	NUM
ijassa-1364	138	3	)	)	PUNCT
ijassa-1364	138	4	in	in	ADP
ijassa-1364	138	5	the	the	DET
ijassa-1364	138	6	space	space	NOUN
ijassa-1364	138	7	r3	r3	NOUN
ijassa-1364	138	8	,	,	PUNCT
ijassa-1364	138	9	consider	consider	VERB
ijassa-1364	138	10	the	the	DET
ijassa-1364	138	11	initial	initial	ADJ
ijassa-1364	138	12	set	set	VERB
ijassa-1364	138	13	m0	m0	NOUN
ijassa-1364	138	14	=	=	SYM
ijassa-1364	138	15	{	{	PUNCT
ijassa-1364	138	16	(	(	PUNCT
ijassa-1364	138	17	0,−1	0,−1	PROPN
ijassa-1364	138	18	,	,	PUNCT
ijassa-1364	138	19	0	0	NUM
ijassa-1364	138	20	)	)	PUNCT
ijassa-1364	138	21	}	}	PUNCT
ijassa-1364	138	22	and	and	CCONJ
ijassa-1364	138	23	the	the	DET
ijassa-1364	138	24	transition	transition	NOUN
ijassa-1364	138	25	hypersurface	hypersurface	NOUN
ijassa-1364	138	26	γ	γ	X
ijassa-1364	138	27	=	=	SYM
ijassa-1364	138	28	{	{	PUNCT
ijassa-1364	138	29	(	(	PUNCT
ijassa-1364	138	30	x1	x1	PROPN
ijassa-1364	138	31	,	,	PUNCT
ijassa-1364	138	32	x2	x2	PROPN
ijassa-1364	138	33	,	,	PUNCT
ijassa-1364	138	34	x3	x3	ADJ
ijassa-1364	138	35	)	)	PUNCT
ijassa-1364	138	36	∈	∈	PROPN
ijassa-1364	138	37	r3|x2	r3|x2	NOUN
ijassa-1364	138	38	=	=	SYM
ijassa-1364	138	39	0	0	NUM
ijassa-1364	138	40	,	,	PUNCT
ijassa-1364	138	41	x3	x3	VERB
ijassa-1364	138	42	≥	≥	NUM
ijassa-1364	138	43	0	0	NUM
ijassa-1364	138	44	}	}	PUNCT
ijassa-1364	138	45	.	.	PUNCT
ijassa-1364	139	1	by	by	ADP
ijassa-1364	139	2	τ	τ	PROPN
ijassa-1364	139	3	denote	denote	VERB
ijassa-1364	139	4	the	the	DET
ijassa-1364	139	5	smallest	small	ADJ
ijassa-1364	139	6	time	time	NOUN
ijassa-1364	139	7	moment	moment	NOUN
ijassa-1364	139	8	at	at	ADP
ijassa-1364	139	9	which	which	PRON
ijassa-1364	139	10	the	the	DET
ijassa-1364	139	11	object	object	NOUN
ijassa-1364	139	12	reaches	reach	VERB
ijassa-1364	139	13	the	the	DET
ijassa-1364	139	14	hypersurface	hypersurface	PROPN
ijassa-1364	139	15	γ	γ	PROPN
ijassa-1364	139	16	.	.	PUNCT
ijassa-1364	140	1	the	the	DET
ijassa-1364	140	2	mapping	mapping	NOUN
ijassa-1364	140	3	that	that	PRON
ijassa-1364	140	4	makes	make	VERB
ijassa-1364	140	5	the	the	DET
ijassa-1364	140	6	transition	transition	NOUN
ijassa-1364	140	7	from	from	ADP
ijassa-1364	140	8	r3	r3	PROPN
ijassa-1364	140	9	to	to	ADP
ijassa-1364	140	10	r2	r2	PROPN
ijassa-1364	140	11	has	have	VERB
ijassa-1364	140	12	the	the	DET
ijassa-1364	140	13	form	form	NOUN
ijassa-1364	140	14	q(x1	q(x1	ADJ
ijassa-1364	140	15	,	,	PUNCT
ijassa-1364	140	16	x2	x2	PROPN
ijassa-1364	140	17	,	,	PUNCT
ijassa-1364	140	18	x3	x3	ADJ
ijassa-1364	140	19	)	)	PUNCT
ijassa-1364	141	1	=	=	SYM
ijassa-1364	141	2	(	(	PUNCT
ijassa-1364	141	3	x1	x1	PROPN
ijassa-1364	141	4	+	+	CCONJ
ijassa-1364	141	5	sin	sin	PROPN
ijassa-1364	141	6	τ	τ	PROPN
ijassa-1364	141	7	,	,	PUNCT
ijassa-1364	141	8	x3	x3	ADJ
ijassa-1364	141	9	)	)	PUNCT
ijassa-1364	141	10	=	=	SYM
ijassa-1364	141	11	(	(	PUNCT
ijassa-1364	141	12	y1	y1	INTJ
ijassa-1364	141	13	,	,	PUNCT
ijassa-1364	141	14	y2	y2	PROPN
ijassa-1364	141	15	)	)	PUNCT
ijassa-1364	141	16	.	.	PUNCT
ijassa-1364	142	1	in	in	ADP
ijassa-1364	142	2	the	the	DET
ijassa-1364	142	3	space	space	NOUN
ijassa-1364	142	4	r2	r2	NOUN
ijassa-1364	142	5	,	,	PUNCT
ijassa-1364	142	6	consider	consider	VERB
ijassa-1364	142	7	the	the	DET
ijassa-1364	142	8	set	set	NOUN
ijassa-1364	142	9	m1	m1	NOUN
ijassa-1364	142	10	=	=	SYM
ijassa-1364	142	11	s1(0,−3	s1(0,−3	PROPN
ijassa-1364	142	12	)	)	PUNCT
ijassa-1364	142	13	.	.	PUNCT
ijassa-1364	143	1	the	the	DET
ijassa-1364	143	2	problem	problem	NOUN
ijassa-1364	143	3	is	be	AUX
ijassa-1364	143	4	to	to	PART
ijassa-1364	143	5	find	find	VERB
ijassa-1364	143	6	conditions	condition	NOUN
ijassa-1364	143	7	for	for	ADP
ijassa-1364	143	8	an	an	DET
ijassa-1364	143	9	object	object	NOUN
ijassa-1364	143	10	described	describe	VERB
ijassa-1364	143	11	by	by	ADP
ijassa-1364	143	12	systems	system	NOUN
ijassa-1364	143	13	(	(	PUNCT
ijassa-1364	143	14	3.12	3.12	NUM
ijassa-1364	143	15	)	)	PUNCT
ijassa-1364	143	16	and	and	CCONJ
ijassa-1364	143	17	(	(	PUNCT
ijassa-1364	143	18	3.13	3.13	NUM
ijassa-1364	143	19	)	)	PUNCT
ijassa-1364	143	20	be	be	AUX
ijassa-1364	143	21	controllable	controllable	ADJ
ijassa-1364	143	22	from	from	ADP
ijassa-1364	143	23	m0	m0	PROPN
ijassa-1364	143	24	to	to	ADP
ijassa-1364	143	25	m1	m1	PROPN
ijassa-1364	143	26	on	on	ADP
ijassa-1364	143	27	the	the	DET
ijassa-1364	143	28	time	time	NOUN
ijassa-1364	143	29	interval	interval	NOUN
ijassa-1364	143	30	[	[	X
ijassa-1364	143	31	0	0	NUM
ijassa-1364	143	32	,	,	PUNCT
ijassa-1364	143	33	t	t	X
ijassa-1364	143	34	]	]	PUNCT
ijassa-1364	143	35	.	.	PUNCT
ijassa-1364	144	1	denote	denote	VERB
ijassa-1364	144	2	by	by	ADP
ijassa-1364	144	3	k(τ	k(τ	PROPN
ijassa-1364	144	4	)	)	PUNCT
ijassa-1364	144	5	the	the	DET
ijassa-1364	144	6	reachability	reachability	NOUN
ijassa-1364	144	7	set	set	NOUN
ijassa-1364	144	8	of	of	ADP
ijassa-1364	144	9	system	system	NOUN
ijassa-1364	144	10	(	(	PUNCT
ijassa-1364	144	11	3.12	3.12	NUM
ijassa-1364	144	12	)	)	PUNCT
ijassa-1364	144	13	from	from	ADP
ijassa-1364	144	14	the	the	DET
ijassa-1364	144	15	set	set	ADJ
ijassa-1364	144	16	m0	m0	NOUN
ijassa-1364	144	17	at	at	ADP
ijassa-1364	144	18	time	time	NOUN
ijassa-1364	144	19	τ	τ	PROPN
ijassa-1364	144	20	.	.	PUNCT
ijassa-1364	145	1	first	first	ADV
ijassa-1364	145	2	,	,	PUNCT
ijassa-1364	145	3	consider	consider	VERB
ijassa-1364	145	4	the	the	DET
ijassa-1364	145	5	motion	motion	NOUN
ijassa-1364	145	6	of	of	ADP
ijassa-1364	145	7	the	the	DET
ijassa-1364	145	8	object	object	NOUN
ijassa-1364	145	9	in	in	ADP
ijassa-1364	145	10	the	the	DET
ijassa-1364	145	11	space	space	NOUN
ijassa-1364	145	12	r3	r3	PROPN
