id	sid	tid	token	lemma	pos
cana-259	1	1	communications	communication	NOUN
cana-259	1	2	on	on	ADP
cana-259	1	3	applied	apply	VERB
cana-259	1	4	nonlinear	nonlinear	ADJ
cana-259	1	5	analysis	analysis	NOUN
cana-259	1	6	issn	issn	NOUN
cana-259	1	7	:	:	PUNCT
cana-259	1	8	1074	1074	NUM
cana-259	1	9	-	-	PUNCT
cana-259	1	10	133x	133x	NUM
cana-259	1	11	vol	vol	NOUN
cana-259	1	12	30	30	NUM
cana-259	1	13	no	no	NOUN
cana-259	1	14	.	.	NOUN
cana-259	1	15	2	2	NUM
cana-259	1	16	(	(	PUNCT
cana-259	1	17	2023	2023	NUM
cana-259	1	18	)	)	PUNCT
cana-259	1	19	1	1	NUM
cana-259	1	20	https://internationalpubls.com	https://internationalpubls.com	X
cana-259	1	21	constructing	construct	VERB
cana-259	1	22	a	a	DET
cana-259	1	23	precise	precise	ADJ
cana-259	1	24	method	method	NOUN
cana-259	1	25	to	to	PART
cana-259	1	26	control	control	VERB
cana-259	1	27	non	non	ADJ
cana-259	1	28	-	-	ADJ
cana-259	1	29	linear	linear	ADJ
cana-259	1	30	systems	system	NOUN
cana-259	1	31	employing	employ	VERB
cana-259	1	32	special	special	ADJ
cana-259	1	33	functions	function	NOUN
cana-259	1	34	and	and	CCONJ
cana-259	1	35	machine	machine	NOUN
cana-259	1	36	learning	learn	VERB
cana-259	1	37	s.k	s.k	PROPN
cana-259	1	38	.	.	PUNCT
cana-259	2	1	sahani1	sahani1	PROPN
cana-259	2	2	*	*	PROPN
cana-259	2	3	,	,	PUNCT
cana-259	2	4	c.	c.	PROPN
cana-259	2	5	yadav2	yadav2	PROPN
cana-259	2	6	,	,	PUNCT
cana-259	2	7	k.	k.	PROPN
cana-259	2	8	sahani3	sahani3	PROPN
cana-259	2	9	*	*	PUNCT
cana-259	2	10	,	,	PUNCT
cana-259	2	11	and	and	CCONJ
cana-259	2	12	v.v	v.v	PROPN
cana-259	2	13	.	.	PROPN
cana-259	2	14	singh4	singh4	PROPN
cana-259	3	1	1department	1department	NUM
cana-259	3	2	of	of	ADP
cana-259	3	3	mathematics	mathematic	NOUN
cana-259	3	4	,	,	PUNCT
cana-259	3	5	janakpur	janakpur	PROPN
cana-259	3	6	campus	campus	PROPN
cana-259	3	7	,	,	PUNCT
cana-259	3	8	t.u	t.u	PROPN
cana-259	3	9	.	.	PROPN
cana-259	3	10	,	,	PUNCT
cana-259	3	11	janakpurdham	janakpurdham	PROPN
cana-259	3	12	,	,	PUNCT
cana-259	3	13	nepal	nepal	NOUN
cana-259	3	14	*	*	PUNCT
cana-259	3	15	2institute	2institute	NUM
cana-259	3	16	of	of	ADP
cana-259	3	17	science	science	NOUN
cana-259	3	18	and	and	CCONJ
cana-259	3	19	technology	technology	NOUN
cana-259	3	20	,	,	PUNCT
cana-259	3	21	patan	patan	ADJ
cana-259	3	22	multiple	multiple	ADJ
cana-259	3	23	campus	campus	NOUN
cana-259	3	24	,	,	PUNCT
cana-259	3	25	t.u	t.u	PROPN
cana-259	3	26	.	.	PROPN
cana-259	3	27	,	,	PUNCT
cana-259	3	28	nepal	nepal	PROPN
cana-259	3	29	3department	3department	NUM
cana-259	3	30	of	of	ADP
cana-259	3	31	civil	civil	ADJ
cana-259	3	32	engineering	engineering	NOUN
cana-259	3	33	,	,	PUNCT
cana-259	3	34	kathmandu	kathmandu	PROPN
cana-259	3	35	university	university	PROPN
cana-259	3	36	,	,	PUNCT
cana-259	3	37	dhulikhel	dhulikhel	PROPN
cana-259	3	38	,	,	PUNCT
cana-259	3	39	nepal	nepal	NOUN
cana-259	3	40	4professor	4professor	NUM
cana-259	3	41	mathematics	mathematic	NOUN
cana-259	3	42	,	,	PUNCT
cana-259	3	43	department	department	PROPN
cana-259	3	44	lingaya	lingaya	PROPN
cana-259	3	45	’s	’s	PART
cana-259	3	46	vidhyapeeth	vidhyapeeth	NOUN
cana-259	3	47	,	,	PUNCT
cana-259	3	48	faridabad	faridabad	PROPN
cana-259	3	49	,	,	PUNCT
cana-259	3	50	india	india	PROPN
cana-259	3	51	email	email	NOUN
cana-259	3	52	:	:	PUNCT
cana-259	3	53	drsks53086@gmail.com1*,chandrakantyadava@gmail.com2,kameshwar.sahani@ku.edu.np3*,singh_vijayvir@yahoo.com4	drsks53086@gmail.com1*,chandrakantyadava@gmail.com2,kameshwar.sahani@ku.edu.np3*,singh_vijayvir@yahoo.com4	PROPN
cana-259	3	54	article	article	NOUN
cana-259	3	55	history	history	NOUN
cana-259	3	56	:	:	PUNCT
cana-259	3	57	received	receive	VERB
cana-259	3	58	:	:	PUNCT
cana-259	3	59	08	08	NUM
cana-259	3	60	-	-	SYM
cana-259	3	61	05	05	NUM
cana-259	3	62	-	-	PUNCT
cana-259	3	63	2023	2023	NUM
cana-259	3	64	revised	revise	VERB
cana-259	3	65	:	:	PUNCT
cana-259	3	66	02	02	NUM
cana-259	3	67	-	-	PUNCT
cana-259	3	68	06	06	NUM
cana-259	3	69	-	-	PUNCT
cana-259	3	70	2023	2023	NUM
cana-259	3	71	accepted	accept	VERB
cana-259	3	72	:	:	PUNCT
cana-259	3	73	15	15	NUM
cana-259	3	74	-	-	SYM
cana-259	3	75	07	07	NUM
cana-259	3	76	-	-	PUNCT
cana-259	3	77	2023	2023	NUM
cana-259	3	78	abstract	abstract	NOUN
cana-259	3	79	:	:	PUNCT
cana-259	3	80	this	this	DET
cana-259	3	81	paper	paper	NOUN
cana-259	3	82	is	be	AUX
cana-259	3	83	about	about	ADP
cana-259	3	84	finding	find	VERB
cana-259	3	85	the	the	DET
cana-259	3	86	best	good	ADJ
cana-259	3	87	way	way	NOUN
cana-259	3	88	to	to	PART
cana-259	3	89	control	control	VERB
cana-259	3	90	certain	certain	ADJ
cana-259	3	91	types	type	NOUN
cana-259	3	92	of	of	ADP
cana-259	3	93	equations	equation	NOUN
cana-259	3	94	that	that	PRON
cana-259	3	95	describe	describe	VERB
cana-259	3	96	heat	heat	NOUN
cana-259	3	97	and	and	CCONJ
cana-259	3	98	diffusion	diffusion	NOUN
cana-259	3	99	using	use	VERB
cana-259	3	100	methods	method	NOUN
cana-259	3	101	that	that	PRON
cana-259	3	102	are	be	AUX
cana-259	3	103	not	not	PART
cana-259	3	104	exact	exact	ADJ
cana-259	3	105	but	but	CCONJ
cana-259	3	106	close	close	ADJ
cana-259	3	107	to	to	ADP
cana-259	3	108	the	the	DET
cana-259	3	109	best	good	ADJ
cana-259	3	110	solution	solution	NOUN
cana-259	3	111	.	.	PUNCT
cana-259	4	1	a	a	DET
cana-259	4	2	new	new	ADJ
cana-259	4	3	way	way	NOUN
cana-259	4	4	to	to	PART
cana-259	4	5	control	control	VERB
cana-259	4	6	things	thing	NOUN
cana-259	4	7	better	well	ADV
cana-259	4	8	is	be	AUX
cana-259	4	9	suggested	suggest	VERB
cana-259	4	10	using	use	VERB
cana-259	4	11	patterns	pattern	NOUN
cana-259	4	12	we	we	PRON
cana-259	4	13	've	have	AUX
cana-259	4	14	seen	see	VERB
cana-259	4	15	before	before	ADV
cana-259	4	16	and	and	CCONJ
cana-259	4	17	computer	computer	NOUN
cana-259	4	18	learning	learning	NOUN
cana-259	4	19	.	.	PUNCT
cana-259	5	1	by	by	ADP
cana-259	5	2	employing	employ	VERB
cana-259	5	3	the	the	DET
cana-259	5	4	data	datum	NOUN
cana-259	5	5	gathered	gather	VERB
cana-259	5	6	from	from	ADP
cana-259	5	7	the	the	DET
cana-259	5	8	eefs	eef	NOUN
cana-259	5	9	are	be	AUX
cana-259	5	10	computed	compute	VERB
cana-259	5	11	using	use	VERB
cana-259	5	12	the	the	DET
cana-259	5	13	karhunen	karhunen	NOUN
cana-259	5	14	-	-	PUNCT
cana-259	5	15	loève	loève	NOUN
cana-259	5	16	decompose	decompose	NOUN
cana-259	5	17	in	in	ADP
cana-259	5	18	the	the	DET
cana-259	5	19	pde	pde	NOUN
cana-259	5	20	computer	computer	NOUN
cana-259	5	21	.	.	PUNCT
cana-259	6	1	the	the	DET
cana-259	6	2	eefs	eef	NOUN
cana-259	6	3	are	be	AUX
cana-259	6	4	used	use	VERB
cana-259	6	5	to	to	PART
cana-259	6	6	convert	convert	VERB
cana-259	6	7	the	the	DET
cana-259	6	8	pde	pde	NOUN
cana-259	6	9	system	system	NOUN
cana-259	6	10	into	into	ADP
cana-259	6	11	a	a	DET
cana-259	6	12	high	high	ADJ
cana-259	6	13	-	-	PUNCT
cana-259	6	14	order	order	NOUN
cana-259	6	15	ode	ode	ADJ
cana-259	6	16	system	system	NOUN
cana-259	6	17	.	.	PUNCT
cana-259	7	1	a	a	PRON
cana-259	7	2	smaller	small	ADJ
cana-259	7	3	model	model	NOUN
cana-259	7	4	(	(	PUNCT
cana-259	7	5	rom	rom	NOUN
cana-259	7	6	)	)	PUNCT
cana-259	7	7	that	that	PRON
cana-259	7	8	may	may	AUX
cana-259	7	9	depict	depict	VERB
cana-259	7	10	the	the	DET
cana-259	7	11	primary	primary	ADJ
cana-259	7	12	behavior	behavior	NOUN
cana-259	7	13	of	of	ADP
cana-259	7	14	the	the	DET
cana-259	7	15	pde	pde	NOUN
cana-259	7	16	subsystem	subsystem	NOUN
cana-259	7	17	is	be	AUX
cana-259	7	18	created	create	VERB
cana-259	7	19	using	use	VERB
cana-259	7	20	the	the	DET
cana-259	7	21	sp	sp	NOUN
cana-259	7	22	approach	approach	NOUN
cana-259	7	23	.	.	PUNCT
cana-259	8	1	this	this	PRON
cana-259	8	2	facilitates	facilitate	VERB
cana-259	8	3	understanding	understanding	NOUN
cana-259	8	4	of	of	ADP
cana-259	8	5	the	the	DET
cana-259	8	6	system	system	NOUN
cana-259	8	7	.	.	PUNCT
cana-259	9	1	in	in	ADP
cana-259	9	2	order	order	NOUN
cana-259	9	3	to	to	PART
cana-259	9	4	reduce	reduce	VERB
cana-259	9	5	its	its	PRON
cana-259	9	6	size	size	NOUN
cana-259	9	7	,	,	PUNCT
cana-259	9	8	a	a	DET
cana-259	9	9	more	more	ADV
cana-259	9	10	basic	basic	ADJ
cana-259	9	11	model	model	NOUN
cana-259	9	12	(	(	PUNCT
cana-259	9	13	rom	rom	NOUN
cana-259	9	14	)	)	PUNCT
cana-259	9	15	that	that	PRON
cana-259	9	16	demonstrates	demonstrate	VERB
cana-259	9	17	the	the	DET
cana-259	9	18	primary	primary	ADJ
cana-259	9	19	motions	motion	NOUN
cana-259	9	20	of	of	ADP
cana-259	9	21	the	the	DET
cana-259	9	22	pde	pde	NOUN
cana-259	9	23	system	system	NOUN
cana-259	9	24	is	be	AUX
cana-259	9	25	created	create	VERB
cana-259	9	26	using	use	VERB
cana-259	9	27	the	the	DET
cana-259	9	28	sp	sp	NOUN
cana-259	9	29	approach	approach	NOUN
cana-259	9	30	.	.	PUNCT
cana-259	10	1	next	next	ADV
cana-259	10	2	,	,	PUNCT
cana-259	10	3	the	the	DET
cana-259	10	4	optimal	optimal	ADJ
cana-259	10	5	controller	controller	NOUN
cana-259	10	6	for	for	ADP
cana-259	10	7	the	the	DET
cana-259	10	8	rom	rom	NOUN
cana-259	10	9	is	be	AUX
cana-259	10	10	designed	design	VERB
cana-259	10	11	using	use	VERB
cana-259	10	12	the	the	DET
cana-259	10	13	hjb	hjb	NOUN
cana-259	10	14	technique	technique	NOUN
cana-259	10	15	.	.	PUNCT
cana-259	11	1	this	this	PRON
cana-259	11	2	ensures	ensure	VERB
cana-259	11	3	that	that	SCONJ
cana-259	11	4	the	the	DET
cana-259	11	5	high	high	ADJ
cana-259	11	6	-	-	PUNCT
cana-259	11	7	order	order	NOUN
cana-259	11	8	ode	ode	NOUN
cana-259	11	9	system	system	NOUN
cana-259	11	10	is	be	AUX
cana-259	11	11	stable	stable	ADJ
cana-259	11	12	using	use	VERB
cana-259	11	13	the	the	DET
cana-259	11	14	sp	sp	NOUN
cana-259	11	15	theory	theory	NOUN
cana-259	11	16	.	.	PUNCT
cana-259	12	1	by	by	ADP
cana-259	12	2	splitting	split	VERB
cana-259	12	3	the	the	DET
cana-259	12	4	best	good	ADJ
cana-259	12	5	way	way	NOUN
cana-259	12	6	to	to	PART
cana-259	12	7	control	control	VERB
cana-259	12	8	something	something	PRON
cana-259	12	9	into	into	ADP
cana-259	12	10	two	two	NUM
cana-259	12	11	sections	section	NOUN
cana-259	12	12	,	,	PUNCT
cana-259	12	13	we	we	PRON
cana-259	12	14	can	can	AUX
cana-259	12	15	solve	solve	VERB
cana-259	12	16	a	a	DET
cana-259	12	17	math	math	NOUN
cana-259	12	18	problem	problem	NOUN
cana-259	12	19	to	to	PART
cana-259	12	20	figure	figure	VERB
cana-259	12	21	out	out	ADP
cana-259	12	22	the	the	DET
cana-259	12	23	first	first	ADJ
cana-259	12	24	part	part	NOUN
cana-259	12	25	and	and	CCONJ
cana-259	12	26	come	come	VERB
cana-259	12	27	up	up	ADP
cana-259	12	28	with	with	ADP
cana-259	12	29	a	a	DET
cana-259	12	30	new	new	ADJ
cana-259	12	31	equation	equation	NOUN
cana-259	12	32	for	for	ADP
cana-259	12	33	the	the	DET
cana-259	12	34	second	second	ADJ
cana-259	12	35	part	part	NOUN
cana-259	12	36	.	.	PUNCT
cana-259	13	1	third	third	ADJ
cana-259	13	2	,	,	PUNCT
cana-259	13	3	a	a	DET
cana-259	13	4	method	method	NOUN
cana-259	13	5	is	be	AUX
cana-259	13	6	suggested	suggest	VERB
cana-259	13	7	for	for	ADP
cana-259	13	8	updating	update	VERB
cana-259	13	9	and	and	CCONJ
cana-259	13	10	controlling	control	VERB
cana-259	13	11	based	base	VERB
cana-259	13	12	on	on	ADP
cana-259	13	13	small	small	ADJ
cana-259	13	14	improvements	improvement	NOUN
cana-259	13	15	to	to	PART
cana-259	13	16	solve	solve	VERB
cana-259	13	17	a	a	DET
cana-259	13	18	specific	specific	ADJ
cana-259	13	19	equation	equation	NOUN
cana-259	13	20	,	,	PUNCT
cana-259	13	21	and	and	CCONJ
cana-259	13	22	it	it	PRON
cana-259	13	23	has	have	AUX
cana-259	13	24	been	be	AUX
cana-259	13	25	proven	prove	VERB
cana-259	13	26	to	to	PART
cana-259	13	27	work	work	VERB
cana-259	13	28	effectively	effectively	ADV
cana-259	13	29	.	.	PUNCT
cana-259	14	1	moreover	moreover	ADV
cana-259	14	2	,	,	PUNCT
cana-259	14	3	we	we	PRON
cana-259	14	4	use	use	VERB
cana-259	14	5	a	a	DET
cana-259	14	6	technique	technique	NOUN
cana-259	14	7	called	call	VERB
cana-259	14	8	the	the	DET
cana-259	14	9	nn	nn	PROPN
cana-259	14	10	approach	approach	NOUN
cana-259	14	11	to	to	PART
cana-259	14	12	estimate	estimate	VERB
cana-259	14	13	the	the	DET
cana-259	14	14	cost	cost	NOUN
cana-259	14	15	function	function	NOUN
cana-259	14	16	.	.	PUNCT
cana-259	15	1	finally	finally	ADV
cana-259	15	2	,	,	PUNCT
cana-259	15	3	the	the	DET
cana-259	15	4	simulation	simulation	NOUN
cana-259	15	5	results	result	NOUN
cana-259	15	6	demonstrate	demonstrate	VERB
cana-259	15	7	the	the	DET
cana-259	15	8	effectiveness	effectiveness	NOUN
cana-259	15	9	of	of	ADP
cana-259	15	10	the	the	DET
cana-259	15	11	proposed	propose	VERB
cana-259	15	12	optimum	optimum	ADJ
cana-259	15	13	control	control	NOUN
cana-259	15	14	approach	approach	NOUN
cana-259	15	15	when	when	SCONJ
cana-259	15	16	applied	apply	VERB
cana-259	15	17	to	to	ADP
cana-259	15	18	a	a	DET
cana-259	15	19	diffusion	diffusion	NOUN
cana-259	15	20	-	-	PUNCT
cana-259	15	21	reaction	reaction	NOUN
cana-259	15	22	process	process	NOUN
cana-259	15	23	using	use	VERB
cana-259	15	24	a	a	DET
cana-259	15	25	unique	unique	ADJ
cana-259	15	26	spatially	spatially	ADJ
cana-259	15	27	component	component	NOUN
cana-259	15	28	.	.	PUNCT
cana-259	16	1	keywords	keyword	NOUN
cana-259	16	2	:	:	PUNCT
cana-259	16	3	the	the	DET
cana-259	16	4	hjb	hjb	NOUN
cana-259	16	5	equation	equation	NOUN
cana-259	16	6	,	,	PUNCT
cana-259	16	7	kld	kld	PROPN
cana-259	16	8	,	,	PUNCT
cana-259	16	9	nn	nn	PROPN
cana-259	16	10	,	,	PUNCT
cana-259	16	11	pde	pde	NOUN
cana-259	16	12	systems	system	NOUN
cana-259	16	13	,	,	PUNCT
cana-259	16	14	optimal	optimal	ADJ
cana-259	16	15	control	control	NOUN
cana-259	16	16	,	,	PUNCT
cana-259	16	17	and	and	CCONJ
cana-259	16	18	sp	sp	NOUN
cana-259	16	19	are	be	AUX
cana-259	16	20	all	all	PRON
cana-259	16	21	complicated	complicated	ADJ
cana-259	16	22	mathematical	mathematical	ADJ
cana-259	16	23	concepts	concept	NOUN
cana-259	16	24	.	.	PUNCT
cana-259	17	1	1	1	X
cana-259	17	2	.	.	X
cana-259	17	3	introduction	introduction	NOUN
cana-259	17	4	optimal	optimal	ADJ
cana-259	17	5	control	control	NOUN
cana-259	17	6	theory	theory	NOUN
cana-259	17	7	is	be	AUX
cana-259	17	8	a	a	DET
cana-259	17	9	useful	useful	ADJ
cana-259	17	10	method	method	NOUN
cana-259	17	11	for	for	ADP
cana-259	17	12	making	make	VERB
cana-259	17	13	controllers	controller	NOUN
cana-259	17	14	.	.	PUNCT
cana-259	18	1	there	there	PRON
cana-259	18	2	have	have	AUX
cana-259	18	3	been	be	AUX
cana-259	18	4	numerous	numerous	ADJ
cana-259	18	5	significant	significant	ADJ
cana-259	18	6	discoveries	discovery	NOUN
cana-259	18	7	regarding	regard	VERB
cana-259	18	8	the	the	DET
cana-259	18	9	optimal	optimal	ADJ
cana-259	18	10	methods	method	NOUN
cana-259	18	11	for	for	ADP
cana-259	18	12	regulating	regulate	VERB
cana-259	18	13	linear	linear	ADJ
cana-259	18	14	or	or	CCONJ
cana-259	18	15	nonlinear	nonlinear	ADJ
cana-259	18	16	systems	system	NOUN
cana-259	18	17	characterized	characterize	VERB
cana-259	18	18	by	by	ADP
cana-259	18	19	ordinary	ordinary	ADJ
cana-259	18	20	differential	differential	ADJ
cana-259	18	21	equations	equation	NOUN
cana-259	18	22	.	.	PUNCT
cana-259	19	1	these	these	DET
cana-259	19	2	elements	element	NOUN
cana-259	19	3	include	include	VERB
cana-259	19	4	the	the	DET
cana-259	19	5	linear	linear	ADJ
cana-259	19	6	parabolic	parabolic	ADJ
cana-259	19	7	controller	controller	NOUN
cana-259	19	8	hypothesis	hypothesis	NOUN
cana-259	19	9	,	,	PUNCT
cana-259	19	10	bellman	bellman	NOUN
cana-259	19	11	dynamic	dynamic	ADJ
cana-259	19	12	programming	programming	NOUN
cana-259	19	13	,	,	PUNCT
cana-259	19	14	and	and	CCONJ
cana-259	19	15	the	the	DET
cana-259	19	16	application	application	NOUN
cana-259	19	17	of	of	ADP
cana-259	19	18	the	the	DET
cana-259	19	19	greatest	great	ADJ
cana-259	19	20	assumption	assumption	NOUN
cana-259	19	21	.	.	PUNCT
cana-259	20	1	[	[	X
cana-259	20	2	1	1	NUM
cana-259	20	3	]	]	PUNCT
cana-259	20	4	,	,	PUNCT
cana-259	20	5	[	[	X
cana-259	20	6	2	2	NUM
cana-259	20	7	]	]	PUNCT
cana-259	20	8	.	.	PUNCT
cana-259	21	1	in	in	ADP
cana-259	21	2	real	real	ADJ
cana-259	21	3	life	life	NOUN
cana-259	21	4	,	,	PUNCT
cana-259	21	5	many	many	ADJ
cana-259	21	6	industrial	industrial	ADJ
cana-259	21	7	processes	process	NOUN
cana-259	21	8	are	be	AUX
cana-259	21	9	spread	spread	VERB
cana-259	21	10	out	out	ADP
cana-259	21	11	in	in	ADP
cana-259	21	12	different	different	ADJ
cana-259	21	13	places	place	NOUN
cana-259	21	14	,	,	PUNCT
cana-259	21	15	so	so	SCONJ
cana-259	21	16	how	how	SCONJ
cana-259	21	17	they	they	PRON
cana-259	21	18	work	work	VERB
cana-259	21	19	depends	depend	VERB
cana-259	21	20	on	on	ADP
cana-259	21	21	where	where	SCONJ
cana-259	21	22	they	they	PRON
cana-259	21	23	are	be	AUX
cana-259	21	24	as	as	ADV
cana-259	21	25	well	well	ADV
cana-259	21	26	as	as	ADP
cana-259	21	27	when	when	SCONJ
cana-259	21	28	they	they	PRON
cana-259	21	29	are	be	AUX
cana-259	21	30	.	.	PUNCT
cana-259	22	1	these	these	DET
cana-259	22	2	systems	system	NOUN
cana-259	22	3	are	be	AUX
cana-259	22	4	often	often	ADV
cana-259	22	5	explained	explain	VERB
cana-259	22	6	using	use	VERB
cana-259	22	7	a	a	DET
cana-259	22	8	group	group	NOUN
cana-259	22	9	of	of	ADP
cana-259	22	10	complex	complex	ADJ
cana-259	22	11	math	math	NOUN
cana-259	22	12	equations	equation	NOUN
cana-259	22	13	with	with	ADP
cana-259	22	14	specific	specific	ADJ
cana-259	22	15	boundary	boundary	ADJ
cana-259	22	16	rules	rule	NOUN
cana-259	22	17	.	.	PUNCT
cana-259	23	1	optimal	optimal	ADJ
cana-259	23	2	control	control	NOUN
cana-259	23	3	methods	method	NOUN
cana-259	23	4	are	be	AUX
cana-259	23	5	difficult	difficult	ADJ
cana-259	23	6	to	to	PART
cana-259	23	7	use	use	VERB
cana-259	23	8	for	for	ADP
cana-259	23	9	designing	design	VERB
cana-259	23	10	a	a	DET
cana-259	23	11	controller	controller	NOUN
cana-259	23	12	in	in	ADP
cana-259	23	13	real	real	ADJ
cana-259	23	14	-	-	PUNCT
cana-259	23	15	time	time	NOUN
cana-259	23	16	with	with	ADP
cana-259	23	17	a	a	DET
cana-259	23	18	regular	regular	ADJ
cana-259	23	19	computer	computer	NOUN
cana-259	23	20	due	due	ADP
cana-259	23	21	to	to	ADP
cana-259	23	22	the	the	DET
cana-259	23	23	complex	complex	ADJ
cana-259	23	24	dimensions	dimension	NOUN
cana-259	23	25	of	of	ADP
cana-259	23	26	pde	pde	NOUN
cana-259	23	27	systems	system	NOUN
cana-259	23	28	.	.	PUNCT
cana-259	24	1	in	in	ADP
cana-259	24	2	the	the	DET
cana-259	24	3	last	last	ADJ
cana-259	24	4	few	few	ADJ
cana-259	24	5	decades	decade	NOUN
cana-259	24	6	,	,	PUNCT
cana-259	24	7	rutkowski	rutkowski	PROPN
cana-259	24	8	[	[	X
cana-259	24	9	3	3	X
cana-259	24	10	]	]	PUNCT
cana-259	24	11	has	have	AUX
cana-259	24	12	done	do	VERB
cana-259	24	13	important	important	ADJ
cana-259	24	14	work	work	NOUN
cana-259	24	15	in	in	ADP
cana-259	24	16	developing	develop	VERB
cana-259	24	17	the	the	DET
cana-259	24	18	best	good	ADJ
cana-259	24	19	way	way	NOUN
cana-259	24	20	to	to	PART
cana-259	24	21	control	control	VERB
cana-259	24	22	pde	pde	NOUN
cana-259	24	23	systems	system	NOUN
cana-259	24	24	[	[	X
cana-259	24	25	3	3	NUM
cana-259	24	26	]	]	PUNCT
cana-259	24	27	,	,	PUNCT
cana-259	24	28	wang	wang	PROPN
cana-259	24	29	,	,	PUNCT
cana-259	24	30	tung	tung	PROPN
cana-259	24	31	,	,	PUNCT
cana-259	24	32	[	[	X
cana-259	24	33	4	4	NUM
cana-259	24	34	]	]	PUNCT
cana-259	24	35	,	,	PUNCT
cana-259	24	36	and	and	CCONJ
cana-259	24	37	lions	lion	NOUN
cana-259	24	38	[	[	X
cana-259	24	39	5	5	NUM
cana-259	24	40	]	]	PUNCT
cana-259	24	41	looked	look	VERB
cana-259	24	42	at	at	ADP
cana-259	24	43	math	math	NOUN
cana-259	24	44	stuff	stuff	NOUN
cana-259	24	45	,	,	PUNCT
cana-259	24	46	and	and	CCONJ
cana-259	24	47	you	you	PRON
cana-259	24	48	can	can	AUX
cana-259	24	49	find	find	VERB
cana-259	24	50	more	more	ADJ
cana-259	24	51	theoretical	theoretical	ADJ
cana-259	24	52	results	result	NOUN
cana-259	24	53	in	in	ADP
cana-259	24	54	other	other	ADJ
cana-259	24	55	places	place	NOUN
cana-259	24	56	too	too	ADV
cana-259	24	57	.	.	PUNCT
cana-259	25	1	meanwhile	meanwhile	ADV
cana-259	25	2	,	,	PUNCT
cana-259	25	3	communications	communication	NOUN
cana-259	25	4	on	on	ADP
cana-259	25	5	applied	apply	VERB
cana-259	25	6	nonlinear	nonlinear	ADJ
cana-259	25	7	analysis	analysis	NOUN
cana-259	25	8	issn	issn	NOUN
cana-259	25	9	:	:	PUNCT
cana-259	25	10	1074	1074	NUM
cana-259	25	11	-	-	PUNCT
cana-259	25	12	133x	133x	NUM
cana-259	25	13	vol	vol	NOUN
cana-259	25	14	30	30	NUM
cana-259	25	15	no	no	NOUN
cana-259	25	16	.	.	NOUN
cana-259	25	17	2	2	NUM
cana-259	25	18	(	(	PUNCT
cana-259	25	19	2023	2023	NUM
cana-259	25	20	)	)	PUNCT
cana-259	25	21	2	2	NUM
cana-259	26	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-259	26	2	people	people	NOUN
cana-259	26	3	have	have	AUX
cana-259	26	4	studied	study	VERB
cana-259	26	5	how	how	SCONJ
cana-259	26	6	to	to	PART
cana-259	26	7	control	control	VERB
cana-259	26	8	pde	pde	NOUN
cana-259	26	9	systems	system	NOUN
cana-259	26	10	effectively	effectively	ADV
cana-259	26	11	.	.	PUNCT
cana-259	27	1	engineers	engineer	NOUN
cana-259	27	2	have	have	AUX
cana-259	27	3	worked	work	VERB
cana-259	27	4	on	on	ADP
cana-259	27	5	ways	way	NOUN
cana-259	27	6	to	to	PART
cana-259	27	7	minimize	minimize	VERB
cana-259	27	8	performance	performance	NOUN
cana-259	27	9	measures	measure	NOUN
cana-259	27	10	using	use	VERB
cana-259	27	11	[	[	X
cana-259	27	12	6	6	NUM
cana-259	27	13	]	]	PUNCT
cana-259	27	14	lq	lq	NOUN
cana-259	27	15	methods	method	NOUN
cana-259	27	16	[	[	X
cana-259	27	17	7	7	NUM
cana-259	27	18	]	]	PUNCT
cana-259	27	19	.	.	PUNCT
cana-259	28	1	meanwhile	meanwhile	ADV
cana-259	28	2	,	,	PUNCT
cana-259	28	3	people	people	NOUN
cana-259	28	4	have	have	AUX
cana-259	28	5	studied	study	VERB
cana-259	28	6	how	how	SCONJ
cana-259	28	7	to	to	PART
cana-259	28	8	control	control	VERB
cana-259	28	9	pde	pde	NOUN
cana-259	28	10	systems	system	NOUN
cana-259	28	11	from	from	ADP
cana-259	28	12	an	an	DET
cana-259	28	13	engineering	engineering	NOUN
cana-259	28	14	perspective	perspective	NOUN
cana-259	28	15	.	.	PUNCT
cana-259	29	1	they	they	PRON
cana-259	29	2	have	have	AUX
cana-259	29	3	focused	focus	VERB
cana-259	29	4	on	on	ADP
cana-259	29	5	methods	method	NOUN
cana-259	29	6	that	that	PRON
cana-259	29	7	use	use	VERB
cana-259	29	8	lq	lq	NOUN
cana-259	29	9	performance	performance	NOUN
cana-259	29	10	indices	index	NOUN
cana-259	29	11	to	to	PART
cana-259	29	12	minimize	minimize	VERB
cana-259	29	13	and	and	CCONJ
cana-259	29	14	improve	improve	VERB
cana-259	29	15	control	control	NOUN
cana-259	29	16	.	.	PUNCT
cana-259	30	1	previous	previous	ADJ
cana-259	30	2	studies	study	NOUN
cana-259	30	3	on	on	ADP
cana-259	30	4	how	how	SCONJ
cana-259	30	5	to	to	PART
cana-259	30	6	make	make	VERB
cana-259	30	7	the	the	DET
cana-259	30	8	best	good	ADJ
cana-259	30	9	controller	controller	NOUN
cana-259	30	10	for	for	ADP
cana-259	30	11	pde	pde	NOUN
cana-259	30	12	systems	system	NOUN
cana-259	30	13	[	[	X
cana-259	30	14	8]–[10	8]–[10	X
cana-259	30	15	]	]	PUNCT
cana-259	30	16	,	,	PUNCT
cana-259	30	17	can	can	AUX
cana-259	30	18	be	be	AUX
cana-259	30	19	divided	divide	VERB
cana-259	30	20	into	into	ADP
cana-259	30	21	two	two	NUM
cana-259	30	22	types	type	NOUN
cana-259	30	23	:	:	PUNCT
cana-259	30	24	first	first	ADV
cana-259	30	25	designing	design	VERB
cana-259	30	26	and	and	CCONJ
cana-259	30	27	then	then	ADV
cana-259	30	28	simplifying	simplify	VERB
cana-259	30	29	,	,	PUNCT
cana-259	30	30	and	and	CCONJ
cana-259	30	31	first	first	ADV
cana-259	30	32	simplifying	simplify	VERB
cana-259	30	33	and	and	CCONJ
cana-259	30	34	then	then	ADV
cana-259	30	35	designing	design	VERB
cana-259	30	36	approaches	approach	NOUN
cana-259	30	37	.	.	PUNCT
cana-259	31	1	in	in	ADP
cana-259	31	2	the	the	DET
cana-259	31	3	first	first	ADJ
cana-259	31	4	,	,	PUNCT
cana-259	31	5	optimal	optimal	ADJ
cana-259	31	6	controller	controller	NOUN
cana-259	31	7	for	for	ADP
cana-259	31	8	pde	pde	NOUN
cana-259	31	9	networks	network	NOUN
cana-259	31	10	are	be	AUX
cana-259	31	11	designed	design	VERB
cana-259	31	12	using	use	VERB
cana-259	31	13	sophisticated	sophisticated	ADJ
cana-259	31	14	mathematics	mathematic	NOUN
cana-259	31	15	.	.	PUNCT
cana-259	32	1	[	[	X
cana-259	32	2	8	8	X
cana-259	32	3	]	]	PUNCT
cana-259	32	4	these	these	DET
cana-259	32	5	controllers	controller	NOUN
cana-259	32	6	are	be	AUX
cana-259	32	7	then	then	ADV
cana-259	32	8	simplified	simplify	VERB
cana-259	32	9	for	for	ADP
cana-259	32	10	use	use	NOUN
cana-259	32	11	.	.	PUNCT
cana-259	33	1	curtain	curtain	NOUN
cana-259	33	2	,	,	PUNCT
cana-259	33	3	zwart	zwart	PROPN
cana-259	33	4	,	,	PUNCT
cana-259	33	5	aksikas	aksika	NOUN
cana-259	33	6	and	and	CCONJ
cana-259	33	7	their	their	PRON
cana-259	33	8	colleagues	colleague	NOUN
cana-259	33	9	[	[	X
cana-259	33	10	9	9	NUM
cana-259	33	11	]	]	PUNCT
cana-259	33	12	using	use	VERB
cana-259	33	13	algebraic	algebraic	ADJ
cana-259	33	14	operator	operator	NOUN
cana-259	33	15	riccati	riccati	PROPN
cana-259	33	16	formulae	formulae	PROPN
cana-259	33	17	,	,	PUNCT
cana-259	33	18	i	i	PRON
cana-259	33	19	was	be	AUX
cana-259	33	20	able	able	ADJ
cana-259	33	21	to	to	PART
cana-259	33	22	solve	solve	VERB
cana-259	33	23	the	the	DET
cana-259	33	24	lq	lq	NOUN
cana-259	33	25	ideal	ideal	ADJ
cana-259	33	26	control	control	NOUN
cana-259	33	27	issue	issue	NOUN
cana-259	33	28	for	for	ADP
cana-259	33	29	devices	device	NOUN
cana-259	33	30	with	with	ADP
cana-259	33	31	a	a	DET
cana-259	33	32	lot	lot	NOUN
cana-259	33	33	of	of	ADP
cana-259	33	34	states	state	NOUN
cana-259	33	35	.	.	PUNCT
cana-259	34	1	aksikas	aksikas	PROPN
cana-259	34	2	together	together	ADV
cana-259	34	3	with	with	ADP
cana-259	34	4	others	other	NOUN
cana-259	34	5	.	.	PUNCT
cana-259	35	1	[	[	X
cana-259	35	2	10	10	NUM
cana-259	35	3	]	]	PUNCT
cana-259	35	4	i	i	PRON
cana-259	35	5	used	use	VERB
cana-259	35	6	a	a	DET
cana-259	35	7	method	method	NOUN
cana-259	35	8	called	call	VERB
cana-259	35	9	spectral	spectral	ADJ