ijassa-1364	145	13	.	.	PUNCT
ijassa-1364	146	1	the	the	DET
ijassa-1364	146	2	support	support	NOUN
ijassa-1364	146	3	function	function	NOUN
ijassa-1364	146	4	of	of	ADP
ijassa-1364	146	5	the	the	DET
ijassa-1364	146	6	reachability	reachability	NOUN
ijassa-1364	146	7	set	set	VERB
ijassa-1364	146	8	k(τ	k(τ	PROPN
ijassa-1364	146	9	)	)	PUNCT
ijassa-1364	146	10	from	from	ADP
ijassa-1364	146	11	(	(	PUNCT
ijassa-1364	146	12	3.10	3.10	NUM
ijassa-1364	146	13	)	)	PUNCT
ijassa-1364	146	14	reads	read	VERB
ijassa-1364	146	15	c(k(τ	c(k(τ	ADP
ijassa-1364	146	16	)	)	PUNCT
ijassa-1364	146	17	,	,	PUNCT
ijassa-1364	146	18	ψ	ψ	X
ijassa-1364	146	19	)	)	PUNCT
ijassa-1364	146	20	=	=	SYM
ijassa-1364	146	21	−ψ1	−ψ1	PROPN
ijassa-1364	146	22	sin	sin	NOUN
ijassa-1364	146	23	τ	τ	PROPN
ijassa-1364	146	24	−	−	PROPN
ijassa-1364	146	25	ψ2	ψ2	NOUN
ijassa-1364	146	26	cos	cos	ADP
ijassa-1364	146	27	τ	τ	PROPN
ijassa-1364	146	28	+	+	CCONJ
ijassa-1364	146	29	τ∥ψ∥	τ∥ψ∥	PROPN
ijassa-1364	146	30	,	,	PUNCT
ijassa-1364	146	31	where	where	SCONJ
ijassa-1364	146	32	∥ψ∥	∥ψ∥	PROPN
ijassa-1364	146	33	is	be	AUX
ijassa-1364	146	34	the	the	DET
ijassa-1364	146	35	standard	standard	ADJ
ijassa-1364	146	36	euclidean	euclidean	ADJ
ijassa-1364	146	37	norm	norm	NOUN
ijassa-1364	146	38	of	of	ADP
ijassa-1364	146	39	the	the	DET
ijassa-1364	146	40	vector	vector	NOUN
ijassa-1364	146	41	ψ	ψ	NOUN
ijassa-1364	146	42	.	.	PUNCT
ijassa-1364	147	1	restoring	restore	VERB
ijassa-1364	147	2	the	the	DET
ijassa-1364	147	3	set	set	PROPN
ijassa-1364	147	4	k(τ	k(τ	PROPN
ijassa-1364	147	5	)	)	PUNCT
ijassa-1364	147	6	by	by	ADP
ijassa-1364	147	7	the	the	DET
ijassa-1364	147	8	its	its	PRON
ijassa-1364	147	9	support	support	NOUN
ijassa-1364	147	10	function	function	NOUN
ijassa-1364	147	11	c(k(τ	c(k(τ	NOUN
ijassa-1364	147	12	)	)	PUNCT
ijassa-1364	147	13	,	,	PUNCT
ijassa-1364	147	14	ψ	ψ	NOUN
ijassa-1364	147	15	)	)	PUNCT
ijassa-1364	147	16	,	,	PUNCT
ijassa-1364	147	17	one	one	PRON
ijassa-1364	147	18	can	can	AUX
ijassa-1364	147	19	easily	easily	ADV
ijassa-1364	147	20	see	see	VERB
ijassa-1364	147	21	that	that	SCONJ
ijassa-1364	147	22	the	the	DET
ijassa-1364	147	23	reachability	reachability	NOUN
ijassa-1364	147	24	set	set	VERB
ijassa-1364	147	25	k(τ	k(τ	PROPN
ijassa-1364	147	26	)	)	PUNCT
ijassa-1364	147	27	is	be	AUX
ijassa-1364	147	28	the	the	DET
ijassa-1364	147	29	circle	circle	NOUN
ijassa-1364	147	30	of	of	ADP
ijassa-1364	147	31	radius	radius	PROPN
ijassa-1364	147	32	τ	τ	PROPN
ijassa-1364	147	33	with	with	ADP
ijassa-1364	147	34	the	the	DET
ijassa-1364	147	35	center	center	NOUN
ijassa-1364	147	36	at	at	ADP
ijassa-1364	147	37	the	the	DET
ijassa-1364	147	38	point	point	NOUN
ijassa-1364	147	39	(	(	PUNCT
ijassa-1364	147	40	−	−	NOUN
ijassa-1364	147	41	sin	sin	NOUN
ijassa-1364	147	42	τ,−	τ,−	VERB
ijassa-1364	147	43	cos	cos	PROPN
ijassa-1364	147	44	τ	τ	PROPN
ijassa-1364	147	45	,	,	PUNCT
ijassa-1364	147	46	0	0	NUM
ijassa-1364	147	47	)	)	PUNCT
ijassa-1364	147	48	.	.	PUNCT
ijassa-1364	148	1	the	the	DET
ijassa-1364	148	2	intersection	intersection	NOUN
ijassa-1364	148	3	of	of	ADP
ijassa-1364	148	4	the	the	DET
ijassa-1364	148	5	reachability	reachability	NOUN
ijassa-1364	148	6	set	set	VERB
ijassa-1364	148	7	with	with	ADP
ijassa-1364	148	8	the	the	DET
ijassa-1364	148	9	transition	transition	NOUN
ijassa-1364	148	10	hypersurface	hypersurface	NOUN
ijassa-1364	148	11	γ	γ	PROPN
ijassa-1364	148	12	occurs	occur	VERB
ijassa-1364	148	13	at	at	ADP
ijassa-1364	148	14	τ	τ	PROPN
ijassa-1364	148	15	>	>	X
ijassa-1364	148	16	1	1	NUM
ijassa-1364	149	1	and	and	CCONJ
ijassa-1364	149	2	it	it	PRON
ijassa-1364	149	3	is	be	AUX
ijassa-1364	149	4	a	a	DET
ijassa-1364	149	5	segment	segment	NOUN
ijassa-1364	149	6	with	with	ADP
ijassa-1364	149	7	the	the	DET
ijassa-1364	149	8	endpoints	endpoint	NOUN
ijassa-1364	149	9	(	(	PUNCT
ijassa-1364	149	10	−	−	PROPN
ijassa-1364	149	11	sin	sin	NOUN
ijassa-1364	149	12	τ	τ	PROPN
ijassa-1364	149	13	−	−	NOUN
ijassa-1364	150	1	√	√	PROPN
ijassa-1364	150	2	τ	τ	PROPN
ijassa-1364	150	3	2	2	NUM
ijassa-1364	150	4	−	−	PROPN
ijassa-1364	150	5	cos2	cos2	PROPN
ijassa-1364	150	6	τ	τ	PROPN
ijassa-1364	150	7	,	,	PUNCT
ijassa-1364	150	8	0	0	NUM
ijassa-1364	150	9	,	,	PUNCT
ijassa-1364	150	10	0	0	NUM
ijassa-1364	150	11	)	)	PUNCT
ijassa-1364	150	12	;	;	PUNCT
ijassa-1364	150	13	(	(	PUNCT
ijassa-1364	150	14	−	−	NOUN
ijassa-1364	150	15	sin	sin	NOUN
ijassa-1364	150	16	τ	τ	PROPN
ijassa-1364	150	17	+	+	CCONJ
ijassa-1364	150	18	√	√	PROPN
ijassa-1364	150	19	τ	τ	SYM
ijassa-1364	150	20	2	2	NUM
ijassa-1364	150	21	−	−	PROPN
ijassa-1364	150	22	cos2	cos2	PROPN
ijassa-1364	150	23	τ	τ	PROPN
ijassa-1364	150	24	,	,	PUNCT
ijassa-1364	150	25	0	0	NUM
ijassa-1364	150	26	,	,	PUNCT
ijassa-1364	150	27	0	0	NUM
ijassa-1364	150	28	)	)	PUNCT
ijassa-1364	150	29	.	.	PUNCT
ijassa-1364	151	1	we	we	PRON
ijassa-1364	151	2	pass	pass	VERB
ijassa-1364	151	3	to	to	ADP
ijassa-1364	151	4	the	the	DET
ijassa-1364	151	5	space	space	NOUN
ijassa-1364	151	6	r2	r2	NOUN
ijassa-1364	151	7	under	under	ADP
ijassa-1364	151	8	the	the	DET
ijassa-1364	151	9	action	action	NOUN
ijassa-1364	151	10	of	of	ADP
ijassa-1364	151	11	the	the	DET
ijassa-1364	151	12	mapping	mapping	NOUN
ijassa-1364	151	13	q.	q.	NOUN
ijassa-1364	151	14	we	we	PRON
ijassa-1364	151	15	obtain	obtain	VERB
ijassa-1364	151	16	the	the	DET
ijassa-1364	151	17	set	set	NOUN
ijassa-1364	151	18	k1(τ	k1(τ	PROPN
ijassa-1364	151	19	)	)	PUNCT
ijassa-1364	151	20	,	,	PUNCT
ijassa-1364	151	21	which	which	PRON
ijassa-1364	151	22	is	be	AUX
ijassa-1364	151	23	the	the	DET
ijassa-1364	151	24	initial	initial	NOUN
ijassa-1364	151	25	for	for	ADP
ijassa-1364	151	26	system	system	NOUN
ijassa-1364	151	27	(	(	PUNCT
ijassa-1364	151	28	3.13	3.13	NUM
ijassa-1364	151	29	)	)	PUNCT
ijassa-1364	151	30	when	when	SCONJ
ijassa-1364	151	31	the	the	DET
ijassa-1364	151	32	object	object	NOUN
ijassa-1364	151	33	moves	move	VERB
ijassa-1364	151	34	in	in	ADP
ijassa-1364	151	35	the	the	DET
ijassa-1364	151	36	space	space	NOUN
ijassa-1364	151	37	r2	r2	NOUN
ijassa-1364	151	38	.	.	PUNCT
ijassa-1364	152	1	the	the	DET
ijassa-1364	152	2	set	set	PROPN
ijassa-1364	152	3	k1(τ	k1(τ	PROPN
ijassa-1364	152	4	)	)	PUNCT
ijassa-1364	152	5	copyright	copyright	NOUN
ijassa-1364	152	6	©	©	ADP
ijassa-1364	152	7	2023	2023	NUM
ijassa-1364	152	8	assa	assa	NOUN
ijassa-1364	152	9	.	.	PUNCT
ijassa-1364	153	1	adv	adv	PROPN
ijassa-1364	153	2	syst	syst	PROPN
ijassa-1364	153	3	sci	sci	PROPN
ijassa-1364	153	4	appl	appl	PROPN
ijassa-1364	153	5	(	(	PUNCT
ijassa-1364	153	6	2023	2023	NUM
ijassa-1364	153	7	)	)	PUNCT
ijassa-1364	153	8	the	the	DET
ijassa-1364	153	9	problem	problem	NOUN
ijassa-1364	153	10	of	of	ADP
ijassa-1364	153	11	controllability	controllability	NOUN
ijassa-1364	153	12	67	67	NUM
ijassa-1364	153	13	is	be	AUX
ijassa-1364	153	14	the	the	DET
ijassa-1364	153	15	segment	segment	NOUN
ijassa-1364	153	16	with	with	ADP
ijassa-1364	153	17	the	the	DET
ijassa-1364	153	18	endpoints	endpoint	NOUN
ijassa-1364	153	19	(	(	PUNCT
ijassa-1364	153	20	−	−	ADP
ijassa-1364	153	21	√	√	PROPN
ijassa-1364	153	22	τ	τ	PROPN
ijassa-1364	153	23	2	2	NUM
ijassa-1364	153	24	−	−	PROPN
ijassa-1364	153	25	cos2	cos2	PROPN
ijassa-1364	153	26	τ	τ	PROPN
ijassa-1364	153	27	,	,	PUNCT
ijassa-1364	153	28	0	0	NUM
ijassa-1364	153	29	)	)	PUNCT
ijassa-1364	153	30	,	,	PUNCT
ijassa-1364	153	31	(	(	PUNCT
ijassa-1364	153	32	√	√	ADV
ijassa-1364	153	33	τ	τ	SYM
ijassa-1364	153	34	2	2	NUM
ijassa-1364	153	35	−	−	PROPN
ijassa-1364	153	36	cos2	cos2	PROPN
ijassa-1364	153	37	τ	τ	PROPN
ijassa-1364	153	38	,	,	PUNCT
ijassa-1364	153	39	0	0	NUM
ijassa-1364	153	40	)	)	PUNCT
ijassa-1364	153	41	.	.	PUNCT
ijassa-1364	154	1	thus	thus	ADV
ijassa-1364	154	2	,	,	PUNCT
ijassa-1364	154	3	we	we	PRON
ijassa-1364	154	4	have	have	VERB
ijassa-1364	154	5	the	the	DET
ijassa-1364	154	6	following	follow	VERB
ijassa-1364	154	7	controllability	controllability	NOUN
ijassa-1364	154	8	problem	problem	NOUN
ijassa-1364	154	9	in	in	ADP
ijassa-1364	154	10	r2	r2	PROPN
ijassa-1364	154	11	:	:	PUNCT
ijassa-1364	154	12	find	find	VERB
ijassa-1364	154	13	such	such	ADJ
ijassa-1364	154	14	conditions	condition	NOUN
ijassa-1364	154	15	on	on	ADP
ijassa-1364	154	16	systems	system	NOUN
ijassa-1364	154	17	(	(	PUNCT
ijassa-1364	154	18	3.12	3.12	NUM
ijassa-1364	154	19	)	)	PUNCT
ijassa-1364	154	20	and	and	CCONJ
ijassa-1364	154	21	(	(	PUNCT
ijassa-1364	154	22	3.13	3.13	NUM
ijassa-1364	154	23	)	)	PUNCT
ijassa-1364	154	24	that	that	SCONJ
ijassa-1364	154	25	the	the	DET
ijassa-1364	154	26	object	object	NOUN
ijassa-1364	154	27	described	describe	VERB
ijassa-1364	154	28	by	by	ADP
ijassa-1364	154	29	these	these	DET
ijassa-1364	154	30	systems	system	NOUN
ijassa-1364	154	31	is	be	AUX
ijassa-1364	154	32	controllable	controllable	ADJ
ijassa-1364	154	33	from	from	ADP
ijassa-1364	154	34	the	the	DET
ijassa-1364	154	35	set	set	PROPN
ijassa-1364	154	36	k1(τ	k1(τ	PROPN
ijassa-1364	154	37	)	)	PUNCT
ijassa-1364	154	38	to	to	ADP
ijassa-1364	154	39	the	the	DET
ijassa-1364	154	40	set	set	ADJ
ijassa-1364	154	41	m1	m1	NOUN
ijassa-1364	154	42	.	.	PUNCT
ijassa-1364	155	1	the	the	DET
ijassa-1364	155	2	controllability	controllability	NOUN
ijassa-1364	155	3	function	function	NOUN
ijassa-1364	155	4	in	in	ADP
ijassa-1364	155	5	this	this	DET
ijassa-1364	155	6	case	case	NOUN
ijassa-1364	155	7	has	have	VERB
ijassa-1364	155	8	the	the	DET
ijassa-1364	155	9	form	form	NOUN
ijassa-1364	155	10	φ(ψ	φ(ψ	NOUN
ijassa-1364	155	11	)	)	PUNCT
ijassa-1364	155	12	=	=	PUNCT
ijassa-1364	156	1	√	√	NUM
ijassa-1364	156	2	τ	τ	SYM
ijassa-1364	156	3	2	2	NUM
ijassa-1364	156	4	−	−	PROPN
ijassa-1364	156	5	cos2	cos2	PROPN
ijassa-1364	156	6	τ	τ	X
ijassa-1364	156	7	·	·	PUNCT
ijassa-1364	156	8	|ψ1|+	|ψ1|+	NUM
ijassa-1364	156	9	∥ψ∥+	∥ψ∥+	NOUN
ijassa-1364	156	10	3ψ2	3ψ2	NUM
ijassa-1364	156	11	+	+	NUM
ijassa-1364	156	12	t−τ∫	t−τ∫	NOUN
ijassa-1364	156	13	0	0	NUM
ijassa-1364	156	14	√	√	NOUN
ijassa-1364	156	15	ψ2	ψ2	NOUN
ijassa-1364	156	16	1	1	NUM
ijassa-1364	156	17	+	+	CCONJ
ijassa-1364	156	18	(	(	PUNCT
ijassa-1364	156	19	sψ1	sψ1	NOUN
ijassa-1364	156	20	+	+	SYM
ijassa-1364	156	21	ψ2)2	ψ2)2	X
ijassa-1364	156	22	ds	ds	PROPN
ijassa-1364	156	23	,	,	PUNCT
ijassa-1364	156	24	(	(	PUNCT
ijassa-1364	156	25	3.14	3.14	NUM
ijassa-1364	156	26	)	)	PUNCT
ijassa-1364	156	27	where	where	SCONJ
ijassa-1364	156	28	∥ψ∥	∥ψ∥	X
ijassa-1364	156	29	=	=	SYM
ijassa-1364	156	30	1	1	NUM
ijassa-1364	156	31	,	,	PUNCT
ijassa-1364	156	32	ψ	ψ	NOUN
ijassa-1364	156	33	=	=	PUNCT
ijassa-1364	156	34	(	(	PUNCT
ijassa-1364	156	35	ψ1	ψ1	NOUN
ijassa-1364	156	36	,	,	PUNCT
ijassa-1364	156	37	ψ2	ψ2	NOUN
ijassa-1364	156	38	,	,	PUNCT
ijassa-1364	156	39	ψ3	ψ3	NOUN
ijassa-1364	156	40	)	)	PUNCT
ijassa-1364	156	41	.	.	PUNCT
ijassa-1364	157	1	the	the	DET
ijassa-1364	157	2	controllability	controllability	NOUN
ijassa-1364	157	3	function	function	NOUN
ijassa-1364	157	4	(	(	PUNCT
ijassa-1364	157	5	3.14	3.14	NUM
ijassa-1364	157	6	)	)	PUNCT
ijassa-1364	157	7	reaches	reach	VERB
ijassa-1364	157	8	its	its	PRON
ijassa-1364	157	9	minimum	minimum	NOUN
ijassa-1364	157	10	at	at	ADP
ijassa-1364	157	11	ψ2	ψ2	NOUN
ijassa-1364	157	12	=	=	SYM
ijassa-1364	157	13	−1	−1	NOUN
ijassa-1364	157	14	,	,	PUNCT