cana-259	35	10	factorization	factorization	NOUN
cana-259	35	11	to	to	PART
cana-259	35	12	find	find	VERB
cana-259	35	13	the	the	DET
cana-259	35	14	feedback	feedback	NOUN
cana-259	35	15	operator	operator	NOUN
cana-259	35	16	by	by	ADP
cana-259	35	17	solving	solve	VERB
cana-259	35	18	a	a	DET
cana-259	35	19	special	special	ADJ
cana-259	35	20	type	type	NOUN
cana-259	35	21	of	of	ADP
cana-259	35	22	mathematical	mathematical	ADJ
cana-259	35	23	equation	equation	NOUN
cana-259	35	24	.	.	PUNCT
cana-259	36	1	a	a	DET
cana-259	36	2	novel	novel	ADJ
cana-259	36	3	approach	approach	NOUN
cana-259	36	4	to	to	ADP
cana-259	36	5	linear	linear	ADJ
cana-259	36	6	parabolic	parabolic	ADJ
cana-259	36	7	pde	pde	NOUN
cana-259	36	8	system	system	NOUN
cana-259	36	9	control	control	NOUN
cana-259	36	10	was	be	AUX
cana-259	36	11	developed	develop	VERB
cana-259	36	12	by	by	ADP
cana-259	36	13	ray	ray	NOUN
cana-259	36	14	at	at	ADP
cana-259	36	15	the	the	DET
cana-259	36	16	age	age	NOUN
cana-259	36	17	of	of	ADP
cana-259	36	18	[	[	X
cana-259	36	19	11	11	NUM
cana-259	36	20	]	]	PUNCT
cana-259	36	21	.	.	PUNCT
cana-259	37	1	he	he	PRON
cana-259	37	2	used	use	VERB
cana-259	37	3	the	the	DET
cana-259	37	4	original	original	ADJ
cana-259	37	5	pde	pde	NOUN
cana-259	37	6	model	model	NOUN
cana-259	37	7	and	and	CCONJ
cana-259	37	8	found	find	VERB
cana-259	37	9	a	a	DET
cana-259	37	10	way	way	NOUN
cana-259	37	11	to	to	PART
cana-259	37	12	control	control	VERB
cana-259	37	13	the	the	DET
cana-259	37	14	system	system	NOUN
cana-259	37	15	by	by	ADP
cana-259	37	16	figuring	figure	VERB
cana-259	37	17	out	out	ADP
cana-259	37	18	a	a	DET
cana-259	37	19	unique	unique	ADJ
cana-259	37	20	equation	equation	NOUN
cana-259	37	21	.	.	PUNCT
cana-259	38	1	conversely	conversely	ADV
cana-259	38	2	,	,	PUNCT
cana-259	38	3	nevertheless	nevertheless	ADV
cana-259	38	4	,	,	PUNCT
cana-259	38	5	the	the	DET
cana-259	38	6	reduce	reduce	VERB
cana-259	38	7	-	-	PUNCT
cana-259	38	8	then	then	ADV
cana-259	38	9	-	-	PUNCT
cana-259	38	10	design	design	NOUN
cana-259	38	11	methods	method	NOUN
cana-259	38	12	first	first	ADV
cana-259	38	13	turn	turn	VERB
cana-259	38	14	the	the	DET
cana-259	38	15	pde	pde	NOUN
cana-259	38	16	system	system	NOUN
cana-259	38	17	into	into	ADP
cana-259	38	18	a	a	DET
cana-259	38	19	simpler	simple	ADJ
cana-259	38	20	ode	ode	NOUN
cana-259	38	21	model	model	NOUN
cana-259	38	22	and	and	CCONJ
cana-259	38	23	then	then	ADV
cana-259	38	24	use	use	VERB
cana-259	38	25	it	it	PRON
cana-259	38	26	for	for	ADP
cana-259	38	27	control	control	NOUN
cana-259	38	28	design	design	NOUN
cana-259	38	29	[	[	X
cana-259	38	30	12]–[19	12]–[19	NUM
cana-259	38	31	]	]	X
cana-259	38	32	.	.	PUNCT
cana-259	39	1	a	a	DET
cana-259	39	2	way	way	NOUN
cana-259	39	3	to	to	PART
cana-259	39	4	control	control	VERB
cana-259	39	5	the	the	DET
cana-259	39	6	amount	amount	NOUN
cana-259	39	7	of	of	ADP
cana-259	39	8	chemicals	chemical	NOUN
cana-259	39	9	in	in	ADP
cana-259	39	10	a	a	DET
cana-259	39	11	reactor	reactor	NOUN
cana-259	39	12	was	be	AUX
cana-259	39	13	suggested	suggest	VERB
cana-259	39	14	in	in	ADP
cana-259	39	15	a	a	DET
cana-259	39	16	book	book	NOUN
cana-259	39	17	.	.	PUNCT
cana-259	40	1	[	[	X
cana-259	40	2	12	12	NUM
cana-259	40	3	]	]	PUNCT
cana-259	40	4	also	also	ADV
cana-259	40	5	,	,	PUNCT
cana-259	40	6	two	two	NUM
cana-259	40	7	methods	method	NOUN
cana-259	40	8	to	to	PART
cana-259	40	9	control	control	VERB
cana-259	40	10	chemical	chemical	ADJ
cana-259	40	11	reactions	reaction	NOUN
cana-259	40	12	were	be	AUX
cana-259	40	13	created	create	VERB
cana-259	40	14	using	use	VERB
cana-259	40	15	different	different	ADJ
cana-259	40	16	techniques	technique	NOUN
cana-259	40	17	.	.	PUNCT
cana-259	41	1	the	the	DET
cana-259	41	2	investigation	investigation	NOUN
cana-259	41	3	was	be	AUX
cana-259	41	4	undertaken	undertake	VERB
cana-259	41	5	by	by	ADP
cana-259	41	6	xu	xu	PROPN
cana-259	41	7	and	and	CCONJ
cana-259	41	8	his	his	PRON
cana-259	41	9	peers	peer	NOUN
cana-259	41	10	.	.	PUNCT
cana-259	42	1	[	[	X
cana-259	42	2	13	13	NUM
cana-259	42	3	]	]	PUNCT
cana-259	42	4	they	they	PRON
cana-259	42	5	studied	study	VERB
cana-259	42	6	a	a	DET
cana-259	42	7	type	type	NOUN
cana-259	42	8	of	of	ADP
cana-259	42	9	math	math	NOUN
cana-259	42	10	problem	problem	NOUN
cana-259	42	11	called	call	VERB
cana-259	42	12	a	a	DET
cana-259	42	13	bilinear	bilinear	ADJ
cana-259	42	14	parabolic	parabolic	ADJ
cana-259	42	15	pde	pde	NOUN
cana-259	42	16	system	system	NOUN
cana-259	42	17	.	.	PUNCT
cana-259	43	1	a	a	DET
cana-259	43	2	plan	plan	NOUN
cana-259	43	3	to	to	PART
cana-259	43	4	make	make	VERB
cana-259	43	5	a	a	DET
cana-259	43	6	not	not	PART
cana-259	43	7	-	-	PUNCT
cana-259	43	8	perfect	perfect	ADJ
cana-259	43	9	controller	controller	NOUN
cana-259	43	10	using	use	VERB
cana-259	43	11	a	a	DET
cana-259	43	12	simple	simple	ADJ
cana-259	43	13	model	model	NOUN
cana-259	43	14	.	.	PUNCT
cana-259	44	1	[	[	X
cana-259	44	2	14	14	NUM
cana-259	44	3	]	]	X
cana-259	44	4	sadek	sadek	PROPN
cana-259	44	5	and	and	CCONJ
cana-259	44	6	bokhari	bokhari	PROPN
cana-259	44	7	used	use	VERB
cana-259	44	8	special	special	ADJ
cana-259	44	9	math	math	NOUN
cana-259	44	10	to	to	PART
cana-259	44	11	estimate	estimate	VERB
cana-259	44	12	the	the	DET
cana-259	44	13	state	state	NOUN
cana-259	44	14	variables	variable	VERB
cana-259	44	15	in	in	ADP
cana-259	44	16	a	a	DET
cana-259	44	17	control	control	NOUN
cana-259	44	18	problem	problem	NOUN
cana-259	44	19	with	with	ADP
cana-259	44	20	linear	linear	ADJ
cana-259	44	21	pdes	pde	NOUN
cana-259	44	22	.	.	PUNCT
cana-259	45	1	[	[	X
cana-259	45	2	15	15	NUM
cana-259	45	3	]	]	PUNCT
cana-259	45	4	the	the	DET
cana-259	45	5	navier	navier	NOUN
cana-259	45	6	-	-	PUNCT
cana-259	45	7	stokes	stoke	NOUN
cana-259	45	8	equation	equation	NOUN
cana-259	45	9	was	be	AUX
cana-259	45	10	outfitted	outfit	VERB
cana-259	45	11	with	with	ADP
cana-259	45	12	a	a	DET
cana-259	45	13	top	top	ADJ
cana-259	45	14	-	-	PUNCT
cana-259	45	15	notch	notch	NOUN
cana-259	45	16	controller	controller	NOUN
cana-259	45	17	by	by	ADP
cana-259	45	18	16	16	NUM
cana-259	45	19	-	-	PUNCT
cana-259	45	20	year	year	NOUN
cana-259	45	21	-	-	PUNCT
cana-259	45	22	old	old	ADJ
cana-259	45	23	ravindra	ravindra	PROPN
cana-259	45	24	,	,	PUNCT
cana-259	45	25	who	who	PRON
cana-259	45	26	employed	employ	VERB
cana-259	45	27	the	the	DET
cana-259	45	28	newton	newton	PROPN
cana-259	45	29	method	method	NOUN
cana-259	45	30	to	to	PART
cana-259	45	31	achieve	achieve	VERB
cana-259	45	32	optimal	optimal	ADJ
cana-259	45	33	functionality	functionality	NOUN
cana-259	45	34	.	.	PUNCT
cana-259	46	1	in	in	ADP
cana-259	46	2	yadav	yadav	PROPN
cana-259	46	3	et	et	PROPN
cana-259	46	4	al	al	PROPN
cana-259	46	5	.	.	PROPN
cana-259	46	6	's	's	PART
cana-259	46	7	research	research	NOUN
cana-259	46	8	,	,	PUNCT
cana-259	46	9	they	they	PRON
cana-259	46	10	used	use	VERB
cana-259	46	11	a	a	DET
cana-259	46	12	method	method	NOUN
cana-259	46	13	called	call	VERB
cana-259	46	14	approximate	approximate	ADJ
cana-259	46	15	dynamic	dynamic	ADJ
cana-259	46	16	programming	programming	NOUN
cana-259	46	17	(	(	PUNCT
cana-259	46	18	adp	adp	PROPN
cana-259	46	19	)	)	PUNCT
cana-259	46	20	.	.	PUNCT
cana-259	47	1	[	[	X
cana-259	47	2	17	17	NUM
cana-259	47	3	]	]	PUNCT
cana-259	47	4	in	in	ADP
cana-259	47	5	the	the	DET
cana-259	47	6	study	study	NOUN
cana-259	47	7	by	by	ADP
cana-259	47	8	padhi	padhi	NOUN
cana-259	47	9	and	and	CCONJ
cana-259	47	10	others	other	NOUN
cana-259	47	11	,	,	PUNCT
cana-259	47	12	make	make	VERB
cana-259	47	13	better	well	ADJ
cana-259	47	14	microcontrollers	microcontroller	NOUN
cana-259	47	15	by	by	ADP
cana-259	47	16	putting	put	VERB
cana-259	47	17	them	they	PRON
cana-259	47	18	together	together	ADV
cana-259	47	19	,	,	PUNCT
cana-259	47	20	[	[	X
cana-259	47	21	18	18	NUM
cana-259	47	22	]	]	PUNCT
cana-259	47	23	,	,	PUNCT
cana-259	47	24	[	[	X
cana-259	47	25	19	19	NUM
cana-259	47	26	]	]	PUNCT
cana-259	47	27	.	.	PUNCT
cana-259	48	1	it	it	PRON
cana-259	48	2	should	should	AUX
cana-259	48	3	be	be	AUX
cana-259	48	4	emphasized	emphasize	VERB
cana-259	48	5	that	that	SCONJ
cana-259	48	6	in	in	ADP
cana-259	48	7	the	the	DET
cana-259	48	8	pde	pde	NOUN
cana-259	48	9	problems	problem	NOUN
cana-259	48	10	covered	cover	VERB
cana-259	48	11	in	in	ADP
cana-259	48	12	those	those	DET
cana-259	48	13	works	work	NOUN
cana-259	48	14	,	,	PUNCT
cana-259	48	15	the	the	DET
cana-259	48	16	spatial	spatial	ADJ
cana-259	48	17	differential	differential	NOUN
cana-259	48	18	operators	operator	NOUN
cana-259	48	19	are	be	AUX
cana-259	48	20	usually	usually	ADV
cana-259	48	21	linear	linear	ADJ
cana-259	48	22	.	.	PUNCT
cana-259	49	1	[	[	X
cana-259	49	2	8]-[10	8]-[10	NUM
cana-259	49	3	]	]	PUNCT
cana-259	49	4	,	,	PUNCT
cana-259	49	5	[	[	X
cana-259	49	6	12]-[19	12]-[19	NUM
cana-259	49	7	]	]	PUNCT
cana-259	49	8	.	.	PUNCT
cana-259	50	1	however	however	ADV
cana-259	50	2	,	,	PUNCT
cana-259	50	3	sdos	sdo	NOUN
cana-259	50	4	in	in	ADP
cana-259	50	5	actual	actual	ADJ
cana-259	50	6	industries	industry	NOUN
cana-259	50	7	are	be	AUX
cana-259	50	8	frequently	frequently	ADV
cana-259	50	9	nonlinear	nonlinear	ADJ
cana-259	50	10	.	.	PUNCT
cana-259	51	1	for	for	ADP
cana-259	51	2	instance	instance	NOUN
cana-259	51	3	,	,	PUNCT
cana-259	51	4	in	in	ADP
cana-259	51	5	the	the	DET
cana-259	51	6	process	process	NOUN
cana-259	51	7	of	of	ADP
cana-259	51	8	rapid	rapid	ADJ
cana-259	51	9	chemical	chemical	NOUN
cana-259	51	10	vapour	vapour	NOUN
cana-259	51	11	deposition	deposition	NOUN
cana-259	51	12	,	,	PUNCT
cana-259	51	13	[	[	X
cana-259	51	14	11	11	NUM
cana-259	51	15	]	]	PUNCT
cana-259	51	16	,	,	PUNCT
cana-259	51	17	[	[	X
cana-259	51	18	20	20	NUM
cana-259	51	19	]	]	PUNCT
cana-259	51	20	,	,	PUNCT
cana-259	51	21	[	[	X
cana-259	51	22	21	21	NUM
cana-259	51	23	]	]	X
cana-259	51	24	dispersion	dispersion	NOUN
cana-259	51	25	and	and	CCONJ
cana-259	51	26	react	react	VERB
cana-259	51	27	are	be	AUX
cana-259	51	28	nonlinear	nonlinear	ADJ
cana-259	51	29	processes	process	NOUN
cana-259	51	30	that	that	PRON
cana-259	51	31	rely	rely	VERB
cana-259	51	32	on	on	ADP
cana-259	51	33	temperatures	temperature	NOUN
cana-259	51	34	and	and	CCONJ
cana-259	51	35	conductivity	conductivity	NOUN
cana-259	51	36	of	of	ADP
cana-259	51	37	heat	heat	NOUN
cana-259	51	38	.	.	PUNCT
cana-259	52	1	[	[	X
cana-259	52	2	22	22	NUM
cana-259	52	3	]	]	PUNCT
cana-259	52	4	,	,	PUNCT
cana-259	52	5	[	[	X
cana-259	52	6	23	23	NUM
cana-259	52	7	]	]	PUNCT
cana-259	52	8	.	.	PUNCT
cana-259	53	1	in	in	ADP
cana-259	53	2	this	this	DET
cana-259	53	3	case	case	NOUN
cana-259	53	4	,	,	PUNCT
cana-259	53	5	we	we	PRON
cana-259	53	6	want	want	VERB
cana-259	53	7	to	to	PART
cana-259	53	8	create	create	VERB
cana-259	53	9	the	the	DET
cana-259	53	10	best	good	ADJ
cana-259	53	11	ways	way	NOUN
cana-259	53	12	to	to	PART
cana-259	53	13	control	control	VERB
cana-259	53	14	non	non	ADJ
cana-259	53	15	-	-	ADJ
cana-259	53	16	linear	linear	ADJ
cana-259	53	17	problems	problem	NOUN
cana-259	53	18	.	.	PUNCT
cana-259	54	1	when	when	SCONJ
cana-259	54	2	the	the	DET
cana-259	54	3	spatial	spatial	ADJ
cana-259	54	4	operator	operator	NOUN
cana-259	54	5	is	be	AUX
cana-259	54	6	not	not	PART
cana-259	54	7	straight	straight	ADJ
cana-259	54	8	,	,	PUNCT
cana-259	54	9	it	it	PRON
cana-259	54	10	's	be	AUX
cana-259	54	11	hard	hard	ADJ
cana-259	54	12	or	or	CCONJ
cana-259	54	13	impossible	impossible	ADJ
cana-259	54	14	to	to	PART
cana-259	54	15	figure	figure	VERB
cana-259	54	16	out	out	ADP
cana-259	54	17	the	the	DET
cana-259	54	18	basic	basic	ADJ
cana-259	54	19	functions	function	NOUN
cana-259	54	20	using	use	VERB
cana-259	54	21	math	math	NOUN
cana-259	54	22	.	.	PUNCT
cana-259	55	1	to	to	PART
cana-259	55	2	get	get	VERB
cana-259	55	3	around	around	ADP
cana-259	55	4	this	this	DET
cana-259	55	5	problem	problem	NOUN
cana-259	55	6	,	,	PUNCT
cana-259	55	7	some	some	DET
cana-259	55	8	ways	way	NOUN
cana-259	55	9	of	of	ADP
cana-259	55	10	using	use	VERB
cana-259	55	11	data	datum	NOUN
cana-259	55	12	to	to	PART
cana-259	55	13	find	find	VERB
cana-259	55	14	patterns	pattern	NOUN
cana-259	55	15	have	have	AUX
cana-259	55	16	been	be	AUX
cana-259	55	17	used	use	VERB
cana-259	55	18	.	.	PUNCT
cana-259	56	1	examples	example	NOUN
cana-259	56	2	of	of	ADP
cana-259	56	3	such	such	ADJ
cana-259	56	4	methods	method	NOUN
cana-259	56	5	are	be	AUX
cana-259	56	6	karhunen	karhunen	NOUN
cana-259	56	7	-	-	PUNCT
cana-259	56	8	loève	loève	NOUN
cana-259	56	9	decomposition	decomposition	NOUN
cana-259	56	10	(	(	PUNCT
cana-259	56	11	kld	kld	PROPN
cana-259	56	12	)	)	PUNCT
cana-259	57	1	[	[	X
cana-259	57	2	14	14	NUM
cana-259	57	3	]	]	PUNCT
cana-259	57	4	,	,	PUNCT
cana-259	57	5	[	[	X
cana-259	57	6	16]–[25	16]–[25	X
cana-259	57	7	]	]	PUNCT
cana-259	57	8	and	and	CCONJ