ijassa-1364	157	15	then	then	ADV
ijassa-1364	157	16	due	due	ADP
ijassa-1364	157	17	to	to	ADP
ijassa-1364	157	18	the	the	DET
ijassa-1364	157	19	fact	fact	NOUN
ijassa-1364	157	20	that	that	SCONJ
ijassa-1364	157	21	∥ψ∥	∥ψ∥	PROPN
ijassa-1364	157	22	=	=	SYM
ijassa-1364	157	23	1	1	NUM
ijassa-1364	157	24	,	,	PUNCT
ijassa-1364	157	25	ψ1	ψ1	ADJ
ijassa-1364	157	26	=	=	SYM
ijassa-1364	157	27	ψ3	ψ3	NOUN
ijassa-1364	157	28	=	=	NOUN
ijassa-1364	157	29	0	0	PROPN
ijassa-1364	157	30	.	.	PUNCT
ijassa-1364	158	1	this	this	PRON
ijassa-1364	158	2	yields	yield	VERB
ijassa-1364	158	3	min	min	PROPN
ijassa-1364	158	4	ψ∈s	ψ∈s	NOUN
ijassa-1364	158	5	φ(ψ	φ(ψ	PROPN
ijassa-1364	158	6	)	)	PUNCT
ijassa-1364	158	7	=	=	SYM
ijassa-1364	158	8	t	t	NOUN
ijassa-1364	158	9	−	−	PROPN
ijassa-1364	159	1	(	(	PUNCT
ijassa-1364	159	2	2	2	NUM
ijassa-1364	159	3	+	+	CCONJ
ijassa-1364	159	4	τ	τ	PROPN
ijassa-1364	159	5	)	)	PUNCT
ijassa-1364	159	6	.	.	PUNCT
ijassa-1364	160	1	therefore	therefore	ADV
ijassa-1364	160	2	,	,	PUNCT
ijassa-1364	160	3	when	when	SCONJ
ijassa-1364	160	4	t	t	PROPN
ijassa-1364	160	5	>	>	X
ijassa-1364	160	6	2	2	NUM
ijassa-1364	160	7	+	+	CCONJ
ijassa-1364	160	8	τ	τ	PROPN
ijassa-1364	160	9	,	,	PUNCT
ijassa-1364	160	10	the	the	DET
ijassa-1364	160	11	object	object	NOUN
ijassa-1364	160	12	described	describe	VERB
ijassa-1364	160	13	by	by	ADP
ijassa-1364	160	14	systems	system	NOUN
ijassa-1364	160	15	(	(	PUNCT
ijassa-1364	160	16	3.12	3.12	NUM
ijassa-1364	160	17	)	)	PUNCT
ijassa-1364	160	18	and	and	CCONJ
ijassa-1364	160	19	(	(	PUNCT
ijassa-1364	160	20	3.13	3.13	NUM
ijassa-1364	160	21	)	)	PUNCT
ijassa-1364	160	22	is	be	AUX
ijassa-1364	160	23	controllable	controllable	ADJ
ijassa-1364	160	24	on	on	ADP
ijassa-1364	160	25	the	the	DET
ijassa-1364	160	26	time	time	NOUN
ijassa-1364	160	27	interval	interval	NOUN
ijassa-1364	160	28	[	[	X
ijassa-1364	160	29	0	0	NUM
ijassa-1364	160	30	,	,	PUNCT
ijassa-1364	160	31	t	t	X
ijassa-1364	160	32	]	]	PUNCT
ijassa-1364	160	33	from	from	ADP
ijassa-1364	160	34	the	the	DET
ijassa-1364	160	35	set	set	ADJ
ijassa-1364	160	36	m0	m0	NOUN
ijassa-1364	160	37	to	to	ADP
ijassa-1364	160	38	the	the	DET
ijassa-1364	160	39	set	set	ADJ
ijassa-1364	160	40	m1	m1	NOUN
ijassa-1364	160	41	.	.	PUNCT
ijassa-1364	161	1	4	4	X
ijassa-1364	161	2	.	.	X
ijassa-1364	161	3	conclusion	conclusion	NOUN
ijassa-1364	161	4	a	a	DET
ijassa-1364	161	5	special	special	ADJ
ijassa-1364	161	6	class	class	NOUN
ijassa-1364	161	7	of	of	ADP
ijassa-1364	161	8	controlled	control	VERB
ijassa-1364	161	9	differential	differential	NOUN
ijassa-1364	161	10	systems	system	NOUN
ijassa-1364	161	11	called	call	VERB
ijassa-1364	161	12	hybrid	hybrid	NOUN
ijassa-1364	161	13	or	or	CCONJ
ijassa-1364	161	14	composite	composite	NOUN
ijassa-1364	161	15	is	be	AUX
ijassa-1364	161	16	considered	consider	VERB
ijassa-1364	161	17	.	.	PUNCT
ijassa-1364	162	1	such	such	ADJ
ijassa-1364	162	2	systems	system	NOUN
ijassa-1364	162	3	are	be	AUX
ijassa-1364	162	4	characterized	characterize	VERB
ijassa-1364	162	5	by	by	ADP
ijassa-1364	162	6	the	the	DET
ijassa-1364	162	7	condition	condition	NOUN
ijassa-1364	162	8	that	that	SCONJ
ijassa-1364	162	9	at	at	ADP
ijassa-1364	162	10	different	different	ADJ
ijassa-1364	162	11	time	time	NOUN
ijassa-1364	162	12	intervals	interval	NOUN
ijassa-1364	162	13	the	the	DET
ijassa-1364	162	14	motion	motion	NOUN
ijassa-1364	162	15	of	of	ADP
ijassa-1364	162	16	the	the	DET
ijassa-1364	162	17	object	object	NOUN
ijassa-1364	162	18	is	be	AUX
ijassa-1364	162	19	described	describe	VERB
ijassa-1364	162	20	by	by	ADP
ijassa-1364	162	21	different	different	ADJ
ijassa-1364	162	22	differential	differential	ADJ
ijassa-1364	162	23	equations	equation	NOUN
ijassa-1364	162	24	and	and	CCONJ
ijassa-1364	162	25	some	some	DET
ijassa-1364	162	26	links	link	NOUN
ijassa-1364	162	27	for	for	ADP
ijassa-1364	162	28	trajectory	trajectory	NOUN
ijassa-1364	162	29	mating	mating	NOUN
ijassa-1364	162	30	.	.	PUNCT
ijassa-1364	163	1	sufficient	sufficient	ADJ
ijassa-1364	163	2	conditions	condition	NOUN
ijassa-1364	163	3	of	of	ADP
ijassa-1364	163	4	the	the	DET
ijassa-1364	163	5	controllability	controllability	NOUN
ijassa-1364	163	6	of	of	ADP
ijassa-1364	163	7	such	such	ADJ
ijassa-1364	163	8	systems	system	NOUN
ijassa-1364	163	9	from	from	ADP
ijassa-1364	163	10	the	the	DET
ijassa-1364	163	11	initial	initial	ADJ
ijassa-1364	163	12	set	set	NOUN
ijassa-1364	163	13	in	in	ADP
ijassa-1364	163	14	one	one	NUM
ijassa-1364	163	15	space	space	NOUN
ijassa-1364	163	16	to	to	ADP
ijassa-1364	163	17	the	the	DET
ijassa-1364	163	18	terminal	terminal	ADJ
ijassa-1364	163	19	set	set	NOUN
ijassa-1364	163	20	of	of	ADP
ijassa-1364	163	21	the	the	DET
ijassa-1364	163	22	other	other	ADJ
ijassa-1364	163	23	space	space	NOUN
ijassa-1364	163	24	are	be	AUX
ijassa-1364	163	25	obtained	obtain	VERB
ijassa-1364	163	26	.	.	PUNCT
ijassa-1364	164	1	sufficient	sufficient	ADJ
ijassa-1364	164	2	controllability	controllability	NOUN
ijassa-1364	164	3	conditions	condition	NOUN
ijassa-1364	164	4	for	for	ADP
ijassa-1364	164	5	the	the	DET
ijassa-1364	164	6	nonlinear	nonlinear	ADJ
ijassa-1364	164	7	case	case	NOUN
ijassa-1364	164	8	are	be	AUX
ijassa-1364	164	9	obtained	obtain	VERB
ijassa-1364	164	10	using	use	VERB
ijassa-1364	164	11	the	the	DET
ijassa-1364	164	12	apparatus	apparatus	NOUN
ijassa-1364	164	13	of	of	ADP
ijassa-1364	164	14	convex	convex	ADJ
ijassa-1364	164	15	analysis	analysis	NOUN
ijassa-1364	164	16	,	,	PUNCT
ijassa-1364	164	17	the	the	DET
ijassa-1364	164	18	theory	theory	NOUN
ijassa-1364	164	19	of	of	ADP