cana-259	57	9	singular	singular	NOUN
cana-259	57	10	-	-	PUNCT
cana-259	57	11	value	value	NOUN
cana-259	57	12	decomposition	decomposition	NOUN
cana-259	57	13	.	.	PUNCT
cana-259	58	1	[	[	X
cana-259	58	2	26	26	NUM
cana-259	58	3	]	]	PUNCT
cana-259	58	4	,	,	PUNCT
cana-259	58	5	[	[	X
cana-259	58	6	27	27	NUM
cana-259	58	7	]	]	PUNCT
cana-259	58	8	.	.	PUNCT
cana-259	59	1	by	by	ADP
cana-259	59	2	making	make	VERB
cana-259	59	3	use	use	NOUN
cana-259	59	4	of	of	ADP
cana-259	59	5	eefs	eef	NOUN
cana-259	59	6	,	,	PUNCT
cana-259	59	7	it	it	PRON
cana-259	59	8	is	be	AUX
cana-259	59	9	possible	possible	ADJ
cana-259	59	10	to	to	PART
cana-259	59	11	generate	generate	VERB
cana-259	59	12	a	a	DET
cana-259	59	13	smaller	small	ADJ
cana-259	59	14	ode	ode	ADJ
cana-259	59	15	system	system	NOUN
cana-259	59	16	that	that	PRON
cana-259	59	17	is	be	AUX
cana-259	59	18	then	then	ADV
cana-259	59	19	applied	apply	VERB
cana-259	59	20	in	in	ADP
cana-259	59	21	the	the	DET
cana-259	59	22	development	development	NOUN
cana-259	59	23	of	of	ADP
cana-259	59	24	a	a	DET
cana-259	59	25	controller	controller	NOUN
cana-259	59	26	.	.	PUNCT
cana-259	60	1	however	however	ADV
cana-259	60	2	,	,	PUNCT
cana-259	60	3	only	only	ADV
cana-259	60	4	a	a	DET
cana-259	60	5	few	few	ADJ
cana-259	60	6	studies	study	NOUN
cana-259	60	7	focused	focus	VERB
cana-259	60	8	on	on	ADP
cana-259	60	9	finding	find	VERB
cana-259	60	10	the	the	DET
cana-259	60	11	best	good	ADJ
cana-259	60	12	way	way	NOUN
cana-259	60	13	to	to	PART
cana-259	60	14	control	control	VERB
cana-259	60	15	something	something	PRON
cana-259	60	16	,	,	PUNCT
cana-259	60	17	like	like	ADP
cana-259	60	18	armaou	armaou	NOUN
cana-259	60	19	and	and	CCONJ
cana-259	60	20	christof	christof	NOUN
cana-259	60	21	ides	ide	NOUN
cana-259	60	22	[	[	X
cana-259	60	23	22	22	NUM
cana-259	60	24	]	]	PUNCT
cana-259	60	25	.	.	PUNCT
cana-259	61	1	decreased	decrease	VERB
cana-259	61	2	gradient	gradient	ADJ
cana-259	61	3	methods	method	NOUN
cana-259	61	4	were	be	AUX
cana-259	61	5	used	use	VERB
cana-259	61	6	to	to	PART
cana-259	61	7	solve	solve	VERB
cana-259	61	8	the	the	DET
cana-259	61	9	dynamical	dynamical	ADJ
cana-259	61	10	nonlinear	nonlinear	PROPN
cana-259	61	11	code	code	NOUN
cana-259	61	12	issue	issue	NOUN
cana-259	61	13	with	with	ADP
cana-259	61	14	equality	equality	NOUN
cana-259	61	15	limitations	limitation	NOUN
cana-259	61	16	that	that	PRON
cana-259	61	17	resulted	result	VERB
cana-259	61	18	from	from	ADP
cana-259	61	19	the	the	DET
cana-259	61	20	transformation	transformation	NOUN
cana-259	61	21	of	of	ADP
cana-259	61	22	the	the	DET
cana-259	61	23	optimum	optimum	ADJ
cana-259	61	24	control	control	NOUN
cana-259	61	25	problem	problem	NOUN
cana-259	61	26	.	.	PUNCT
cana-259	62	1	in	in	ADP
cana-259	62	2	recent	recent	ADJ
cana-259	62	3	years	year	NOUN
cana-259	62	4	,	,	PUNCT
cana-259	62	5	the	the	DET
cana-259	62	6	hjb	hjb	NOUN
cana-259	62	7	method	method	NOUN
cana-259	62	8	has	have	AUX
cana-259	62	9	been	be	AUX
cana-259	62	10	useful	useful	ADJ
cana-259	62	11	for	for	ADP
cana-259	62	12	designing	design	VERB
cana-259	62	13	the	the	DET
cana-259	62	14	best	good	ADJ
cana-259	62	15	way	way	NOUN
cana-259	62	16	to	to	PART
cana-259	62	17	control	control	VERB
cana-259	62	18	nonlinear	nonlinear	ADJ
cana-259	62	19	systems	system	NOUN
cana-259	62	20	.	.	PUNCT
cana-259	63	1	some	some	DET
cana-259	63	2	important	important	ADJ
cana-259	63	3	progress	progress	NOUN
cana-259	63	4	has	have	AUX
cana-259	63	5	also	also	ADV
cana-259	63	6	been	be	AUX
cana-259	63	7	made	make	VERB
cana-259	63	8	for	for	ADP
cana-259	63	9	lpss	lpss	PROPN
cana-259	63	10	.	.	PUNCT
cana-259	64	1	nevertheless	nevertheless	ADV
cana-259	64	2	up	up	ADP
cana-259	64	3	until	until	ADP
cana-259	64	4	now	now	ADV
cana-259	64	5	,	,	PUNCT
cana-259	64	6	solving	solve	VERB
cana-259	64	7	the	the	DET
cana-259	64	8	hjb	hjb	NOUN
cana-259	64	9	formulas	formula	NOUN
cana-259	64	10	with	with	ADP
cana-259	64	11	algebra	algebra	NOUN
cana-259	64	12	or	or	CCONJ
cana-259	64	13	numbers	number	NOUN
cana-259	64	14	has	have	AUX
cana-259	64	15	proven	prove	VERB
cana-259	64	16	to	to	PART
cana-259	64	17	be	be	AUX
cana-259	64	18	extremely	extremely	ADV
cana-259	64	19	difficult	difficult	ADJ
cana-259	64	20	.	.	PUNCT
cana-259	65	1	recently	recently	ADV
cana-259	65	2	,	,	PUNCT
cana-259	65	3	researchers	researcher	NOUN
cana-259	65	4	have	have	AUX
cana-259	65	5	used	use	VERB
cana-259	65	6	adp	adp	PROPN
cana-259	65	7	to	to	PART
cana-259	65	8	solve	solve	VERB
cana-259	65	9	this	this	DET
cana-259	65	10	problem	problem	NOUN
cana-259	65	11	in	in	ADP
cana-259	65	12	a	a	DET
cana-259	65	13	specific	specific	ADJ
cana-259	65	14	way	way	NOUN
cana-259	65	15	.	.	PUNCT
cana-259	66	1	[	[	X
cana-259	66	2	16]–[19	16]–[19	NUM
cana-259	66	3	]	]	X
cana-259	66	4	,	,	PUNCT
cana-259	66	5	[	[	X
cana-259	66	6	28]–[36	28]–[36	NUM
cana-259	66	7	]	]	PUNCT
cana-259	66	8	this	this	DET
cana-259	66	9	method	method	NOUN
cana-259	66	10	has	have	AUX
cana-259	66	11	been	be	AUX
cana-259	66	12	used	use	VERB
cana-259	66	13	to	to	ADP
cana-259	66	14	communications	communication	NOUN
cana-259	66	15	on	on	ADP
cana-259	66	16	applied	apply	VERB
cana-259	66	17	nonlinear	nonlinear	ADJ
cana-259	66	18	analysis	analysis	NOUN
cana-259	66	19	issn	issn	NOUN
cana-259	66	20	:	:	PUNCT
cana-259	66	21	1074	1074	NUM
cana-259	66	22	-	-	PUNCT
cana-259	66	23	133x	133x	NUM
cana-259	66	24	vol	vol	NOUN
cana-259	66	25	30	30	NUM
cana-259	66	26	no	no	NOUN
cana-259	66	27	.	.	NOUN
cana-259	66	28	2	2	NUM
cana-259	66	29	(	(	PUNCT
cana-259	66	30	2023	2023	NUM
cana-259	66	31	)	)	PUNCT
cana-259	66	32	3	3	NUM
cana-259	66	33	https://internationalpubls.com	https://internationalpubls.com	X
cana-259	66	34	solve	solve	VERB
cana-259	66	35	this	this	DET
cana-259	66	36	problem	problem	NOUN
cana-259	66	37	in	in	ADP
cana-259	66	38	a	a	DET
cana-259	66	39	careful	careful	ADJ
cana-259	66	40	and	and	CCONJ
cana-259	66	41	quiet	quiet	ADJ
cana-259	66	42	way	way	NOUN
cana-259	66	43	.	.	PUNCT
cana-259	67	1	adp	adp	PROPN
cana-259	67	2	was	be	AUX
cana-259	67	3	suggested	suggest	VERB
cana-259	67	4	in	in	ADP
cana-259	67	5	[	[	X
cana-259	67	6	28	28	NUM
cana-259	67	7	]	]	PUNCT
cana-259	67	8	.	.	PUNCT
cana-259	68	1	there	there	PRON
cana-259	68	2	are	be	VERB
cana-259	68	3	two	two	NUM
cana-259	68	4	primary	primary	ADJ
cana-259	68	5	categories	category	NOUN
cana-259	68	6	:	:	PUNCT
cana-259	68	7	bidirectional	bidirectional	ADJ
cana-259	68	8	robust	robust	ADJ
cana-259	68	9	computer	computer	NOUN
cana-259	68	10	and	and	CCONJ
cana-259	68	11	heuristic	heuristic	ADJ
cana-259	68	12	dynamic	dynamic	ADJ
cana-259	68	13	programming	programming	NOUN
cana-259	68	14	[	[	X
cana-259	68	15	29]–[33	29]–[33	X
cana-259	68	16	]	]	X
cana-259	68	17	,	,	PUNCT
cana-259	68	18	[	[	X
cana-259	68	19	31	31	NUM
cana-259	68	20	]	]	PUNCT
cana-259	68	21	,	,	PUNCT
cana-259	68	22	[	[	X
cana-259	68	23	34	34	NUM
cana-259	68	24	]	]	PUNCT
cana-259	68	25	.	.	PUNCT
cana-259	69	1	more	more	ADJ
cana-259	69	2	algorithms	algorithm	NOUN
cana-259	69	3	and	and	CCONJ
cana-259	69	4	a	a	DET
cana-259	69	5	scheme	scheme	NOUN
cana-259	69	6	for	for	ADP
cana-259	69	7	all	all	DET
cana-259	69	8	adp	adp	PROPN
cana-259	69	9	kinds	kind	NOUN
cana-259	69	10	were	be	AUX
cana-259	69	11	developed	develop	VERB
cana-259	69	12	by	by	ADP
cana-259	69	13	prokhorov	prokhorov	PROPN
cana-259	69	14	and	and	CCONJ
cana-259	69	15	wunsch	wunsch	PROPN
cana-259	69	16	.	.	PUNCT
cana-259	70	1	check	check	VERB
cana-259	70	2	out	out	ADP
cana-259	70	3	the	the	DET
cana-259	70	4	special	special	ADJ
cana-259	70	5	issue	issue	NOUN
cana-259	70	6	[	[	X
cana-259	70	7	36	36	NUM
cana-259	70	8	]	]	PUNCT
cana-259	70	9	for	for	ADP
cana-259	70	10	further	further	ADJ
cana-259	70	11	details	detail	NOUN
cana-259	70	12	on	on	ADP
cana-259	70	13	the	the	DET
cana-259	70	14	use	use	NOUN
cana-259	70	15	of	of	ADP
cana-259	70	16	adp	adp	PROPN
cana-259	70	17	to	to	PART
cana-259	70	18	provide	provide	VERB
cana-259	70	19	input	input	NOUN
cana-259	70	20	regulation	regulation	NOUN
cana-259	70	21	.	.	PUNCT
cana-259	71	1	a	a	DET
cana-259	71	2	method	method	NOUN
cana-259	71	3	for	for	ADP
cana-259	71	4	solving	solve	VERB
cana-259	71	5	the	the	DET
cana-259	71	6	hjb	hjb	NOUN
cana-259	71	7	problem	problem	NOUN
cana-259	71	8	for	for	ADP
cana-259	71	9	continuously	continuously	ADV
cana-259	71	10	running	run	VERB
cana-259	71	11	systems	system	NOUN
cana-259	71	12	was	be	AUX
cana-259	71	13	created	create	VERB
cana-259	71	14	by	by	ADP
cana-259	71	15	saridis	saridis	PROPN
cana-259	71	16	and	and	CCONJ
cana-259	71	17	lee	lee	PROPN
cana-259	71	18	,	,	PUNCT
cana-259	71	19	but	but	CCONJ
cana-259	71	20	they	they	PRON
cana-259	71	21	did	do	AUX
cana-259	71	22	n't	not	PART
cana-259	71	23	figure	figure	VERB
cana-259	71	24	out	out	ADP
cana-259	71	25	how	how	SCONJ
cana-259	71	26	to	to	PART
cana-259	71	27	find	find	VERB
cana-259	71	28	the	the	DET
cana-259	71	29	cost	cost	NOUN
cana-259	71	30	function	function	NOUN
cana-259	71	31	for	for	ADP
cana-259	71	32	each	each	DET
cana-259	71	33	step	step	NOUN
cana-259	71	34	of	of	ADP
cana-259	71	35	the	the	DET
cana-259	71	36	process	process	NOUN
cana-259	71	37	.	.	PUNCT
cana-259	72	1	beard	beard	NOUN
cana-259	72	2	and	and	CCONJ
cana-259	72	3	others	other	NOUN
cana-259	73	1	[	[	X
cana-259	73	2	38	38	NUM
cana-259	73	3	]	]	PUNCT
cana-259	73	4	,	,	PUNCT
cana-259	73	5	[	[	X
cana-259	73	6	39	39	NUM
cana-259	73	7	]	]	PUNCT
cana-259	73	8	proposed	propose	VERB
cana-259	73	9	a	a	DET
cana-259	73	10	way	way	NOUN
cana-259	73	11	to	to	PART
cana-259	73	12	solve	solve	VERB
cana-259	73	13	the	the	DET
cana-259	73	14	hjb	hjb	NOUN
cana-259	73	15	equation	equation	NOUN
cana-259	73	16	by	by	ADP
cana-259	73	17	solving	solve	VERB
cana-259	73	18	a	a	DET
cana-259	73	19	series	series	NOUN
cana-259	73	20	of	of	ADP
cana-259	73	21	simpler	simple	ADJ
cana-259	73	22	equations	equation	NOUN
cana-259	73	23	using	use	VERB
cana-259	73	24	a	a	DET
cana-259	73	25	method	method	NOUN
cana-259	73	26	called	call	VERB
cana-259	73	27	successive	successive	ADJ
cana-259	73	28	approximation	approximation	NOUN
cana-259	73	29	.	.	PUNCT
cana-259	74	1	this	this	DET
cana-259	74	2	method	method	NOUN
cana-259	74	3	uses	use	VERB
cana-259	74	4	galerkin	galerkin	ADJ
cana-259	74	5	approximation	approximation	NOUN
cana-259	74	6	to	to	PART
cana-259	74	7	solve	solve	VERB
cana-259	74	8	the	the	DET
cana-259	74	9	equations	equation	NOUN
cana-259	74	10	.	.	PUNCT
cana-259	75	1	abu	abu	PROPN
cana-259	75	2	-	-	PUNCT
cana-259	75	3	khalaf	khalaf	PROPN
cana-259	75	4	and	and	CCONJ
cana-259	75	5	clark	clark	PROPN
cana-259	76	1	[	[	X
cana-259	76	2	40	40	NUM
cana-259	76	3	]	]	PUNCT
cana-259	76	4	and	and	CCONJ
cana-259	76	5	[	[	X
cana-259	76	6	41	41	NUM
cana-259	76	7	]	]	PUNCT
cana-259	76	8	created	create	VERB
cana-259	76	9	near	near	ADP
cana-259	76	10	-	-	PUNCT
cana-259	76	11	optimal	optimal	ADJ
cana-259	76	12	state	state	NOUN
cana-259	76	13	feedback	feedback	NOUN
cana-259	76	14	controllers	controller	NOUN
cana-259	76	15	for	for	ADP
cana-259	76	16	continuous	continuous	ADJ
cana-259	76	17	nonlinear	nonlinear	ADJ
cana-259	76	18	systems	system	NOUN
cana-259	76	19	where	where	SCONJ
cana-259	76	20	control	control	NOUN
cana-259	76	21	restrictions	restriction	NOUN
cana-259	76	22	are	be	AUX
cana-259	76	23	present	present	ADJ
cana-259	76	24	,	,	PUNCT
cana-259	76	25	drawing	draw	VERB
cana-259	76	26	inspiration	inspiration	NOUN
cana-259	76	27	from	from	ADP
cana-259	76	28	the	the	DET
cana-259	76	29	work	work	NOUN
cana-259	76	30	of	of	ADP
cana-259	76	31	[	[	X
cana-259	76	32	37	37	NUM
cana-259	76	33	]	]	PUNCT
cana-259	76	34	–	–	PUNCT
cana-259	76	35	[	[	X
cana-259	76	36	39	39	NUM
cana-259	76	37	]	]	PUNCT
cana-259	76	38	.	.	PUNCT
cana-259	77	1	cheng	cheng	PROPN
cana-259	77	2	et	et	PROPN
cana-259	77	3	al	al	PROPN
cana-259	77	4	.	.	PUNCT
cana-259	78	1	[	[	X
cana-259	78	2	42	42	NUM
cana-259	78	3	]	]	PUNCT
cana-259	78	4	and	and	CCONJ
cana-259	78	5	[	[	X
cana-259	78	6	43	43	NUM
cana-259	78	7	]	]	PUNCT
cana-259	78	8	employed	employ	VERB
cana-259	78	9	neural	neural	ADJ
cana-259	78	10	networks	network	NOUN
cana-259	78	11	instead	instead	ADV
cana-259	78	12	of	of	ADP
cana-259	78	13	a	a	DET
cana-259	78	14	policy	policy	NOUN
cana-259	78	15	iteration	iteration	NOUN
cana-259	78	16	to	to	PART
cana-259	78	17	answer	answer	VERB
cana-259	78	18	the	the	DET
cana-259	78	19	evolving	evolve	VERB
cana-259	78	20	hjb	hjb	NOUN
cana-259	78	21	equation	equation	NOUN
cana-259	78	22	.	.	PUNCT
cana-259	79	1	they	they	PRON
cana-259	79	2	also	also	ADV
cana-259	79	3	applied	apply	VERB
cana-259	79	4	this	this	DET
cana-259	79	5	approach	approach	NOUN
cana-259	79	6	to	to	ADP
cana-259	79	7	the	the	DET
cana-259	79	8	situation	situation	NOUN