ijassa-1364	164	20	multivalued	multivalued	ADJ
ijassa-1364	164	21	mappings	mapping	NOUN
ijassa-1364	164	22	,	,	PUNCT
ijassa-1364	164	23	and	and	CCONJ
ijassa-1364	164	24	the	the	DET
ijassa-1364	164	25	control	control	NOUN
ijassa-1364	164	26	theory	theory	NOUN
ijassa-1364	164	27	.	.	PUNCT
ijassa-1364	165	1	this	this	DET
ijassa-1364	165	2	class	class	NOUN
ijassa-1364	165	3	of	of	ADP
ijassa-1364	165	4	composite	composite	ADJ
ijassa-1364	165	5	systems	system	NOUN
ijassa-1364	165	6	has	have	AUX
ijassa-1364	165	7	not	not	PART
ijassa-1364	165	8	been	be	AUX
ijassa-1364	165	9	considered	consider	VERB
ijassa-1364	165	10	before	before	ADV
ijassa-1364	165	11	.	.	PUNCT
ijassa-1364	166	1	an	an	DET
ijassa-1364	166	2	actual	actual	ADJ
ijassa-1364	166	3	application	application	NOUN
ijassa-1364	166	4	of	of	ADP
ijassa-1364	166	5	the	the	DET
ijassa-1364	166	6	proposed	propose	VERB
ijassa-1364	166	7	approaches	approach	NOUN
ijassa-1364	166	8	and	and	CCONJ
ijassa-1364	166	9	results	result	NOUN
ijassa-1364	166	10	lies	lie	VERB
ijassa-1364	166	11	in	in	ADP
ijassa-1364	166	12	the	the	DET
ijassa-1364	166	13	field	field	NOUN
ijassa-1364	166	14	of	of	ADP
ijassa-1364	166	15	mathematical	mathematical	ADJ
ijassa-1364	166	16	biology	biology	NOUN
ijassa-1364	166	17	(	(	PUNCT
ijassa-1364	166	18	see	see	VERB
ijassa-1364	166	19	[	[	X
ijassa-1364	166	20	15	15	NUM
ijassa-1364	166	21	]	]	PUNCT
ijassa-1364	166	22	)	)	PUNCT
ijassa-1364	166	23	and	and	CCONJ
ijassa-1364	166	24	mathematical	mathematical	ADJ
ijassa-1364	166	25	economics	economic	NOUN
ijassa-1364	166	26	with	with	ADP
ijassa-1364	166	27	control	control	NOUN
ijassa-1364	166	28	input	input	NOUN
ijassa-1364	166	29	,	,	PUNCT
ijassa-1364	166	30	for	for	ADP
ijassa-1364	166	31	instance	instance	NOUN
ijassa-1364	166	32	,	,	PUNCT
ijassa-1364	166	33	dynamic	dynamic	ADJ
ijassa-1364	166	34	market	market	NOUN
ijassa-1364	166	35	models	model	NOUN
ijassa-1364	166	36	with	with	ADP
ijassa-1364	166	37	continuous	continuous	ADJ
ijassa-1364	166	38	,	,	PUNCT
ijassa-1364	166	39	see	see	ADJ
ijassa-1364	166	40	,	,	PUNCT
ijassa-1364	166	41	e.g.	e.g.	ADV
ijassa-1364	166	42	,	,	PUNCT
ijassa-1364	166	43	[	[	X
ijassa-1364	166	44	1	1	NUM
ijassa-1364	166	45	,	,	PUNCT
ijassa-1364	166	46	13	13	NUM
ijassa-1364	166	47	]	]	PUNCT
ijassa-1364	166	48	.	.	PUNCT
ijassa-1364	167	1	references	reference	NOUN
ijassa-1364	167	2	1	1	NUM
ijassa-1364	167	3	.	.	PUNCT
ijassa-1364	168	1	arutyunov	arutyunov	PROPN
ijassa-1364	168	2	,	,	PUNCT
ijassa-1364	168	3	a.	a.	PROPN
ijassa-1364	168	4	v.	v.	PROPN
ijassa-1364	168	5	&	&	CCONJ
ijassa-1364	168	6	pavlova	pavlova	PROPN
ijassa-1364	168	7	,	,	PUNCT
ijassa-1364	168	8	n.	n.	PROPN
ijassa-1364	168	9	g.	g.	PROPN
ijassa-1364	168	10	(	(	PUNCT
ijassa-1364	168	11	2022	2022	NUM
ijassa-1364	168	12	)	)	PUNCT
ijassa-1364	168	13	.	.	PUNCT
ijassa-1364	169	1	equilibrium	equilibrium	NOUN
ijassa-1364	169	2	in	in	ADP
ijassa-1364	169	3	market	market	NOUN
ijassa-1364	169	4	models	model	NOUN
ijassa-1364	169	5	described	describe	VERB
ijassa-1364	169	6	by	by	ADP
ijassa-1364	169	7	differential	differential	ADJ
ijassa-1364	169	8	equations	equation	NOUN
ijassa-1364	169	9	,	,	PUNCT
ijassa-1364	169	10	differ	differ	VERB
ijassa-1364	169	11	.	.	PUNCT
ijassa-1364	170	1	equ	equ	PROPN
ijassa-1364	170	2	.	.	PROPN
ijassa-1364	170	3	,	,	PUNCT
ijassa-1364	170	4	58(9	58(9	NOUN
ijassa-1364	170	5	)	)	PUNCT
ijassa-1364	170	6	,	,	PUNCT
ijassa-1364	170	7	1267–1276	1267–1276	NUM
ijassa-1364	170	8	.	.	NOUN
ijassa-1364	170	9	2	2	NUM
ijassa-1364	170	10	.	.	X
ijassa-1364	170	11	ashepkov	ashepkov	PROPN
ijassa-1364	170	12	,	,	PUNCT
ijassa-1364	170	13	l.	l.	PROPN
ijassa-1364	170	14	t.	t.	PROPN
ijassa-1364	170	15	(	(	PUNCT
ijassa-1364	170	16	1981	1981	NUM
ijassa-1364	170	17	)	)	PUNCT
ijassa-1364	170	18	.	.	PUNCT
ijassa-1364	171	1	optimal	optimal	ADJ
ijassa-1364	171	2	system	system	NOUN
ijassa-1364	171	3	control	control	NOUN
ijassa-1364	171	4	with	with	ADP
ijassa-1364	171	5	intermediate	intermediate	ADJ
ijassa-1364	171	6	conditions	condition	NOUN
ijassa-1364	171	7	,	,	PUNCT
ijassa-1364	171	8	applied	apply	VERB
ijassa-1364	171	9	mathem	mathem	NOUN
ijassa-1364	171	10	.	.	PUNCT
ijassa-1364	172	1	mech	mech	PROPN
ijassa-1364	172	2	.	.	PUNCT
ijassa-1364	172	3	,	,	PUNCT
ijassa-1364	172	4	45(2	45(2	NOUN
ijassa-1364	172	5	)	)	PUNCT
ijassa-1364	172	6	,	,	PUNCT
ijassa-1364	172	7	215–222	215–222	NUM
ijassa-1364	172	8	.	.	PUNCT
ijassa-1364	173	1	[	[	X
ijassa-1364	173	2	in	in	ADP
ijassa-1364	173	3	russian	russian	NOUN
ijassa-1364	173	4	]	]	X
ijassa-1364	173	5	3	3	X
ijassa-1364	173	6	.	.	X
ijassa-1364	173	7	bargsegayn	bargsegayn	NOUN
ijassa-1364	173	8	,	,	PUNCT
ijassa-1364	173	9	v.	v.	PROPN
ijassa-1364	173	10	r.	r.	PROPN
ijassa-1364	173	11	(	(	PUNCT
ijassa-1364	173	12	2012	2012	NUM
ijassa-1364	173	13	)	)	PUNCT
ijassa-1364	173	14	.	.	PUNCT
ijassa-1364	174	1	constructive	constructive	ADJ
ijassa-1364	174	2	approach	approach	NOUN
ijassa-1364	174	3	to	to	ADP
ijassa-1364	174	4	the	the	DET
ijassa-1364	174	5	study	study	NOUN
ijassa-1364	174	6	of	of	ADP
ijassa-1364	174	7	control	control	NOUN
ijassa-1364	174	8	problems	problem	NOUN
ijassa-1364	174	9	of	of	ADP
ijassa-1364	174	10	linear	linear	ADJ
ijassa-1364	174	11	composite	composite	ADJ
ijassa-1364	174	12	systems	system	NOUN
ijassa-1364	174	13	,	,	PUNCT
ijassa-1364	174	14	control	control	NOUN
ijassa-1364	174	15	problems	problem	NOUN
ijassa-1364	174	16	,	,	PUNCT
ijassa-1364	174	17	4	4	NUM
ijassa-1364	174	18	,	,	PUNCT
ijassa-1364	174	19	11–17	11–17	NUM
ijassa-1364	174	20	.	.	PUNCT
ijassa-1364	175	1	4	4	NUM