cana-259	79	9	where	where	SCONJ
cana-259	79	10	inputs	input	NOUN
cana-259	79	11	are	be	AUX
cana-259	79	12	restricted	restrict	VERB
cana-259	79	13	.	.	PUNCT
cana-259	80	1	the	the	DET
cana-259	80	2	authors	author	NOUN
cana-259	80	3	have	have	VERB
cana-259	80	4	limited	limit	VERB
cana-259	80	5	knowledge	knowledge	NOUN
cana-259	80	6	of	of	ADP
cana-259	80	7	research	research	NOUN
cana-259	80	8	on	on	ADP
cana-259	80	9	the	the	DET
cana-259	80	10	most	most	ADV
cana-259	80	11	effective	effective	ADJ
cana-259	80	12	approach	approach	NOUN
cana-259	80	13	to	to	ADP
cana-259	80	14	managing	manage	VERB
cana-259	80	15	pde	pde	NOUN
cana-259	80	16	problems	problem	NOUN
cana-259	80	17	employing	employ	VERB
cana-259	80	18	hjb	hjb	NOUN
cana-259	80	19	equations	equation	NOUN
cana-259	80	20	and	and	CCONJ
cana-259	80	21	a	a	DET
cana-259	80	22	regressive	regressive	ADJ
cana-259	80	23	sdo	sdo	NOUN
cana-259	80	24	.	.	PUNCT
cana-259	81	1	in	in	ADP
cana-259	81	2	this	this	DET
cana-259	81	3	paper	paper	NOUN
cana-259	81	4	,	,	PUNCT
cana-259	81	5	we	we	PRON
cana-259	81	6	create	create	VERB
cana-259	81	7	a	a	DET
cana-259	81	8	simpler	simple	ADJ
cana-259	81	9	controller	controller	NOUN
cana-259	81	10	for	for	ADP
cana-259	81	11	systems	system	NOUN
cana-259	81	12	with	with	ADP
cana-259	81	13	certain	certain	ADJ
cana-259	81	14	equations	equation	NOUN
cana-259	81	15	using	use	VERB
cana-259	81	16	a	a	DET
cana-259	81	17	special	special	ADJ
cana-259	81	18	framework	framework	NOUN
cana-259	81	19	.	.	PUNCT
cana-259	82	1	we	we	PRON
cana-259	82	2	base	base	VERB
cana-259	82	3	our	our	PRON
cana-259	82	4	work	work	NOUN
cana-259	82	5	on	on	ADP
cana-259	82	6	certain	certain	ADJ
cana-259	82	7	functions	function	NOUN
cana-259	82	8	and	and	CCONJ
cana-259	82	9	neural	neural	ADJ
cana-259	82	10	networks	network	NOUN
cana-259	82	11	.	.	PUNCT
cana-259	83	1	we	we	PRON
cana-259	83	2	start	start	VERB
cana-259	83	3	by	by	ADP
cana-259	83	4	using	use	VERB
cana-259	83	5	the	the	DET
cana-259	83	6	kld	kld	PROPN
cana-259	83	7	to	to	PART
cana-259	83	8	figure	figure	VERB
cana-259	83	9	out	out	ADP
cana-259	83	10	the	the	DET
cana-259	83	11	eefs	eef	NOUN
cana-259	83	12	using	use	VERB
cana-259	83	13	snapshots	snapshot	NOUN
cana-259	83	14	.	.	PUNCT
cana-259	84	1	the	the	DET
cana-259	84	2	pde	pde	PROPN
cana-259	84	3	network	network	NOUN
cana-259	84	4	is	be	AUX
cana-259	84	5	constructed	construct	VERB
cana-259	84	6	using	use	VERB
cana-259	84	7	the	the	DET
cana-259	84	8	eefs	eef	NOUN
cana-259	84	9	as	as	ADP
cana-259	84	10	a	a	DET
cana-259	84	11	high	high	ADV
cana-259	84	12	-	-	PUNCT
cana-259	84	13	dimensional	dimensional	ADJ
cana-259	84	14	,	,	PUNCT
cana-259	84	15	singularly	singularly	ADV
cana-259	84	16	perturbed	perturb	VERB
cana-259	84	17	mathematical	mathematical	ADJ
cana-259	84	18	representation	representation	NOUN
cana-259	84	19	of	of	ADP
cana-259	84	20	odes	ode	NOUN
cana-259	84	21	.	.	PUNCT
cana-259	85	1	the	the	DET
cana-259	85	2	sp	sp	NOUN
cana-259	85	3	technique	technique	NOUN
cana-259	85	4	helps	help	VERB
cana-259	85	5	to	to	PART
cana-259	85	6	create	create	VERB
cana-259	85	7	a	a	DET
cana-259	85	8	simpler	simple	ADJ
cana-259	85	9	model	model	NOUN
cana-259	85	10	that	that	PRON
cana-259	85	11	focuses	focus	VERB
cana-259	85	12	on	on	ADP
cana-259	85	13	the	the	DET
cana-259	85	14	most	most	ADV
cana-259	85	15	important	important	ADJ
cana-259	85	16	parts	part	NOUN
cana-259	85	17	of	of	ADP
cana-259	85	18	the	the	DET
cana-259	85	19	pde	pde	NOUN
cana-259	85	20	system	system	NOUN
cana-259	85	21	.	.	PUNCT
cana-259	86	1	the	the	DET
cana-259	86	2	optimal	optimal	ADJ
cana-259	86	3	controls	control	NOUN
cana-259	86	4	for	for	ADP
cana-259	86	5	the	the	DET
cana-259	86	6	system	system	NOUN
cana-259	86	7	are	be	AUX
cana-259	86	8	designed	design	VERB
cana-259	86	9	using	use	VERB
cana-259	86	10	the	the	DET
cana-259	86	11	rom	rom	NOUN
cana-259	86	12	.	.	PUNCT
cana-259	87	1	this	this	PRON
cana-259	87	2	guarantees	guarantee	VERB
cana-259	87	3	the	the	DET
cana-259	87	4	long	long	ADJ
cana-259	87	5	-	-	PUNCT
cana-259	87	6	term	term	NOUN
cana-259	87	7	stability	stability	NOUN
cana-259	87	8	of	of	ADP
cana-259	87	9	the	the	DET
cana-259	87	10	high	high	ADJ
cana-259	87	11	-	-	PUNCT
cana-259	87	12	order	order	NOUN
cana-259	87	13	ode	ode	ADJ
cana-259	87	14	system	system	NOUN
cana-259	87	15	.	.	PUNCT
cana-259	88	1	to	to	PART
cana-259	88	2	solve	solve	VERB
cana-259	88	3	the	the	DET
cana-259	88	4	hjb	hjb	NOUN
cana-259	88	5	-	-	PUNCT
cana-259	88	6	like	like	ADJ
cana-259	88	7	equation	equation	NOUN
cana-259	88	8	,	,	PUNCT
cana-259	88	9	we	we	PRON
cana-259	88	10	suggest	suggest	VERB
cana-259	88	11	a	a	DET
cana-259	88	12	method	method	NOUN
cana-259	88	13	that	that	PRON
cana-259	88	14	uses	use	VERB
cana-259	88	15	gradual	gradual	ADJ
cana-259	88	16	improvements	improvement	NOUN
cana-259	88	17	and	and	CCONJ
cana-259	88	18	neural	neural	ADJ
cana-259	88	19	networks	network	NOUN
cana-259	88	20	.	.	PUNCT
cana-259	89	1	we	we	PRON
cana-259	89	2	also	also	ADV
cana-259	89	3	show	show	VERB
cana-259	89	4	that	that	SCONJ
cana-259	89	5	this	this	DET
cana-259	89	6	method	method	NOUN
cana-259	89	7	will	will	AUX
cana-259	89	8	always	always	ADV
cana-259	89	9	work	work	VERB
cana-259	89	10	.	.	PUNCT
cana-259	90	1	finally	finally	ADV
cana-259	90	2	,	,	PUNCT
cana-259	90	3	we	we	PRON
cana-259	90	4	did	do	VERB
cana-259	90	5	some	some	DET
cana-259	90	6	tests	test	NOUN
cana-259	90	7	on	on	ADP
cana-259	90	8	a	a	DET
cana-259	90	9	computer	computer	NOUN
cana-259	90	10	to	to	PART
cana-259	90	11	see	see	VERB
cana-259	90	12	how	how	SCONJ
cana-259	90	13	well	well	ADV
cana-259	90	14	our	our	PRON
cana-259	90	15	suggested	suggested	ADJ
cana-259	90	16	way	way	NOUN
cana-259	90	17	of	of	ADP
cana-259	90	18	controlling	control	VERB
cana-259	90	19	a	a	DET
cana-259	90	20	chemical	chemical	NOUN
cana-259	90	21	reaction	reaction	NOUN
cana-259	90	22	works	work	VERB
cana-259	90	23	.	.	PUNCT
cana-259	91	1	we	we	PRON
cana-259	91	2	found	find	VERB
cana-259	91	3	that	that	SCONJ
cana-259	91	4	it	it	PRON
cana-259	91	5	worked	work	VERB
cana-259	91	6	well	well	ADV
cana-259	91	7	.	.	PUNCT
cana-259	92	1	to	to	PART
cana-259	92	2	sum	sum	VERB
cana-259	92	3	up	up	ADP
cana-259	92	4	,	,	PUNCT
cana-259	92	5	this	this	DET
cana-259	92	6	study	study	NOUN
cana-259	92	7	's	's	PART
cana-259	92	8	key	key	ADJ
cana-259	92	9	contributions	contribution	NOUN
cana-259	92	10	can	can	AUX
cana-259	92	11	be	be	AUX
cana-259	92	12	categorized	categorize	VERB
cana-259	92	13	into	into	ADP
cana-259	92	14	three	three	NUM
cana-259	92	15	main	main	ADJ
cana-259	92	16	areas	area	NOUN
cana-259	92	17	.	.	PUNCT
cana-259	93	1	create	create	VERB
cana-259	93	2	a	a	DET
cana-259	93	3	way	way	NOUN
cana-259	93	4	to	to	PART
cana-259	93	5	make	make	VERB
cana-259	93	6	a	a	DET
cana-259	93	7	complex	complex	ADJ
cana-259	93	8	math	math	NOUN
cana-259	93	9	method	method	NOUN
cana-259	93	10	simpler	simple	ADJ
cana-259	93	11	for	for	ADP
cana-259	93	12	parabolic	parabolic	ADJ
cana-259	93	13	equations	equation	NOUN
cana-259	93	14	with	with	ADP
cana-259	93	15	a	a	DET
cana-259	93	16	nonlinear	nonlinear	ADJ
cana-259	93	17	part	part	NOUN
cana-259	93	18	.	.	PUNCT
cana-259	94	1	suggest	suggest	VERB
cana-259	94	2	a	a	DET
cana-259	94	3	better	well	ADJ
cana-259	94	4	way	way	NOUN
cana-259	94	5	to	to	PART
cana-259	94	6	control	control	VERB
cana-259	94	7	non	non	ADJ
cana-259	94	8	-	-	ADJ
cana-259	94	9	linear	linear	ADJ
cana-259	94	10	pde	pde	NOUN
cana-259	94	11	systems	system	NOUN
cana-259	94	12	and	and	CCONJ
cana-259	94	13	come	come	VERB
cana-259	94	14	up	up	ADP
cana-259	94	15	with	with	ADP
cana-259	94	16	a	a	DET
cana-259	94	17	new	new	ADJ
cana-259	94	18	type	type	NOUN
cana-259	94	19	of	of	ADP
cana-259	94	20	equation	equation	NOUN
cana-259	94	21	.	.	PUNCT
cana-259	95	1	the	the	DET
cana-259	95	2	sp	sp	NOUN
cana-259	95	3	technique	technique	NOUN
cana-259	95	4	proves	prove	VERB
cana-259	95	5	that	that	SCONJ
cana-259	95	6	the	the	DET
cana-259	95	7	closed	closed	ADJ
cana-259	95	8	-	-	PUNCT
cana-259	95	9	loop	loop	NOUN
cana-259	95	10	high	high	ADJ
cana-259	95	11	-	-	PUNCT
cana-259	95	12	order	order	NOUN
cana-259	95	13	ode	ode	NOUN
cana-259	95	14	system	system	NOUN
cana-259	95	15	is	be	AUX
cana-259	95	16	stable	stable	ADJ
cana-259	95	17	in	in	ADP
cana-259	95	18	the	the	DET
cana-259	95	19	long	long	ADJ
cana-259	95	20	run	run	NOUN
cana-259	95	21	.	.	PUNCT
cana-259	96	1	create	create	VERB
cana-259	96	2	a	a	DET
cana-259	96	3	plan	plan	NOUN
cana-259	96	4	to	to	PART
cana-259	96	5	update	update	VERB
cana-259	96	6	controls	control	NOUN
cana-259	96	7	to	to	PART
cana-259	96	8	solve	solve	VERB
cana-259	96	9	a	a	DET
cana-259	96	10	specific	specific	ADJ
cana-259	96	11	equation	equation	NOUN
cana-259	96	12	using	use	VERB
cana-259	96	13	a	a	DET
cana-259	96	14	method	method	NOUN
cana-259	96	15	that	that	PRON
cana-259	96	16	makes	make	VERB
cana-259	96	17	small	small	ADJ
cana-259	96	18	changes	change	NOUN
cana-259	96	19	and	and	CCONJ
cana-259	96	20	neural	neural	ADJ
cana-259	96	21	networks	network	NOUN
cana-259	96	22	.	.	PUNCT
cana-259	97	1	then	then	ADV
cana-259	97	2	show	show	VERB
cana-259	97	3	that	that	SCONJ
cana-259	97	4	this	this	DET
cana-259	97	5	plan	plan	NOUN
cana-259	97	6	will	will	AUX
cana-259	97	7	work	work	VERB
cana-259	97	8	.	.	PUNCT
cana-259	98	1	this	this	PRON
cana-259	98	2	is	be	AUX
cana-259	98	3	how	how	SCONJ
cana-259	98	4	the	the	DET
cana-259	98	5	remainder	remainder	NOUN
cana-259	98	6	of	of	ADP
cana-259	98	7	the	the	DET
cana-259	98	8	paper	paper	NOUN
cana-259	98	9	is	be	AUX
cana-259	98	10	structured	structure	VERB
cana-259	98	11	:	:	PUNCT
cana-259	98	12	the	the	DET
cana-259	98	13	definition	definition	NOUN
cana-259	98	14	of	of	ADP
cana-259	98	15	elliptic	elliptic	ADJ
cana-259	98	16	pde	pde	NOUN
cana-259	98	17	systems	system	NOUN
cana-259	98	18	is	be	AUX
cana-259	98	19	given	give	VERB
cana-259	98	20	in	in	ADP
cana-259	98	21	section	section	PROPN
cana-259	98	22	ii	ii	PROPN
cana-259	98	23	.	.	PUNCT
cana-259	99	1	in	in	ADP
cana-259	99	2	the	the	DET
cana-259	99	3	third	third	ADJ
cana-259	99	4	part	part	NOUN
cana-259	99	5	,	,	PUNCT
cana-259	99	6	the	the	DET
cana-259	99	7	kld	kld	PROPN
cana-259	99	8	approach	approach	NOUN
cana-259	99	9	and	and	CCONJ
cana-259	99	10	the	the	DET
cana-259	99	11	sp	sp	NOUN
cana-259	99	12	technique	technique	NOUN
cana-259	99	13	are	be	AUX
cana-259	99	14	used	use	VERB
cana-259	99	15	to	to	PART
cana-259	99	16	generate	generate	VERB
cana-259	99	17	a	a	DET
cana-259	99	18	rom	rom	NOUN
cana-259	99	19	.	.	PUNCT
cana-259	100	1	the	the	DET
cana-259	100	2	best	good	ADJ
cana-259	100	3	controller	controller	NOUN
cana-259	100	4	is	be	AUX
cana-259	100	5	made	make	VERB
cana-259	100	6	and	and	CCONJ
cana-259	100	7	explained	explain	VERB
cana-259	100	8	in	in	ADP
cana-259	100	9	section	section	NOUN
cana-259	100	10	iv	iv	PROPN
cana-259	100	11	.	.	PUNCT
cana-259	100	12	section	section	PROPN
cana-259	100	13	v	v	NOUN
cana-259	100	14	is	be	AUX
cana-259	100	15	about	about	ADP
cana-259	100	16	testing	test	VERB
cana-259	100	17	a	a	DET
cana-259	100	18	model	model	NOUN
cana-259	100	19	,	,	PUNCT
cana-259	100	20	and	and	CCONJ
cana-259	100	21	section	section	NOUN
cana-259	100	22	vi	vi	PROPN
cana-259	100	23	is	be	AUX
cana-259	100	24	the	the	DET
cana-259	100	25	ending	ending	NOUN
cana-259	100	26	.	.	PUNCT
cana-259	101	1	in	in	ADP
cana-259	101	2	short	short	ADJ
cana-259	101	3	,	,	PUNCT
cana-259	101	4	this	this	DET
cana-259	101	5	study	study	NOUN
cana-259	101	6	has	have	VERB
cana-259	101	7	three	three	NUM
cana-259	101	8	main	main	ADJ
cana-259	101	9	contributions	contribution	NOUN
cana-259	101	10	.	.	PUNCT
cana-259	102	1	1	1	X
cana-259	102	2	.	.	X
cana-259	102	3	simplify	simplify	VERB
cana-259	102	4	a	a	DET
cana-259	102	5	way	way	NOUN
cana-259	102	6	to	to	PART
cana-259	102	7	make	make	VERB
cana-259	102	8	parabolic	parabolic	ADJ
cana-259	102	9	pde	pde	NOUN
cana-259	102	10	systems	system	NOUN
cana-259	102	11	with	with	ADP
cana-259	102	12	a	a	DET
cana-259	102	13	nonlinear	nonlinear	ADJ
cana-259	102	14	sdo	sdo	NOUN
cana-259	102	15	smaller	smaller	ADV
cana-259	102	16	using	use	VERB
cana-259	102	17	kld	kld	PROPN
cana-259	102	18	and	and	CCONJ
cana-259	102	19	sp	sp	ADP
cana-259	102	20	technique	technique	NOUN
cana-259	102	21	.	.	PUNCT
cana-259	103	1	2	2	X
cana-259	103	2	.	.	X
cana-259	103	3	suggest	suggest	VERB
cana-259	103	4	a	a	DET
cana-259	103	5	good	good	ADJ
cana-259	103	6	way	way	NOUN
cana-259	103	7	to	to	PART
cana-259	103	8	control	control	VERB
cana-259	103	9	systems	system	NOUN
cana-259	103	10	that	that	PRON
cana-259	103	11	follow	follow	VERB
cana-259	103	12	a	a	DET
cana-259	103	13	certain	certain	ADJ
cana-259	103	14	mathematical	mathematical	ADJ
cana-259	103	15	rule	rule	NOUN