ijassa-1364	175	2	.	.	X
ijassa-1364	175	3	bargsegayn	bargsegayn	NOUN
ijassa-1364	175	4	,	,	PUNCT
ijassa-1364	175	5	v.	v.	PROPN
ijassa-1364	175	6	r.	r.	PROPN
ijassa-1364	175	7	(	(	PUNCT
ijassa-1364	175	8	2016	2016	NUM
ijassa-1364	175	9	)	)	PUNCT
ijassa-1364	175	10	.	.	PUNCT
ijassa-1364	176	1	controls	control	NOUN
ijassa-1364	176	2	of	of	ADP
ijassa-1364	176	3	composite	composite	ADJ
ijassa-1364	176	4	dynamical	dynamical	ADJ
ijassa-1364	176	5	systems	system	NOUN
ijassa-1364	176	6	with	with	ADP
ijassa-1364	176	7	multipoint	multipoint	NOUN
ijassa-1364	176	8	intermediate	intermediate	ADJ
ijassa-1364	176	9	conditions	condition	NOUN
ijassa-1364	176	10	,	,	PUNCT
ijassa-1364	176	11	moscow	moscow	PROPN
ijassa-1364	176	12	,	,	PUNCT
ijassa-1364	176	13	russia	russia	PROPN
ijassa-1364	176	14	:	:	PUNCT
ijassa-1364	176	15	nauka	nauka	PROPN
ijassa-1364	177	1	[	[	X
ijassa-1364	177	2	in	in	ADP
ijassa-1364	177	3	russian	russian	PROPN
ijassa-1364	177	4	]	]	PUNCT
ijassa-1364	177	5	.	.	PUNCT
ijassa-1364	177	6	5	5	X
ijassa-1364	177	7	.	.	X
ijassa-1364	177	8	blagodatskikh	blagodatskikh	PROPN
ijassa-1364	177	9	,	,	PUNCT
ijassa-1364	177	10	v.	v.	PROPN
ijassa-1364	177	11	i.	i.	PROPN
ijassa-1364	177	12	(	(	PUNCT
ijassa-1364	177	13	2001	2001	NUM
ijassa-1364	177	14	)	)	PUNCT
ijassa-1364	177	15	.	.	PUNCT
ijassa-1364	178	1	introduction	introduction	NOUN
ijassa-1364	178	2	to	to	ADP
ijassa-1364	178	3	optimal	optimal	ADJ
ijassa-1364	178	4	control	control	NOUN
ijassa-1364	178	5	,	,	PUNCT
ijassa-1364	178	6	moscow	moscow	PROPN
ijassa-1364	178	7	,	,	PUNCT
ijassa-1364	178	8	russia	russia	PROPN
ijassa-1364	178	9	:	:	PUNCT
ijassa-1364	178	10	visshaya	visshaya	PROPN
ijassa-1364	178	11	shkola	shkola	PROPN
ijassa-1364	178	12	,	,	PUNCT
ijassa-1364	179	1	[	[	X
ijassa-1364	179	2	in	in	ADP
ijassa-1364	179	3	russian	russian	PROPN
ijassa-1364	179	4	]	]	PUNCT
ijassa-1364	179	5	.	.	PUNCT
ijassa-1364	179	6	6	6	NUM
ijassa-1364	179	7	.	.	X
ijassa-1364	179	8	blagodatskih	blagodatskih	PROPN
ijassa-1364	179	9	,	,	PUNCT
ijassa-1364	179	10	v.	v.	PROPN
ijassa-1364	179	11	i.	i.	PROPN
ijassa-1364	179	12	&	&	CCONJ
ijassa-1364	179	13	filippov	filippov	PROPN
ijassa-1364	179	14	a.	a.	PROPN
ijassa-1364	179	15	f.	f.	PROPN
ijassa-1364	179	16	(	(	PUNCT
ijassa-1364	179	17	1986	1986	NUM
ijassa-1364	179	18	)	)	PUNCT
ijassa-1364	179	19	.	.	PUNCT
ijassa-1364	180	1	differential	differential	ADJ
ijassa-1364	180	2	inclusions	inclusion	NOUN
ijassa-1364	180	3	and	and	CCONJ
ijassa-1364	180	4	optimal	optimal	ADJ
ijassa-1364	180	5	control	control	NOUN
ijassa-1364	180	6	,	,	PUNCT
ijassa-1364	180	7	proc	proc	PROPN
ijassa-1364	180	8	.	.	PUNCT
ijassa-1364	180	9	steklov	steklov	PROPN
ijassa-1364	180	10	inst	inst	PROPN
ijassa-1364	180	11	.	.	PUNCT
ijassa-1364	180	12	math	math	NOUN
ijassa-1364	180	13	.	.	PUNCT
ijassa-1364	180	14	,	,	PUNCT
ijassa-1364	180	15	169	169	NUM
ijassa-1364	180	16	,	,	PUNCT
ijassa-1364	180	17	199–259	199–259	NUM
ijassa-1364	180	18	.	.	PUNCT
ijassa-1364	181	1	7	7	X
ijassa-1364	181	2	.	.	NUM
ijassa-1364	181	3	boltyanskii	boltyanskii	VERB
ijassa-1364	181	4	,	,	PUNCT
ijassa-1364	181	5	v.	v.	PROPN
ijassa-1364	181	6	g.	g.	PROPN
ijassa-1364	181	7	(	(	PUNCT
ijassa-1364	181	8	1983	1983	NUM
ijassa-1364	181	9	)	)	PUNCT
ijassa-1364	181	10	.	.	PUNCT
ijassa-1364	182	1	the	the	DET
ijassa-1364	182	2	optimization	optimization	NOUN
ijassa-1364	182	3	problem	problem	NOUN
ijassa-1364	182	4	with	with	ADP
ijassa-1364	182	5	phase	phase	NOUN
ijassa-1364	182	6	space	space	NOUN
ijassa-1364	182	7	change	change	NOUN
ijassa-1364	182	8	,	,	PUNCT
ijassa-1364	182	9	differ	differ	VERB
ijassa-1364	182	10	.	.	PUNCT
ijassa-1364	183	1	equ	equ	PROPN
ijassa-1364	183	2	.	.	PROPN
ijassa-1364	183	3	,	,	PUNCT
ijassa-1364	183	4	19(3	19(3	NUM
ijassa-1364	183	5	)	)	PUNCT
ijassa-1364	183	6	,	,	PUNCT
ijassa-1364	183	7	518–521	518–521	NUM
ijassa-1364	183	8	.	.	NOUN
ijassa-1364	183	9	8	8	NUM
ijassa-1364	183	10	.	.	X
ijassa-1364	184	1	borisovich	borisovich	NOUN
ijassa-1364	184	2	,	,	PUNCT
ijassa-1364	184	3	yu	yu	PROPN
ijassa-1364	184	4	.	.	PROPN
ijassa-1364	184	5	g.	g.	PROPN
ijassa-1364	184	6	,	,	PUNCT
ijassa-1364	184	7	gel’man	gel’man	PROPN
ijassa-1364	184	8	,	,	PUNCT
ijassa-1364	184	9	b.	b.	PROPN
ijassa-1364	184	10	d.	d.	PROPN
ijassa-1364	184	11	,	,	PUNCT
ijassa-1364	184	12	myshkis	myshki	NOUN
ijassa-1364	184	13	,	,	PUNCT
ijassa-1364	184	14	a.	a.	PROPN
ijassa-1364	184	15	d.	d.	PROPN
ijassa-1364	184	16	&	&	CCONJ
ijassa-1364	184	17	obukhovskii	obukhovskii	PROPN
ijassa-1364	184	18	,	,	PUNCT
ijassa-1364	184	19	v.	v.	ADP
ijassa-1364	184	20	v.	v.	CCONJ
ijassa-1364	184	21	(	(	PUNCT
ijassa-1364	184	22	1999	1999	NUM
ijassa-1364	184	23	)	)	PUNCT
ijassa-1364	184	24	.	.	PUNCT
ijassa-1364	185	1	introduction	introduction	NOUN
ijassa-1364	185	2	to	to	ADP
ijassa-1364	185	3	the	the	DET
ijassa-1364	185	4	theory	theory	NOUN
ijassa-1364	185	5	of	of	ADP
ijassa-1364	185	6	multivalued	multivalued	ADJ
ijassa-1364	185	7	mappings	mapping	NOUN
ijassa-1364	185	8	and	and	CCONJ
ijassa-1364	185	9	differential	differential	ADJ
ijassa-1364	185	10	inclusions	inclusion	NOUN
ijassa-1364	185	11	,	,	PUNCT
ijassa-1364	185	12	dordrecht	dordrecht	PROPN
ijassa-1364	185	13	,	,	PUNCT
ijassa-1364	185	14	netherlands	netherlands	PROPN
ijassa-1364	185	15	:	:	PUNCT
ijassa-1364	185	16	kluwer	kluwer	NOUN
ijassa-1364	185	17	academic	academic	ADJ
ijassa-1364	185	18	publishers	publisher	NOUN
ijassa-1364	185	19	.	.	PUNCT
ijassa-1364	186	1	copyright	copyright	NOUN
ijassa-1364	186	2	©	©	PROPN
ijassa-1364	186	3	2023	2023	NUM
ijassa-1364	186	4	assa	assa	NOUN