cana-259	103	16	,	,	PUNCT
cana-259	103	17	and	and	CCONJ
cana-259	103	18	come	come	VERB
cana-259	103	19	up	up	ADP
cana-259	103	20	with	with	ADP
cana-259	103	21	a	a	DET
cana-259	103	22	new	new	ADJ
cana-259	103	23	type	type	NOUN
cana-259	103	24	of	of	ADP
cana-259	103	25	mathematical	mathematical	ADJ
cana-259	103	26	equation	equation	NOUN
cana-259	103	27	to	to	PART
cana-259	103	28	help	help	VERB
cana-259	103	29	with	with	ADP
cana-259	103	30	this	this	PRON
cana-259	103	31	.	.	PUNCT
cana-259	104	1	the	the	DET
cana-259	104	2	long	long	ADJ
cana-259	104	3	-	-	PUNCT
cana-259	104	4	term	term	NOUN
cana-259	104	5	stability	stability	NOUN
cana-259	104	6	of	of	ADP
cana-259	104	7	the	the	DET
cana-259	104	8	closed	closed	ADJ
cana-259	104	9	-	-	PUNCT
cana-259	104	10	loop	loop	NOUN
cana-259	104	11	high	high	ADJ
cana-259	104	12	-	-	PUNCT
cana-259	104	13	order	order	NOUN
cana-259	104	14	ode	ode	NOUN
cana-259	104	15	system	system	NOUN
cana-259	104	16	is	be	AUX
cana-259	104	17	demonstrated	demonstrate	VERB
cana-259	104	18	by	by	ADP
cana-259	104	19	the	the	DET
cana-259	104	20	sp	sp	NOUN
cana-259	104	21	approach	approach	NOUN
cana-259	104	22	.	.	PUNCT
cana-259	105	1	communications	communication	NOUN
cana-259	105	2	on	on	ADP
cana-259	105	3	applied	apply	VERB
cana-259	105	4	nonlinear	nonlinear	ADJ
cana-259	105	5	analysis	analysis	NOUN
cana-259	105	6	issn	issn	NOUN
cana-259	105	7	:	:	PUNCT
cana-259	105	8	1074	1074	NUM
cana-259	105	9	-	-	PUNCT
cana-259	105	10	133x	133x	NUM
cana-259	105	11	vol	vol	NOUN
cana-259	105	12	30	30	NUM
cana-259	105	13	no	no	NOUN
cana-259	105	14	.	.	NOUN
cana-259	105	15	2	2	NUM
cana-259	105	16	(	(	PUNCT
cana-259	105	17	2023	2023	NUM
cana-259	105	18	)	)	PUNCT
cana-259	105	19	4	4	NUM
cana-259	105	20	https://internationalpubls.com	https://internationalpubls.com	X
cana-259	105	21	3	3	NUM
cana-259	105	22	.	.	PUNCT
cana-259	105	23	create	create	VERB
cana-259	105	24	a	a	DET
cana-259	105	25	plan	plan	NOUN
cana-259	105	26	to	to	PART
cana-259	105	27	update	update	VERB
cana-259	105	28	the	the	DET
cana-259	105	29	control	control	NOUN
cana-259	105	30	in	in	ADP
cana-259	105	31	order	order	NOUN
cana-259	105	32	to	to	PART
cana-259	105	33	solve	solve	VERB
cana-259	105	34	a	a	DET
cana-259	105	35	specific	specific	ADJ
cana-259	105	36	equation	equation	NOUN
cana-259	105	37	using	use	VERB
cana-259	105	38	a	a	DET
cana-259	105	39	method	method	NOUN
cana-259	105	40	where	where	SCONJ
cana-259	105	41	we	we	PRON
cana-259	105	42	keep	keep	VERB
cana-259	105	43	improving	improve	VERB
cana-259	105	44	our	our	PRON
cana-259	105	45	solution	solution	NOUN
cana-259	105	46	step	step	NOUN
cana-259	105	47	by	by	ADP
cana-259	105	48	step	step	NOUN
cana-259	105	49	and	and	CCONJ
cana-259	105	50	also	also	ADV
cana-259	105	51	use	use	VERB
cana-259	105	52	a	a	DET
cana-259	105	53	neural	neural	ADJ
cana-259	105	54	network	network	NOUN
cana-259	105	55	.	.	PUNCT
cana-259	106	1	then	then	ADV
cana-259	106	2	show	show	VERB
cana-259	106	3	that	that	SCONJ
cana-259	106	4	this	this	DET
cana-259	106	5	plan	plan	NOUN
cana-259	106	6	works	work	VERB
cana-259	106	7	and	and	CCONJ
cana-259	106	8	our	our	PRON
cana-259	106	9	solution	solution	NOUN
cana-259	106	10	keeps	keep	VERB
cana-259	106	11	getting	get	VERB
cana-259	106	12	better	well	ADJ
cana-259	106	13	.	.	PUNCT
cana-259	107	1	symbols	symbol	NOUN
cana-259	107	2	:	:	PUNCT
cana-259	107	3	rn×m	rn×m	NOUN
cana-259	107	4	stands	stand	VERB
cana-259	107	5	for	for	ADP
cana-259	107	6	all	all	DET
cana-259	107	7	real	real	ADJ
cana-259	107	8	n	n	NUM
cana-259	107	9	×	×	NOUN
cana-259	107	10	m	m	NOUN
cana-259	107	11	matrices	matrix	NOUN
cana-259	107	12	as	as	SCONJ
cana-259	107	13	r	r	NOUN
cana-259	107	14	represents	represent	VERB
cana-259	107	15	n	n	CCONJ
cana-259	107	16	-	-	PUNCT
cana-259	107	17	dimensional	dimensional	ADJ
cana-259	107	18	space	space	NOUN
cana-259	107	19	,	,	PUNCT
cana-259	107	20	and	and	CCONJ
cana-259	107	21	r	r	NOUN
cana-259	107	22	is	be	AUX
cana-259	107	23	actual	actual	ADJ
cana-259	107	24	amounts	amount	NOUN
cana-259	107	25	.	.	PUNCT
cana-259	108	1	rn	rn	PROPN
cana-259	108	2	and	and	CCONJ
cana-259	108	3	d	d	ADP
cana-259	108	4	stand	stand	VERB
cana-259	108	5	for	for	ADP
cana-259	108	6	the	the	DET
cana-259	108	7	usual	usual	ADJ
cana-259	108	8	way	way	NOUN
cana-259	108	9	of	of	ADP
cana-259	108	10	multiplying	multiply	VERB
cana-259	108	11	things	thing	NOUN
cana-259	108	12	together	together	ADV
cana-259	108	13	and	and	CCONJ
cana-259	108	14	measuring	measure	VERB
cana-259	108	15	their	their	PRON
cana-259	108	16	length	length	NOUN
cana-259	108	17	in	in	ADP
cana-259	108	18	rn	rn	PROPN
cana-259	108	19	,	,	PUNCT
cana-259	108	20	in	in	ADP
cana-259	108	21	that	that	DET
cana-259	108	22	order	order	NOUN
cana-259	108	23	.	.	PUNCT
cana-259	109	1	if	if	SCONJ
cana-259	109	2	a	a	DET
cana-259	109	3	matrix	matrix	NOUN
cana-259	109	4	m	m	VERB
cana-259	109	5	is	be	AUX
cana-259	109	6	symmetrical	symmetrical	ADJ
cana-259	109	7	,	,	PUNCT
cana-259	109	8	m	m	VERB
cana-259	109	9	>	>	X
cana-259	109	10	(	(	PUNCT
cana-259	109	11	<	<	X
cana-259	109	12	)	)	PUNCT
cana-259	109	13	0	0	NUM
cana-259	109	14	means	mean	VERB
cana-259	109	15	it	it	PRON
cana-259	109	16	is	be	AUX
cana-259	109	17	positive	positive	ADJ
cana-259	109	18	(	(	PUNCT
cana-259	109	19	negative	negative	ADJ
cana-259	109	20	)	)	PUNCT
cana-259	109	21	definite	definite	ADJ
cana-259	109	22	.	.	PUNCT
cana-259	110	1	the	the	DET
cana-259	110	2	symbols	symbols	PROPN
cana-259	110	3	σ	σ	PROPN
cana-259	110	4	(	(	PUNCT
cana-259	110	5	)	)	PUNCT
cana-259	110	6	and	and	CCONJ
cana-259	110	7	σ	σ	PROPN
cana-259	110	8	(	(	PUNCT
cana-259	110	9	)	)	PUNCT
cana-259	110	10	represent	represent	VERB
cana-259	110	11	the	the	DET
cana-259	110	12	biggest	big	ADJ
cana-259	110	13	and	and	CCONJ
cana-259	110	14	smallest	small	ADJ
cana-259	110	15	singular	singular	ADJ
cana-259	110	16	values	value	NOUN
cana-259	110	17	of	of	ADP
cana-259	110	18	a	a	DET
cana-259	110	19	matrix	matrix	NOUN
cana-259	110	20	.	.	PUNCT
cana-259	111	1	the	the	DET
cana-259	111	2	small	small	ADJ
cana-259	111	3	letter	letter	NOUN
cana-259	111	4	t	t	PROPN
cana-259	111	5	written	write	VERB
cana-259	111	6	above	above	ADP
cana-259	111	7	a	a	DET
cana-259	111	8	matrix	matrix	NOUN
cana-259	111	9	means	mean	VERB
cana-259	111	10	to	to	PART
cana-259	111	11	switch	switch	VERB
cana-259	111	12	the	the	DET
cana-259	111	13	rows	row	NOUN
cana-259	111	14	and	and	CCONJ
cana-259	111	15	columns	column	NOUN
cana-259	111	16	.	.	PUNCT
cana-259	112	1	l2([z	l2([z	NOUN
cana-259	112	2	,	,	PUNCT
cana-259	112	3	z	z	NOUN
cana-259	112	4	]	]	X
cana-259	112	5	,	,	PUNCT
cana-259	112	6	rn	rn	PROPN
cana-259	112	7	)	)	PUNCT
cana-259	112	8	is	be	AUX
cana-259	112	9	a	a	DET
cana-259	112	10	big	big	ADJ
cana-259	112	11	space	space	NOUN
cana-259	112	12	of	of	ADP
cana-259	112	13	vectors	vector	NOUN
cana-259	112	14	with	with	ADP
cana-259	112	15	a	a	DET
cana-259	112	16	certain	certain	ADJ
cana-259	112	17	kind	kind	NOUN
cana-259	112	18	of	of	ADP
cana-259	112	19	math	math	NOUN
cana-259	112	20	inside	inside	ADV
cana-259	112	21	,	,	PUNCT
cana-259	112	22	and	and	CCONJ
cana-259	112	23	it	it	PRON
cana-259	112	24	's	be	AUX
cana-259	112	25	related	relate	VERB
cana-259	112	26	to	to	ADP
cana-259	112	27	a	a	DET
cana-259	112	28	type	type	NOUN
cana-259	112	29	of	of	ADP
cana-259	112	30	function	function	NOUN
cana-259	112	31	called	call	VERB
cana-259	112	32	square	square	PROPN
cana-259	112	33	integrable	integrable	ADJ
cana-259	112	34	.	.	PUNCT
cana-259	113	1	it	it	PRON
cana-259	113	2	's	be	AUX
cana-259	113	3	used	use	VERB
cana-259	113	4	for	for	ADP
cana-259	113	5	working	work	VERB
cana-259	113	6	with	with	ADP
cana-259	113	7	vectors	vector	NOUN
cana-259	113	8	in	in	ADP
cana-259	113	9	a	a	DET
cana-259	113	10	certain	certain	ADJ
cana-259	113	11	way	way	NOUN
cana-259	113	12	,	,	PUNCT
cana-259	113	13	and	and	CCONJ
cana-259	113	14	has	have	VERB
cana-259	113	15	a	a	DET
cana-259	113	16	specific	specific	ADJ
cana-259	113	17	way	way	NOUN
cana-259	113	18	of	of	ADP
cana-259	113	19	measuring	measure	VERB
cana-259	113	20	their	their	PRON
cana-259	113	21	size	size	NOUN
cana-259	113	22	and	and	CCONJ
cana-259	113	23	how	how	SCONJ
cana-259	113	24	they	they	PRON
cana-259	113	25	relate	relate	VERB
cana-259	113	26	to	to	ADP
cana-259	113	27	each	each	DET
cana-259	113	28	other	other	ADJ
cana-259	113	29	.	.	PUNCT
cana-259	114	1	explanation	explanation	NOUN
cana-259	114	2	of	of	ADP
cana-259	114	3	curved	curved	ADJ
cana-259	114	4	pde	pde	NOUN
cana-259	114	5	systems	system	NOUN
cana-259	114	6	in	in	ADP
cana-259	114	7	this	this	DET
cana-259	114	8	paper	paper	NOUN
cana-259	114	9	,	,	PUNCT
cana-259	114	10	we	we	PRON
cana-259	114	11	study	study	VERB
cana-259	114	12	a	a	DET
cana-259	114	13	group	group	NOUN
cana-259	114	14	of	of	ADP
cana-259	114	15	curved	curved	ADJ
cana-259	114	16	pde	pde	NOUN
cana-259	114	17	equations	equation	NOUN
cana-259	114	18	in	in	ADP
cana-259	114	19	one	one	NUM
cana-259	114	20	direction	direction	NOUN
cana-259	114	21	with	with	ADP
cana-259	114	22	a	a	DET
cana-259	114	23	certain	certain	ADJ
cana-259	114	24	way	way	NOUN
cana-259	114	25	of	of	ADP
cana-259	114	26	representing	represent	VERB
cana-259	114	27	the	the	DET
cana-259	114	28	state	state	NOUN
cana-259	114	29	.	.	PUNCT
cana-259	115	1	yt(z	yt(z	NUM
cana-259	115	2	,	,	PUNCT
cana-259	115	3	t	t	PROPN
cana-259	115	4	)	)	PUNCT
cana-259	115	5	=	=	SYM
cana-259	116	1	a	a	PRON
cana-259	116	2	(	(	PUNCT
cana-259	116	3	y(z	y(z	PROPN
cana-259	116	4	,	,	PUNCT
cana-259	116	5	t	t	PROPN
cana-259	116	6	)	)	PUNCT
cana-259	116	7	)	)	PUNCT
cana-259	117	1	+	+	CCONJ
cana-259	117	2	f	f	X
cana-259	117	3	(	(	PUNCT
cana-259	117	4	y(z	y(z	PROPN
cana-259	117	5	,	,	PUNCT
cana-259	117	6	t	t	PROPN
cana-259	117	7	)	)	PUNCT
cana-259	117	8	)	)	PUNCT
cana-259	118	1	+	+	CCONJ
cana-259	118	2	b(z)u(t	b(z)u(t	NOUN
cana-259	118	3	)	)	PUNCT
cana-259	118	4	(	(	PUNCT
cana-259	118	5	1	1	X
cana-259	118	6	)	)	PUNCT
cana-259	118	7	dependent	dependent	ADJ
cana-259	118	8	on	on	ADP
cana-259	118	9	the	the	DET
cana-259	118	10	limits	limit	NOUN
cana-259	118	11	or	or	CCONJ
cana-259	118	12	rules	rule	NOUN
cana-259	118	13	.	.	PUNCT
cana-259	119	1	and	and	CCONJ
cana-259	119	2	the	the	DET
cana-259	119	3	initial	initial	ADJ
cana-259	119	4	condition	condition	NOUN
cana-259	119	5	y	y	PROPN
cana-259	119	6	(	(	PUNCT
cana-259	119	7	z	z	PROPN
cana-259	119	8	,	,	PUNCT
cana-259	119	9	0	0	NUM
cana-259	119	10	)	)	PUNCT
cana-259	119	11	=	=	SYM
cana-259	119	12	y0(z	y0(z	PROPN
cana-259	119	13	)	)	PUNCT
cana-259	119	14	(	(	PUNCT
cana-259	119	15	3	3	X
cana-259	119	16	)	)	PUNCT
cana-259	119	17	the	the	DET
cana-259	119	18	suffixes	suffix	NOUN
cana-259	119	19	z	z	PROPN
cana-259	119	20	and	and	CCONJ
cana-259	119	21	t	t	PROPN
cana-259	119	22	are	be	AUX
cana-259	119	23	part	part	NOUN
cana-259	119	24	derivatives	derivative	NOUN
cana-259	119	25	with	with	ADP
cana-259	119	26	a	a	DET
cana-259	119	27	relationship	relationship	NOUN
cana-259	119	28	with	with	ADP
cana-259	119	29	z	z	PROPN
cana-259	119	30	and	and	CCONJ
cana-259	119	31	t	t	PROPN
cana-259	119	32	,	,	PUNCT
cana-259	119	33	while	while	SCONJ
cana-259	119	34	y(z	y(z	PROPN
cana-259	119	35	,	,	PUNCT
cana-259	119	36	t	t	PROPN
cana-259	119	37	)	)	PUNCT
cana-259	119	38	is	be	AUX
cana-259	119	39	the	the	DET
cana-259	119	40	state	state	NOUN
cana-259	119	41	function	function	NOUN
cana-259	119	42	with	with	ADP
cana-259	119	43	components	component	NOUN
cana-259	119	44	y1(z	y1(z	PROPN
cana-259	119	45	,	,	PUNCT
cana-259	119	46	t	t	PROPN
cana-259	119	47	)	)	PUNCT
cana-259	119	48	to	to	ADP
cana-259	119	49	yn(z	yn(z	NUM
cana-259	119	50	,	,	PUNCT
cana-259	119	51	t	t	PROPN
cana-259	119	52	)	)	PUNCT
cana-259	119	53	.	.	PUNCT
cana-259	120	1	what	what	PRON
cana-259	120	2	is	be	AUX
cana-259	120	3	written	write	VERB
cana-259	120	4	as	as	ADP
cana-259	120	5	y(z	y(z	PROPN
cana-259	120	6	,	,	PUNCT
cana-259	120	7	t	t	PROPN
cana-259	120	8	)	)	PUNCT
cana-259	120	9	is	be	AUX
cana-259	120	10	the	the	DET
cana-259	120	11	state	state	NOUN
cana-259	120	12	.	.	PUNCT
cana-259	121	1	the	the	DET
cana-259	121	2	letters	letter	NOUN
cana-259	121	3	z	z	PROPN
cana-259	121	4	and	and	CCONJ
cana-259	121	5	t	t	PROPN
cana-259	121	6	represent	represent	VERB
cana-259	121	7	partial	partial	ADJ
cana-259	121	8	derivatives	derivative	NOUN
cana-259	121	9	.	.	PUNCT
cana-259	122	1	the	the	DET
cana-259	122	2	definition	definition	NOUN
cana-259	122	3	is	be	AUX
cana-259	122	4	related	relate	VERB
cana-259	122	5	to	to	ADP
cana-259	122	6	the	the	DET
cana-259	122	7	time	time	NOUN
cana-259	122	8	coordinate	coordinate	NOUN
cana-259	122	9	,	,	PUNCT
cana-259	122	10	which	which	PRON
cana-259	122	11	is	be	AUX
cana-259	122	12	represented	represent	VERB
cana-259	122	13	by	by	ADP
cana-259	122	14	the	the	DET
cana-259	122	15	symbol	symbol	NOUN
cana-259	122	16	[	[	X
cana-259	122	17	0	0	NUM
cana-259	122	18	,	,	PUNCT
cana-259	122	19	)	)	PUNCT
cana-259	122	20	.	.	PUNCT
cana-259	123	1	the	the	DET
cana-259	123	2	letter	letter	NOUN
cana-259	123	3	"	"	PUNCT
cana-259	123	4	u	u	NOUN
cana-259	123	5	"	"	PUNCT
cana-259	123	6	of	of	ADP
cana-259	123	7	time	time	NOUN
cana-259	123	8	"	"	PUNCT
cana-259	123	9	t	t	PROPN
cana-259	123	10	"	"	PUNCT
cana-259	123	11	rp	rp	NOUN
cana-259	123	12	is	be	AUX
cana-259	123	13	the	the	DET
cana-259	123	14	input	input	NOUN
cana-259	123	15	that	that	PRON
cana-259	123	16	is	be	AUX
cana-259	123	17	controlled	control	VERB
cana-259	123	18	.	.	PUNCT
cana-259	124	1	(	(	PUNCT
cana-259	124	2	y	y	X
cana-259	124	3	)	)	PUNCT
cana-259	124	4	is	be	AUX
cana-259	124	5	a	a	DET
cana-259	124	6	curved	curved	ADJ
cana-259	124	7	sdo	sdo	NOUN
cana-259	124	8	that	that	PRON
cana-259	124	9	involves	involve	VERB
cana-259	124	10	some	some	DET
cana-259	124	11	math	math	NOUN
cana-259	124	12	stuff	stuff	NOUN
cana-259	124	13	and	and	CCONJ
cana-259	124	14	follows	follow	VERB
cana-259	124	15	a	a	DET
cana-259	124	16	certain	certain	ADJ
cana-259	124	17	rule	rule	NOUN
cana-259	124	18	.	.	PUNCT
cana-259	125	1	t	t	X
cana-259	126	1	[	[	X
cana-259	126	2	0	0	NUM
cana-259	126	3	,	,	PUNCT
cana-259	126	4	)	)	PUNCT
cana-259	126	5	is	be	AUX
cana-259	126	6	the	the	DET
cana-259	126	7	time	time	NOUN
cana-259	126	8	coordinate	coordinate	NOUN
cana-259	126	9	and	and	CCONJ
cana-259	126	10	represents	represent	VERB
cana-259	126	11	the	the	DET
cana-259	126	12	values	value	NOUN
cana-259	126	13	greater	great	ADJ
cana-259	126	14	than	than	ADP
cana-259	126	15	or	or	CCONJ
cana-259	126	16	equal	equal	ADJ
cana-259	126	17	to	to	ADP
cana-259	126	18	0	0	NUM
cana-259	126	19	.	.	PUNCT
cana-259	127	1	the	the	DET
cana-259	127	2	manipulated	manipulate	VERB
cana-259	127	3	input	input	NOUN
cana-259	127	4	is	be	AUX
cana-259	127	5	u(t	u(t	NOUN
cana-259	127	6	)	)	PUNCT
cana-259	127	7	rp	rp	NOUN
cana-259	127	8	.	.	PUNCT
cana-259	128	1	the	the	DET
cana-259	128	2	equation	equation	NOUN
cana-259	128	3	(	(	PUNCT
cana-259	128	4	y	y	NOUN
cana-259	128	5	)	)	PUNCT
cana-259	128	6	is	be	AUX
cana-259	128	7	a	a	DET
cana-259	128	8	curved	curved	ADJ
cana-259	128	9	line	line	NOUN
cana-259	128	10	with	with	ADP
cana-259	128	11	some	some	DET
cana-259	128	12	rules	rule	NOUN
cana-259	128	13	that	that	PRON
cana-259	128	14	involves	involve	VERB
cana-259	128	15	different	different	ADJ
cana-259	128	16	types	type	NOUN
cana-259	128	17	of	of	ADP
cana-259	128	18	math	math	NOUN
cana-259	128	19	and	and	CCONJ
cana-259	128	20	meets	meet	VERB
cana-259	128	21	a	a	DET
cana-259	128	22	certain	certain	ADJ
cana-259	128	23	condition	condition	NOUN
cana-259	128	24	.	.	PUNCT
cana-259	129	1	communications	communication	NOUN
cana-259	129	2	on	on	ADP
cana-259	129	3	applied	apply	VERB
cana-259	129	4	nonlinear	nonlinear	ADJ
cana-259	129	5	analysis	analysis	NOUN
cana-259	129	6	issn	issn	NOUN
cana-259	129	7	:	:	PUNCT
cana-259	129	8	1074	1074	NUM
cana-259	129	9	-	-	PUNCT
cana-259	129	10	133x	133x	NUM
cana-259	129	11	vol	vol	NOUN
cana-259	129	12	30	30	NUM
cana-259	129	13	no	no	NOUN
cana-259	129	14	.	.	NOUN
cana-259	129	15	2	2	NUM
cana-259	129	16	(	(	PUNCT
cana-259	129	17	2023	2023	NUM
cana-259	129	18	)	)	PUNCT
cana-259	129	19	5	5	NUM
cana-259	129	20	https://internationalpubls.com	https://internationalpubls.com	X
cana-259	129	21	where	where	SCONJ
cana-259	129	22	a1	a1	NOUN
cana-259	129	23	,	,	PUNCT
cana-259	129	24	a2	a2	PROPN
cana-259	129	25	,	,	PUNCT
cana-259	129	26	and	and	CCONJ
cana-259	129	27	a3	a3	NOUN
cana-259	129	28	are	be	AUX
cana-259	129	29	real	real	ADJ
cana-259	129	30	numbers	number	NOUN
cana-259	129	31	that	that	PRON
cana-259	129	32	are	be	AUX
cana-259	129	33	positive	positive	ADJ
cana-259	129	34	.	.	PUNCT
cana-259	130	1	f	f	X
cana-259	130	2	(	(	PUNCT
cana-259	130	3	y	y	NOUN
cana-259	130	4	)	)	PUNCT
cana-259	130	5	is	be	AUX
cana-259	130	6	a	a	DET
cana-259	130	7	function	function	NOUN
cana-259	130	8	that	that	PRON
cana-259	130	9	does	do	AUX
cana-259	130	10	n't	not	PART
cana-259	130	11	follow	follow	VERB
cana-259	130	12	a	a	DET
cana-259	130	13	straight	straight	ADJ
cana-259	130	14	line	line	NOUN
cana-259	130	15	and	and	CCONJ
cana-259	130	16	meets	meet	VERB
cana-259	130	17	the	the	DET
cana-259	130	18	condition	condition	NOUN
cana-259	130	19	f	f	X
cana-259	130	20	(	(	PUNCT
cana-259	130	21	0	0	NUM
cana-259	130	22	)	)	PUNCT
cana-259	130	23	=	=	NOUN
cana-259	131	1	0	0	X
cana-259	131	2	.	.	PUNCT
cana-259	132	1	it	it	PRON
cana-259	132	2	is	be	AUX
cana-259	132	3	also	also	ADV
cana-259	132	4	continuous	continuous	ADJ
cana-259	132	5	in	in	ADP
cana-259	132	6	a	a	DET
cana-259	132	7	small	small	ADJ
cana-259	132	8	neighborhood	neighborhood	NOUN
cana-259	132	9	around	around	ADP
cana-259	132	10	each	each	DET
cana-259	132	11	point	point	NOUN
cana-259	132	12	.	.	PUNCT
cana-259	133	1	b	b	X
cana-259	133	2	(	(	PUNCT
cana-259	133	3	z	z	NOUN
cana-259	133	4	)	)	PUNCT
cana-259	133	5	is	be	AUX
cana-259	133	6	a	a	DET
cana-259	133	7	smooth	smooth	ADJ
cana-259	133	8	matrix	matrix	NOUN
cana-259	133	9	function	function	NOUN
cana-259	133	10	that	that	PRON
cana-259	133	11	shows	show	VERB
cana-259	133	12	how	how	SCONJ
cana-259	133	13	control	control	ADJ
cana-259	133	14	actions	action	NOUN
cana-259	133	15	are	be	AUX
cana-259	133	16	spread	spread	VERB
cana-259	133	17	out	out	ADP
cana-259	133	18	in	in	ADP
cana-259	133	19	different	different	ADJ
cana-259	133	20	areas	area	NOUN
cana-259	133	21	.	.	PUNCT
cana-259	134	1	where	where	SCONJ
cana-259	134	2	genuine	genuine	ADJ
cana-259	134	3	negative	negative	ADJ
cana-259	134	4	integers	integer	NOUN
cana-259	134	5	a1	a1	NOUN
cana-259	134	6	,	,	PUNCT
cana-259	134	7	a2	a2	PROPN
cana-259	134	8	,	,	PUNCT
cana-259	134	9	and	and	CCONJ
cana-259	134	10	a3	a3	NOUN
cana-259	134	11	are	be	AUX
cana-259	134	12	involved	involve	VERB
cana-259	134	13	.	.	PUNCT
cana-259	135	1	f	f	X
cana-259	135	2	(	(	PUNCT
cana-259	135	3	y	y	NOUN
cana-259	135	4	)	)	PUNCT
cana-259	135	5	is	be	AUX
cana-259	135	6	a	a	DET
cana-259	135	7	globally	globally	ADV
cana-259	135	8	a	a	DET
cana-259	135	9	lipschitz	lipschitz	NOUN
cana-259	135	10	continuously	continuously	ADV
cana-259	135	11	nonlinear	nonlinear	ADJ
cana-259	135	12	vector	vector	NOUN
cana-259	135	13	function	function	NOUN
cana-259	135	14	that	that	PRON
cana-259	135	15	satisfies	satisfy	VERB
cana-259	135	16	f	f	X
cana-259	135	17	(	(	PUNCT
cana-259	135	18	0	0	NUM
cana-259	135	19	)	)	PUNCT
cana-259	135	20	=	=	NOUN
cana-259	136	1	0	0	X
cana-259	136	2	.	.	PUNCT
cana-259	137	1	the	the	DET
cana-259	137	2	adequate	adequate	ADJ
cana-259	137	3	smooth	smooth	ADJ
cana-259	137	4	matrix	matrix	NOUN
cana-259	137	5	function	function	NOUN
cana-259	137	6	of	of	ADP
cana-259	137	7	dimension	dimension	NOUN
cana-259	137	8	suitable	suitable	ADJ
cana-259	137	9	,	,	PUNCT
cana-259	137	10	the	the	DET
cana-259	137	11	distribution	distribution	NOUN
cana-259	137	12	of	of	ADP
cana-259	137	13	control	control	NOUN
cana-259	137	14	operations	operation	NOUN
cana-259	137	15	in	in	ADP
cana-259	137	16	spatial	spatial	ADJ
cana-259	137	17	domains	domain	NOUN
cana-259	137	18	is	be	AUX
cana-259	137	19	believed	believe	VERB
cana-259	137	20	to	to	PART
cana-259	137	21	be	be	AUX
cana-259	137	22	characterized	characterize	VERB
cana-259	137	23	by	by	ADP
cana-259	137	24	b(z	b(z	NOUN
cana-259	137	25	)	)	PUNCT
cana-259	137	26	.	.	PUNCT
cana-259	138	1	the	the	DET
cana-259	138	2	starting	starting	NOUN
cana-259	138	3	point	point	NOUN
cana-259	138	4	is	be	AUX
cana-259	138	5	y0(z	y0(z	PROPN
cana-259	138	6	)	)	PUNCT
cana-259	138	7	,	,	PUNCT
cana-259	138	8	continuous	continuous	ADJ
cana-259	138	9	vector	vector	NOUN
cana-259	138	10	d1	d1	PROPN
cana-259	138	11	and	and	CCONJ
cana-259	138	12	d2	d2	PROPN
cana-259	138	13	are	be	AUX
cana-259	138	14	constant	constant	ADJ
cana-259	138	15	matrix	matrix	NOUN
cana-259	138	16	m1	m1	NOUN
cana-259	138	17	,	,	PUNCT
cana-259	138	18	n1	n1	PROPN
cana-259	138	19	,	,	PUNCT
cana-259	138	20	m	m	NOUN
cana-259	138	21	2	2	NUM
cana-259	138	22	,	,	PUNCT
cana-259	138	23	and	and	CCONJ
cana-259	138	24	n2	n2	ADJ
cana-259	138	25	.	.	PUNCT
cana-259	139	1	in	in	ADP
cana-259	139	2	this	this	DET
cana-259	139	3	research	research	NOUN
cana-259	139	4	,	,	PUNCT
cana-259	139	5	it	it	PRON
cana-259	139	6	is	be	AUX
cana-259	139	7	assumed	assume	VERB
cana-259	139	8	that	that	SCONJ
cana-259	139	9	the	the	DET
cana-259	139	10	freeand	freeand	ADJ
cana-259	139	11	closed	close	VERB
cana-259	139	12	-	-	PUNCT
cana-259	139	13	loop	loop	NOUN
cana-259	139	14	cases	case	NOUN
cana-259	139	15	of	of	ADP
cana-259	139	16	the	the	DET
cana-259	139	17	pde	pde	NOUN
cana-259	139	18	system	system	NOUN
cana-259	139	19	(	(	PUNCT
cana-259	139	20	1)–(3	1)–(3	NUM
cana-259	139	21	)	)	PUNCT
cana-259	139	22	are	be	AUX
cana-259	139	23	well	well	ADV
cana-259	139	24	-	-	PUNCT
cana-259	139	25	stated	state	VERB
cana-259	139	26	.	.	PUNCT
cana-259	140	1	complex	complex	ADJ
cana-259	140	2	calculations	calculation	NOUN
cana-259	140	3	will	will	AUX
cana-259	140	4	be	be	AUX
cana-259	140	5	needed	need	VERB
cana-259	140	6	for	for	ADP
cana-259	140	7	the	the	DET
cana-259	140	8	well	well	ADJ
cana-259	140	9	-	-	PUNCT
cana-259	140	10	posedness	posedness	NOUN
cana-259	140	11	analysis	analysis	NOUN
cana-259	140	12	of	of	ADP
cana-259	140	13	the	the	DET
cana-259	140	14	pde	pde	NOUN
cana-259	140	15	system	system	NOUN
cana-259	140	16	(	(	PUNCT
cana-259	140	17	1)–(3	1)–(3	NUM
cana-259	140	18	)	)	PUNCT
cana-259	140	19	,	,	PUNCT
cana-259	140	20	even	even	ADV
cana-259	140	21	for	for	ADP
cana-259	140	22	basic	basic	ADJ
cana-259	140	23	pde	pde	NOUN
cana-259	140	24	networking	networking	NOUN
cana-259	140	25	with	with	ADP
cana-259	140	26	linear	linear	ADJ
cana-259	140	27	sdos	sdo	NOUN
cana-259	140	28	.	.	PUNCT
cana-259	141	1	[	[	X
cana-259	141	2	44	44	NUM
cana-259	141	3	]	]	PUNCT
cana-259	141	4	.	.	PUNCT
cana-259	142	1	we	we	PRON
cana-259	142	2	leave	leave	VERB
cana-259	142	3	it	it	PRON
cana-259	142	4	for	for	ADP
cana-259	142	5	future	future	ADJ
cana-259	142	6	research	research	NOUN
cana-259	142	7	because	because	SCONJ
cana-259	142	8	the	the	DET
cana-259	142	9	controller	controller	NOUN
cana-259	142	10	's	's	PART
cana-259	142	11	architecture	architecture	NOUN
cana-259	142	12	is	be	AUX
cana-259	142	13	the	the	DET
cana-259	142	14	primary	primary	ADJ
cana-259	142	15	topic	topic	NOUN
cana-259	142	16	of	of	ADP
cana-259	142	17	this	this	DET
cana-259	142	18	paper	paper	NOUN
cana-259	142	19	.	.	PUNCT
cana-259	143	1	the	the	DET
cana-259	143	2	operator	operator	NOUN
cana-259	143	3	a	a	PRON
cana-259	143	4	has	have	VERB
cana-259	143	5	a	a	DET
cana-259	143	6	specific	specific	ADJ
cana-259	143	7	domain	domain	NOUN
cana-259	143	8	,	,	PUNCT
cana-259	143	9	and	and	CCONJ
cana-259	143	10	the	the	DET
cana-259	143	11	input	input	NOUN
cana-259	143	12	operator	operator	NOUN
cana-259	143	13	is	be	AUX
cana-259	143	14	defined	define	VERB
cana-259	143	15	as	as	ADP
cana-259	143	16	u	u	NOUN
cana-259	143	17	=	=	NOUN
cana-259	143	18	b(z)u(t	b(z)u(t	NOUN
cana-259	143	19	)	)	PUNCT
cana-259	143	20	.	.	PUNCT
cana-259	144	1	therefore	therefore	ADV
cana-259	144	2	,	,	PUNCT
cana-259	144	3	the	the	DET
cana-259	144	4	nonlinear	nonlinear	ADJ
cana-259	144	5	pde	pde	NOUN
cana-259	144	6	system	system	NOUN
cana-259	144	7	(	(	PUNCT
cana-259	144	8	1)-(3	1)-(3	NOUN
cana-259	144	9	)	)	PUNCT
cana-259	144	10	can	can	AUX
cana-259	144	11	be	be	AUX
cana-259	144	12	restated	restate	VERB
cana-259	144	13	in	in	ADP
cana-259	144	14	a	a	DET
cana-259	144	15	simpler	simple	ADJ
cana-259	144	16	way	way	NOUN
cana-259	144	17	.	.	PUNCT
cana-259	145	1	iii	iii	NOUN
cana-259	145	2	means	mean	VERB
cana-259	145	3	the	the	DET
cana-259	145	4	third	third	ADJ
cana-259	145	5	in	in	ADP
cana-259	145	6	a	a	DET
cana-259	145	7	sequence	sequence	NOUN
cana-259	145	8	or	or	CCONJ
cana-259	145	9	the	the	DET
cana-259	145	10	roman	roman	ADJ
cana-259	145	11	numeral	numeral	ADJ
cana-259	145	12	for	for	ADP
cana-259	145	13	3	3	NUM
cana-259	145	14	.	.	PUNCT
cana-259	145	15	simplifying	simplify	VERB
cana-259	145	16	the	the	DET
cana-259	145	17	reduced	reduce	VERB
cana-259	145	18	-	-	PUNCT
cana-259	145	19	order	order	NOUN
cana-259	145	20	ode	ode	NOUN
cana-259	145	21	system	system	NOUN
cana-259	145	22	formula	formula	VERB
cana-259	145	23	the	the	DET
cana-259	145	24	nonlinear	nonlinear	ADJ
cana-259	145	25	sdo	sdo	NOUN
cana-259	145	26	of	of	ADP
cana-259	145	27	pde	pde	NOUN
cana-259	145	28	structure	structure	NOUN
cana-259	145	29	(	(	PUNCT
cana-259	145	30	5	5	NUM
cana-259	145	31	)	)	PUNCT
cana-259	145	32	prevents	prevent	VERB
cana-259	145	33	the	the	DET