ijassa-1364	186	5	.	.	PUNCT
ijassa-1364	187	1	adv	adv	PROPN
ijassa-1364	187	2	syst	syst	PROPN
ijassa-1364	187	3	sci	sci	PROPN
ijassa-1364	187	4	appl	appl	PROPN
ijassa-1364	187	5	(	(	PUNCT
ijassa-1364	187	6	2023	2023	NUM
ijassa-1364	187	7	)	)	PUNCT
ijassa-1364	187	8	68	68	NUM
ijassa-1364	187	9	i.	i.	NOUN
ijassa-1364	187	10	maximova	maximova	NOUN
ijassa-1364	187	11	9	9	NUM
ijassa-1364	187	12	.	.	X
ijassa-1364	187	13	kalman	kalman	PROPN
ijassa-1364	187	14	,	,	PUNCT
ijassa-1364	187	15	r.	r.	PROPN
ijassa-1364	187	16	,	,	PUNCT
ijassa-1364	187	17	falb	falb	NOUN
ijassa-1364	187	18	,	,	PUNCT
ijassa-1364	187	19	p.	p.	NOUN
ijassa-1364	187	20	,	,	PUNCT
ijassa-1364	187	21	&	&	CCONJ
ijassa-1364	187	22	arbib	arbib	NOUN
ijassa-1364	187	23	,	,	PUNCT
ijassa-1364	187	24	m.	m.	NOUN
ijassa-1364	187	25	(	(	PUNCT
ijassa-1364	187	26	1969	1969	NUM
ijassa-1364	187	27	)	)	PUNCT
ijassa-1364	187	28	.	.	PUNCT
ijassa-1364	188	1	topics	topic	NOUN
ijassa-1364	188	2	in	in	ADP
ijassa-1364	188	3	mathematical	mathematical	ADJ
ijassa-1364	188	4	system	system	NOUN
ijassa-1364	188	5	theory	theory	NOUN
ijassa-1364	188	6	,	,	PUNCT
ijassa-1364	188	7	new	new	PROPN
ijassa-1364	188	8	york	york	PROPN
ijassa-1364	188	9	,	,	PUNCT
ijassa-1364	188	10	ny	ny	PROPN
ijassa-1364	188	11	:	:	PUNCT
ijassa-1364	188	12	mcgraw	mcgraw	PROPN
ijassa-1364	188	13	-	-	PUNCT
ijassa-1364	188	14	hill	hill	NOUN
ijassa-1364	188	15	.	.	PUNCT
ijassa-1364	189	1	10	10	NUM
ijassa-1364	189	2	.	.	X
ijassa-1364	190	1	kramar	kramar	PROPN
ijassa-1364	190	2	,	,	PUNCT
ijassa-1364	190	3	v.	v.	PROPN
ijassa-1364	190	4	,	,	PUNCT
ijassa-1364	190	5	alchakov	alchakov	PROPN
ijassa-1364	190	6	,	,	PUNCT
ijassa-1364	190	7	v.	v.	PROPN
ijassa-1364	190	8	,	,	PUNCT
ijassa-1364	190	9	&	&	CCONJ
ijassa-1364	190	10	osadchenko	osadchenko	PROPN
ijassa-1364	190	11	,	,	PUNCT
ijassa-1364	190	12	a.	a.	NOUN
ijassa-1364	190	13	(	(	PUNCT
ijassa-1364	190	14	2021	2021	NUM
ijassa-1364	190	15	)	)	PUNCT
ijassa-1364	190	16	.	.	PUNCT
ijassa-1364	191	1	the	the	DET
ijassa-1364	191	2	optimal	optimal	ADJ
ijassa-1364	191	3	control	control	NOUN
ijassa-1364	191	4	of	of	ADP
ijassa-1364	191	5	the	the	DET
ijassa-1364	191	6	vessel	vessel	NOUN
ijassa-1364	191	7	’s	’s	PART
ijassa-1364	191	8	automatic	automatic	ADJ
ijassa-1364	191	9	dynamic	dynamic	ADJ
ijassa-1364	191	10	positioning	positioning	NOUN
ijassa-1364	191	11	system	system	NOUN
ijassa-1364	191	12	under	under	ADP
ijassa-1364	191	13	deviation	deviation	NOUN
ijassa-1364	191	14	,	,	PUNCT
ijassa-1364	191	15	adv	adv	PROPN
ijassa-1364	191	16	.	.	PUNCT
ijassa-1364	191	17	syst	syst	PROPN
ijassa-1364	191	18	.	.	PUNCT
ijassa-1364	192	1	sci	sci	PROPN
ijassa-1364	192	2	.	.	PUNCT
ijassa-1364	192	3	appl	appl	PROPN
ijassa-1364	192	4	.	.	PROPN
ijassa-1364	192	5	,	,	PUNCT
ijassa-1364	192	6	21(1	21(1	NUM
ijassa-1364	192	7	)	)	PUNCT
ijassa-1364	192	8	,	,	PUNCT
ijassa-1364	192	9	1–10	1–10	NOUN
ijassa-1364	192	10	.	.	PUNCT
ijassa-1364	193	1	11	11	NUM
ijassa-1364	193	2	.	.	X
ijassa-1364	194	1	maksimova	maksimova	PROPN
ijassa-1364	194	2	,	,	PUNCT
ijassa-1364	194	3	i.	i.	PROPN
ijassa-1364	194	4	s.	s.	PROPN
ijassa-1364	194	5	(	(	PUNCT
ijassa-1364	194	6	2012	2012	NUM
ijassa-1364	194	7	)	)	PUNCT
ijassa-1364	194	8	.	.	PUNCT
ijassa-1364	195	1	necessary	necessary	ADJ
ijassa-1364	195	2	conditions	condition	NOUN
ijassa-1364	195	3	of	of	ADP
ijassa-1364	195	4	optimality	optimality	NOUN
ijassa-1364	195	5	in	in	ADP
ijassa-1364	195	6	the	the	DET
ijassa-1364	195	7	problem	problem	NOUN
ijassa-1364	195	8	with	with	ADP
ijassa-1364	195	9	changing	change	VERB
ijassa-1364	195	10	phase	phase	NOUN
ijassa-1364	195	11	spaces	space	NOUN
ijassa-1364	195	12	,	,	PUNCT
ijassa-1364	195	13	rudn	rudn	ADJ
ijassa-1364	195	14	reports	report	NOUN
ijassa-1364	195	15	.	.	PUNCT
ijassa-1364	196	1	series	series	NOUN
ijassa-1364	196	2	:	:	PUNCT
ijassa-1364	197	1	mathematics	mathematic	NOUN
ijassa-1364	197	2	.	.	PUNCT
ijassa-1364	198	1	computer	computer	NOUN
ijassa-1364	198	2	science	science	NOUN
ijassa-1364	198	3	.	.	PUNCT
ijassa-1364	199	1	physics	physics	NOUN
ijassa-1364	199	2	,	,	PUNCT
ijassa-1364	199	3	4	4	NUM
ijassa-1364	199	4	,	,	PUNCT
ijassa-1364	199	5	5–14	5–14	PROPN
ijassa-1364	199	6	.	.	PUNCT
ijassa-1364	200	1	[	[	X
ijassa-1364	200	2	in	in	ADP
ijassa-1364	200	3	russian	russian	NOUN
ijassa-1364	200	4	]	]	X
ijassa-1364	200	5	12	12	NUM
ijassa-1364	200	6	.	.	PUNCT
ijassa-1364	201	1	maksimova	maksimova	X
ijassa-1364	201	2	,	,	PUNCT
ijassa-1364	201	3	i.	i.	PROPN
ijassa-1364	201	4	s.	s.	PROPN
ijassa-1364	201	5	&	&	CCONJ
ijassa-1364	201	6	rozova	rozova	PROPN
ijassa-1364	201	7	,	,	PUNCT
ijassa-1364	201	8	v.	v.	ADP
ijassa-1364	201	9	n.	n.	PROPN
ijassa-1364	201	10	(	(	PUNCT
ijassa-1364	201	11	2017	2017	NUM
ijassa-1364	201	12	)	)	PUNCT
ijassa-1364	201	13	.	.	PUNCT
ijassa-1364	202	1	local	local	ADJ
ijassa-1364	202	2	controllability	controllability	NOUN
ijassa-1364	202	3	in	in	ADP
ijassa-1364	202	4	the	the	DET
ijassa-1364	202	5	problem	problem	NOUN
ijassa-1364	202	6	with	with	ADP
ijassa-1364	202	7	phase	phase	NOUN
ijassa-1364	202	8	space	space	NOUN
ijassa-1364	202	9	change	change	NOUN
ijassa-1364	202	10	,	,	PUNCT
ijassa-1364	202	11	rudn	rudn	ADJ
ijassa-1364	202	12	reports	report	NOUN
ijassa-1364	202	13	.	.	PUNCT
ijassa-1364	203	1	series	series	NOUN
ijassa-1364	203	2	:	:	PUNCT
ijassa-1364	203	3	natural	natural	ADJ
ijassa-1364	203	4	and	and	CCONJ
ijassa-1364	203	5	technical	technical	ADJ
ijassa-1364	203	6	sciences	science	NOUN
ijassa-1364	203	7	25(4	25(4	NOUN
ijassa-1364	203	8	)	)	PUNCT
ijassa-1364	203	9	,	,	PUNCT
ijassa-1364	203	10	331	331	NUM
ijassa-1364	203	11	–	–	PUNCT
ijassa-1364	203	12	338	338	NUM
ijassa-1364	203	13	.	.	PUNCT
ijassa-1364	204	1	[	[	X
ijassa-1364	204	2	in	in	ADP
ijassa-1364	204	3	russian	russian	NOUN
ijassa-1364	204	4	]	]	X
ijassa-1364	204	5	13	13	NUM
ijassa-1364	204	6	.	.	PUNCT
ijassa-1364	204	7	pavlova	pavlova	PROPN
ijassa-1364	204	8	,	,	PUNCT
ijassa-1364	204	9	n.	n.	PROPN
ijassa-1364	204	10	g.	g.	PROPN
ijassa-1364	204	11	(	(	PUNCT
ijassa-1364	204	12	2019	2019	NUM
ijassa-1364	204	13	)	)	PUNCT
ijassa-1364	204	14	.	.	PUNCT
ijassa-1364	205	1	study	study	NOUN
ijassa-1364	205	2	of	of	ADP
ijassa-1364	205	3	the	the	DET
ijassa-1364	205	4	continuous	continuous	ADJ
ijassa-1364	205	5	-	-	PUNCT
ijassa-1364	205	6	time	time	NOUN
ijassa-1364	205	7	open	open	ADJ
ijassa-1364	205	8	dynamic	dynamic	ADJ
ijassa-1364	205	9	leontief	leontief	ADJ
ijassa-1364	205	10	model	model	NOUN
ijassa-1364	205	11	as	as	ADP
ijassa-1364	205	12	a	a	DET
ijassa-1364	205	13	linear	linear	ADJ
ijassa-1364	205	14	dynamical	dynamical	ADJ
ijassa-1364	205	15	control	control	NOUN
ijassa-1364	205	16	system	system	NOUN
ijassa-1364	205	17	,	,	PUNCT
ijassa-1364	205	18	differ	differ	VERB
ijassa-1364	205	19	.	.	PUNCT
ijassa-1364	206	1	equ	equ	PROPN
ijassa-1364	206	2	.	.	PROPN
ijassa-1364	206	3	,	,	PUNCT
ijassa-1364	206	4	55(1	55(1	NOUN
ijassa-1364	206	5	)	)	PUNCT
ijassa-1364	206	6	,	,	PUNCT
ijassa-1364	206	7	113–119	113–119	NUM
ijassa-1364	206	8	.	.	PUNCT
ijassa-1364	206	9	14	14	NUM
ijassa-1364	206	10	.	.	PUNCT
ijassa-1364	207	1	rozova	rozova	PROPN
ijassa-1364	207	2	,	,	PUNCT
ijassa-1364	207	3	v.	v.	ADP
ijassa-1364	207	4	n.	n.	PROPN
ijassa-1364	207	5	(	(	PUNCT
ijassa-1364	207	6	2006	2006	NUM
ijassa-1364	207	7	)	)	PUNCT
ijassa-1364	207	8	.	.	PUNCT
ijassa-1364	208	1	optimal	optimal	ADJ
ijassa-1364	208	2	control	control	NOUN
ijassa-1364	208	3	of	of	ADP
ijassa-1364	208	4	step	step	NOUN
ijassa-1364	208	5	systems	system	NOUN
ijassa-1364	208	6	,	,	PUNCT
ijassa-1364	208	7	rudn	rudn	ADJ
ijassa-1364	208	8	reports	report	NOUN
ijassa-1364	208	9	.	.	PUNCT
ijassa-1364	209	1	series	series	NOUN
ijassa-1364	209	2	:	:	PUNCT
ijassa-1364	209	3	natural	natural	ADJ
ijassa-1364	209	4	and	and	CCONJ
ijassa-1364	209	5	technical	technical	ADJ
ijassa-1364	209	6	sciences	science	NOUN
ijassa-1364	209	7	,	,	PUNCT
ijassa-1364	209	8	3	3	NUM
ijassa-1364	209	9	,	,	PUNCT
ijassa-1364	209	10	15–23	15–23	NUM
ijassa-1364	209	11	.	.	PUNCT
ijassa-1364	210	1	[	[	X
ijassa-1364	210	2	in	in	ADP
ijassa-1364	210	3	russian	russian	NOUN
ijassa-1364	210	4	]	]	X
ijassa-1364	210	5	15	15	X
ijassa-1364	210	6	.	.	PUNCT
ijassa-1364	210	7	svirezhev	svirezhev	PROPN
ijassa-1364	210	8	,	,	PUNCT
ijassa-1364	210	9	yu	yu	PROPN
ijassa-1364	210	10	.	.	PROPN
ijassa-1364	210	11	m.	m.	NOUN
ijassa-1364	210	12	(	(	PUNCT
ijassa-1364	210	13	1987	1987	NUM
ijassa-1364	210	14	)	)	PUNCT
ijassa-1364	210	15	.	.	PUNCT
ijassa-1364	211	1	nonlinear	nonlinear	ADJ
ijassa-1364	211	2	waves	wave	NOUN
ijassa-1364	211	3	,	,	PUNCT
ijassa-1364	211	4	dissipative	dissipative	ADJ
ijassa-1364	211	5	structures	structure	NOUN
ijassa-1364	211	6	,	,	PUNCT
ijassa-1364	211	7	and	and	CCONJ
ijassa-1364	211	8	catastrophes	catastrophe	NOUN
ijassa-1364	211	9	in	in	ADP
ijassa-1364	211	10	ecology	ecology	NOUN
ijassa-1364	211	11	,	,	PUNCT
ijassa-1364	211	12	moscow	moscow	PROPN
ijassa-1364	211	13	,	,	PUNCT
ijassa-1364	211	14	russia	russia	PROPN
ijassa-1364	211	15	:	:	PUNCT
ijassa-1364	211	16	nauka	nauka	PROPN
ijassa-1364	211	17	.	.	PUNCT
ijassa-1364	212	1	[	[	X
ijassa-1364	212	2	in	in	ADP
ijassa-1364	212	3	russian	russian	NOUN
ijassa-1364	212	4	]	]	X
ijassa-1364	212	5	16	16	NUM
ijassa-1364	212	6	.	.	PUNCT
ijassa-1364	212	7	velichenko	velichenko	PROPN
ijassa-1364	212	8	,	,	PUNCT
ijassa-1364	212	9	v.	v.	PROPN
ijassa-1364	212	10	v.	v.	PROPN
ijassa-1364	212	11	(	(	PUNCT
ijassa-1364	212	12	1966	1966	NUM
ijassa-1364	212	13	)	)	PUNCT
ijassa-1364	212	14	.	.	PUNCT
ijassa-1364	213	1	on	on	ADP
ijassa-1364	213	2	optimal	optimal	ADJ
ijassa-1364	213	3	control	control	NOUN
ijassa-1364	213	4	problems	problem	NOUN
ijassa-1364	213	5	for	for	ADP
ijassa-1364	213	6	equations	equation	NOUN
ijassa-1364	213	7	with	with	ADP
ijassa-1364	213	8	discontinuous	discontinuous	ADJ
ijassa-1364	213	9	right	right	ADJ
ijassa-1364	213	10	sides	side	NOUN
ijassa-1364	213	11	,	,	PUNCT
ijassa-1364	213	12	automation	automation	NOUN
ijassa-1364	213	13	and	and	CCONJ
ijassa-1364	213	14	telemechanics	telemechanic	NOUN
ijassa-1364	213	15	,	,	PUNCT
ijassa-1364	213	16	7	7	NUM
ijassa-1364	213	17	,	,	PUNCT
ijassa-1364	213	18	20–30	20–30	NUM
ijassa-1364	213	19	.	.	PUNCT
ijassa-1364	214	1	[	[	X
ijassa-1364	214	2	in	in	ADP
ijassa-1364	214	3	russian	russian	PROPN
ijassa-1364	214	4	]	]	PUNCT
ijassa-1364	214	5	copyright	copyright	NOUN
ijassa-1364	214	6	©	©	PROPN
ijassa-1364	214	7	2023	2023	NUM
ijassa-1364	214	8	assa	assa	NOUN
ijassa-1364	214	9	.	.	PUNCT
ijassa-1364	215	1	adv	adv	PROPN
ijassa-1364	215	2	syst	syst	PROPN
ijassa-1364	215	3	sci	sci	PROPN
ijassa-1364	215	4	appl	appl	PROPN
ijassa-1364	215	5	(	(	PUNCT
ijassa-1364	215	6	2023	2023	NUM
ijassa-1364	215	7	)	)	PUNCT
ijassa-1364	215	8	introduction	introduction	NOUN
ijassa-1364	215	9	nonlinear	nonlinear	PROPN
ijassa-1364	215	10	systems	systems	PROPN
ijassa-1364	215	11	linear	linear	PROPN
ijassa-1364	215	12	systems	system	NOUN
ijassa-1364	215	13	problem	problem	NOUN
ijassa-1364	215	14	statement	statement	NOUN
ijassa-1364	215	15	main	main	ADJ
ijassa-1364	215	16	result	result	NOUN
ijassa-1364	215	17	example	example	NOUN
ijassa-1364	215	18	conclusion	conclusion	NOUN