cana-259	145	34	computation	computation	NOUN
cana-259	145	35	of	of	ADP
cana-259	145	36	the	the	DET
cana-259	145	37	mathematical	mathematical	ADJ
cana-259	145	38	formulae	formulae	NOUN
cana-259	145	39	for	for	ADP
cana-259	145	40	the	the	DET
cana-259	145	41	eigenvalues	eigenvalue	NOUN
cana-259	145	42	and	and	CCONJ
cana-259	145	43	eigenfunctions	eigenfunction	NOUN
cana-259	145	44	of	of	ADP
cana-259	145	45	the	the	DET
cana-259	145	46	pde	pde	NOUN
cana-259	145	47	system	system	NOUN
cana-259	145	48	.	.	PUNCT
cana-259	146	1	as	as	ADP
cana-259	146	2	a	a	DET
cana-259	146	3	result	result	NOUN
cana-259	146	4	,	,	PUNCT
cana-259	146	5	they	they	PRON
cana-259	146	6	prohibit	prohibit	VERB
cana-259	146	7	the	the	DET
cana-259	146	8	direct	direct	ADJ
cana-259	146	9	creation	creation	NOUN
cana-259	146	10	of	of	ADP
cana-259	146	11	finite	finite	ADJ
cana-259	146	12	-	-	ADJ
cana-259	146	13	dimensional	dimensional	ADJ
cana-259	146	14	approximations	approximation	NOUN
cana-259	146	15	of	of	ADP
cana-259	146	16	the	the	DET
cana-259	146	17	pde	pde	NOUN
cana-259	146	18	system	system	NOUN
cana-259	146	19	using	use	VERB
cana-259	146	20	conventional	conventional	ADJ
cana-259	146	21	basis	basis	NOUN
cana-259	146	22	symbol	symbol	NOUN
cana-259	146	23	sets	set	NOUN
cana-259	146	24	in	in	ADP
cana-259	146	25	combination	combination	NOUN
cana-259	146	26	with	with	ADP
cana-259	146	27	model	model	NOUN
cana-259	146	28	reduction	reduction	NOUN
cana-259	146	29	strategies	strategy	NOUN
cana-259	146	30	like	like	ADP
cana-259	146	31	galerkin	galerkin	PROPN
cana-259	146	32	's	's	PART
cana-259	146	33	approach	approach	NOUN
cana-259	146	34	and	and	CCONJ
cana-259	146	35	symmetric	symmetric	ADJ
cana-259	146	36	collocation	collocation	NOUN
cana-259	146	37	.	.	PUNCT
cana-259	147	1	to	to	PART
cana-259	147	2	circumvent	circumvent	VERB
cana-259	147	3	this	this	DET
cana-259	147	4	issue	issue	NOUN
cana-259	147	5	,	,	PUNCT
cana-259	147	6	we	we	PRON
cana-259	147	7	calculate	calculate	VERB
cana-259	147	8	a	a	DET
cana-259	147	9	collection	collection	NOUN
cana-259	147	10	of	of	ADP
cana-259	147	11	eefs	eef	NOUN
cana-259	147	12	(	(	PUNCT
cana-259	147	13	dominant	dominant	ADJ
cana-259	147	14	spatial	spatial	ADJ
cana-259	147	15	patterns	pattern	NOUN
cana-259	147	16	)	)	PUNCT
cana-259	147	17	of	of	ADP
cana-259	147	18	the	the	DET
cana-259	147	19	pde	pde	NOUN
cana-259	147	20	system	system	NOUN
cana-259	147	21	via	via	ADP
cana-259	147	22	the	the	DET
cana-259	147	23	retrospective	retrospective	ADJ
cana-259	147	24	technique	technique	NOUN
cana-259	147	25	first	first	ADV
cana-259	147	26	,	,	PUNCT
cana-259	147	27	using	use	VERB
cana-259	147	28	kld	kld	PROPN
cana-259	147	29	[	[	X
cana-259	147	30	24	24	NUM
cana-259	147	31	]	]	PUNCT
cana-259	147	32	.	.	PUNCT
cana-259	148	1	these	these	DET
cana-259	148	2	eefs	eef	NOUN
cana-259	148	3	will	will	AUX
cana-259	148	4	then	then	ADV
cana-259	148	5	be	be	AUX
cana-259	148	6	applied	apply	VERB
cana-259	148	7	in	in	ADP
cana-259	148	8	conjunction	conjunction	NOUN
cana-259	148	9	with	with	ADP
cana-259	148	10	the	the	DET
cana-259	148	11	sp	sp	NOUN
cana-259	148	12	method	method	NOUN
cana-259	148	13	to	to	PART
cana-259	148	14	obtain	obtain	VERB
cana-259	148	15	a	a	DET
cana-259	148	16	rom	rom	NOUN
cana-259	148	17	that	that	PRON
cana-259	148	18	precisely	precisely	ADV
cana-259	148	19	explains	explain	VERB
cana-259	148	20	the	the	DET
cana-259	148	21	prevailing	prevail	VERB
cana-259	148	22	dynamics	dynamic	NOUN
cana-259	148	23	of	of	ADP
cana-259	148	24	the	the	DET
cana-259	148	25	nonlinear	nonlinear	ADJ
cana-259	148	26	pde	pde	NOUN
cana-259	148	27	system	system	NOUN
cana-259	148	28	.	.	PUNCT
cana-259	149	1	a.	a.	PROPN
cana-259	149	2	eef	eef	PROPN
cana-259	149	3	computation	computation	NOUN
cana-259	149	4	using	use	VERB
cana-259	149	5	kld	kld	PROPN
cana-259	149	6	in	in	ADP
cana-259	149	7	many	many	ADJ
cana-259	149	8	engineering	engineering	NOUN
cana-259	149	9	domains	domain	NOUN
cana-259	149	10	,	,	PUNCT
cana-259	149	11	kld	kld	PROPN
cana-259	149	12	is	be	AUX
cana-259	149	13	a	a	DET
cana-259	149	14	well	well	ADV
cana-259	149	15	-	-	PUNCT
cana-259	149	16	liked	like	VERB
cana-259	149	17	statistical	statistical	ADJ
cana-259	149	18	pattern	pattern	NOUN
cana-259	149	19	analysis	analysis	NOUN
cana-259	149	20	technique	technique	NOUN
cana-259	149	21	for	for	ADP
cana-259	149	22	identifying	identify	VERB
cana-259	149	23	the	the	DET
cana-259	149	24	dominating	dominating	NOUN
cana-259	149	25	structure	structure	NOUN
cana-259	149	26	in	in	ADP
cana-259	149	27	a	a	DET
cana-259	149	28	collection	collection	NOUN
cana-259	149	29	of	of	ADP
cana-259	149	30	a	a	DET
cana-259	149	31	multidimensional	multidimensional	ADJ
cana-259	149	32	process	process	NOUN
cana-259	149	33	and	and	CCONJ
cana-259	149	34	deriving	derive	VERB
cana-259	149	35	low	low	ADJ
cana-259	149	36	-	-	PUNCT
cana-259	149	37	dimensional	dimensional	ADJ
cana-259	149	38	accurate	accurate	ADJ
cana-259	149	39	descriptions	description	NOUN
cana-259	149	40	.	.	PUNCT
cana-259	150	1	given	give	VERB
cana-259	150	2	a	a	DET
cana-259	150	3	set	set	NOUN
cana-259	150	4	of	of	ADP
cana-259	150	5	data	datum	NOUN
cana-259	150	6	,	,	PUNCT
cana-259	150	7	kld	kld	PROPN
cana-259	150	8	gives	give	VERB
cana-259	150	9	an	an	DET
cana-259	150	10	estimate	estimate	NOUN
cana-259	150	11	of	of	ADP
cana-259	150	12	how	how	SCONJ
cana-259	150	13	much	much	ADJ
cana-259	150	14	each	each	DET
cana-259	150	15	eef	eef	PROPN
cana-259	150	16	contributes	contribute	VERB
cana-259	150	17	in	in	ADP
cana-259	150	18	relation	relation	NOUN
cana-259	150	19	to	to	ADP
cana-259	150	20	the	the	DET
cana-259	150	21	group	group	NOUN
cana-259	150	22	's	's	PART
cana-259	150	23	total	total	ADJ
cana-259	150	24	"	"	PUNCT
cana-259	150	25	electricity	electricity	NOUN
cana-259	150	26	"	"	PUNCT
cana-259	150	27	(	(	PUNCT
cana-259	150	28	mean	mean	ADJ
cana-259	150	29	-	-	PUNCT
cana-259	150	30	square	square	NOUN
cana-259	150	31	fluctuation	fluctuation	NOUN
cana-259	150	32	)	)	PUNCT
cana-259	150	33	.	.	PUNCT
cana-259	151	1	in	in	ADP
cana-259	151	2	addition	addition	NOUN
cana-259	151	3	,	,	PUNCT
cana-259	151	4	it	it	PRON
cana-259	151	5	generates	generate	VERB
cana-259	151	6	a	a	DET
cana-259	151	7	collection	collection	NOUN
cana-259	151	8	of	of	ADP
cana-259	151	9	orthogonal	orthogonal	ADJ
cana-259	151	10	eefs	eef	NOUN
cana-259	151	11	for	for	ADP
cana-259	151	12	the	the	DET
cana-259	151	13	mathematical	mathematical	ADJ
cana-259	151	14	model	model	NOUN
cana-259	151	15	that	that	PRON
cana-259	151	16	comprise	comprise	VERB
cana-259	151	17	the	the	DET
cana-259	151	18	community	community	NOUN
cana-259	151	19	.	.	PUNCT
cana-259	152	1	the	the	DET
cana-259	152	2	image	image	NOUN
cana-259	152	3	of	of	ADP
cana-259	152	4	the	the	DET
cana-259	152	5	trimmed	trim	VERB
cana-259	152	6	series	series	NOUN
cana-259	152	7	of	of	ADP
cana-259	152	8	games	game	NOUN
cana-259	152	9	,	,	PUNCT
cana-259	152	10	as	as	SCONJ
cana-259	152	11	has	have	VERB
cana-259	152	12	a	a	DET
cana-259	152	13	lower	low	ADJ
cana-259	152	14	mean	mean	ADJ
cana-259	152	15	-	-	PUNCT
cana-259	152	16	square	square	NOUN
cana-259	152	17	error	error	NOUN
cana-259	152	18	than	than	ADP
cana-259	152	19	the	the	DET
cana-259	152	20	other	other	ADJ
cana-259	152	21	basis	basis	NOUN
cana-259	152	22	of	of	ADP
cana-259	152	23	one	one	NUM
cana-259	152	24	dimensions	dimension	NOUN
cana-259	152	25	is	be	AUX
cana-259	152	26	thus	thus	ADV
cana-259	152	27	best	well	ADV
cana-259	152	28	served	serve	VERB
cana-259	152	29	by	by	ADP
cana-259	152	30	the	the	DET
cana-259	152	31	eefs	eef	NOUN
cana-259	152	32	as	as	ADP
cana-259	152	33	an	an	DET
cana-259	152	34	ideal	ideal	ADJ
cana-259	152	35	basis	basis	NOUN
cana-259	152	36	.	.	PUNCT
cana-259	153	1	stated	state	VERB
cana-259	153	2	differently	differently	ADV
cana-259	153	3	,	,	PUNCT
cana-259	153	4	more	more	ADJ
cana-259	153	5	energy	energy	NOUN
cana-259	153	6	is	be	AUX
cana-259	153	7	captured	capture	VERB
cana-259	153	8	by	by	ADP
cana-259	153	9	the	the	DET
cana-259	153	10	communications	communication	NOUN
cana-259	153	11	on	on	ADP
cana-259	153	12	applied	apply	VERB
cana-259	153	13	nonlinear	nonlinear	ADJ
cana-259	153	14	analysis	analysis	NOUN
cana-259	153	15	issn	issn	NOUN
cana-259	153	16	:	:	PUNCT
cana-259	153	17	1074	1074	NUM
cana-259	153	18	-	-	PUNCT
cana-259	153	19	133x	133x	NUM
cana-259	153	20	vol	vol	NOUN
cana-259	153	21	30	30	NUM
cana-259	153	22	no	no	NOUN
cana-259	153	23	.	.	NOUN
cana-259	153	24	2	2	NUM
cana-259	153	25	(	(	PUNCT
cana-259	153	26	2023	2023	NUM
cana-259	153	27	)	)	PUNCT
cana-259	153	28	6	6	NUM
cana-259	153	29	https://internationalpubls.com	https://internationalpubls.com	X
cana-259	153	30	projection	projection	NOUN
cana-259	153	31	onto	onto	ADP
cana-259	153	32	the	the	DET
cana-259	153	33	first	first	ADJ
cana-259	153	34	few	few	ADJ
cana-259	153	35	eefs	eef	NOUN
cana-259	153	36	than	than	ADP
cana-259	153	37	by	by	ADP
cana-259	153	38	any	any	DET
cana-259	153	39	subsequent	subsequent	ADJ
cana-259	153	40	projection	projection	NOUN
cana-259	153	41	.	.	PUNCT
cana-259	154	1	because	because	SCONJ
cana-259	154	2	of	of	ADP
cana-259	154	3	these	these	DET
cana-259	154	4	characteristics	characteristic	NOUN
cana-259	154	5	,	,	PUNCT
cana-259	154	6	the	the	DET
cana-259	154	7	eefs	eef	NOUN
cana-259	154	8	are	be	AUX
cana-259	154	9	a	a	DET
cana-259	154	10	suitable	suitable	ADJ
cana-259	154	11	choice	choice	NOUN
cana-259	154	12	to	to	PART
cana-259	154	13	take	take	VERB
cana-259	154	14	into	into	ADP
cana-259	154	15	account	account	NOUN
cana-259	154	16	while	while	SCONJ
cana-259	154	17	reducing	reduce	VERB
cana-259	154	18	models	model	NOUN
cana-259	154	19	.	.	PUNCT
cana-259	155	1	we	we	PRON
cana-259	155	2	now	now	ADV
cana-259	155	3	quickly	quickly	ADV
cana-259	155	4	go	go	VERB
cana-259	155	5	over	over	ADP
cana-259	155	6	the	the	DET
cana-259	155	7	kld	kld	NOUN
cana-259	155	8	process	process	NOUN
cana-259	155	9	for	for	ADP
cana-259	155	10	composing	compose	VERB
cana-259	155	11	eefs	eef	NOUN
cana-259	155	12	using	use	VERB
cana-259	155	13	the	the	DET
cana-259	155	14	quick	quick	ADJ
cana-259	155	15	snapshot	snapshot	NOUN
cana-259	155	16	technique	technique	NOUN
cana-259	155	17	within	within	ADP
cana-259	155	18	the	the	DET
cana-259	155	19	context	context	NOUN
cana-259	155	20	of	of	ADP
cana-259	155	21	divergent	divergent	ADJ
cana-259	155	22	dynamic	dynamic	ADJ
cana-259	155	23	pde	pde	NOUN
cana-259	155	24	circuits	circuit	NOUN
cana-259	155	25	.	.	PUNCT
cana-259	156	1	collect	collect	AUX
cana-259	156	2	m	m	AUX
cana-259	156	3	sampling	sample	VERB
cana-259	156	4	states	state	NOUN
cana-259	156	5	of	of	ADP
cana-259	156	6	the	the	DET
cana-259	156	7	pde	pde	NOUN
cana-259	156	8	system	system	NOUN
cana-259	156	9	(	(	PUNCT
cana-259	156	10	with	with	ADP
cana-259	156	11	u	u	NOUN
cana-259	156	12	0	0	NUM
cana-259	156	13	)	)	PUNCT
cana-259	156	14	(	(	PUNCT
cana-259	156	15	5	5	NUM
cana-259	156	16	)	)	PUNCT
cana-259	156	17	,	,	PUNCT
cana-259	156	18	represented	represent	VERB
cana-259	156	19	as	as	ADP
cana-259	156	20	yi(z	yi(z	NOUN
cana-259	156	21	)	)	PUNCT
cana-259	156	22	,	,	PUNCT
cana-259	156	23	so	so	SCONJ
cana-259	156	24	that	that	SCONJ
cana-259	156	25	the	the	DET
cana-259	156	26	set	set	NOUN
cana-259	156	27	is	be	AUX
cana-259	156	28	sufficiently	sufficiently	ADV
cana-259	156	29	big	big	ADJ
cana-259	156	30	(	(	PUNCT
cana-259	156	31	referred	refer	VERB
cana-259	156	32	to	to	ADP
cana-259	156	33	as	as	ADP
cana-259	156	34	an	an	DET
cana-259	156	35	ensemble	ensemble	ADJ
cana-259	156	36	)	)	PUNCT
cana-259	156	37	.	.	PUNCT
cana-259	157	1	yi(z	yi(z	NOUN
cana-259	157	2	)	)	PUNCT
cana-259	157	3	,	,	PUNCT
cana-259	157	4	i	i	PRON
cana-259	157	5	=	=	NOUN
cana-259	157	6	1,	1,	NUM
cana-259	157	7	...	...	PUNCT
cana-259	157	8	,m	,m	PUNCT
cana-259	157	9	,	,	PUNCT
cana-259	157	10	are	be	AUX
cana-259	157	11	referred	refer	VERB
cana-259	157	12	to	to	ADP
cana-259	157	13	as	as	ADP
cana-259	157	14	"	"	PUNCT
cana-259	157	15	pictures	picture	NOUN
cana-259	157	16	"	"	PUNCT
cana-259	157	17	of	of	ADP
cana-259	157	18	the	the	DET
cana-259	157	19	(	(	PUNCT
cana-259	157	20	5	5	NUM
cana-259	157	21	)	)	PUNCT
cana-259	157	22	solution	solution	NOUN
cana-259	157	23	.	.	PUNCT
cana-259	158	1	given	give	VERB
cana-259	158	2	the	the	DET
cana-259	158	3	assumption	assumption	NOUN
cana-259	158	4	that	that	SCONJ
cana-259	158	5	the	the	DET
cana-259	158	6	snapshots	snapshot	NOUN
cana-259	158	7	yi(z	yi(z	NOUN
cana-259	158	8	)	)	PUNCT
cana-259	158	9	obtained	obtain	VERB
cana-259	158	10	from	from	ADP
cana-259	158	11	the	the	DET
cana-259	158	12	pde	pde	NOUN
cana-259	158	13	system	system	NOUN
cana-259	158	14	(	(	PUNCT
cana-259	158	15	5	5	X
cana-259	158	16	)	)	PUNCT
cana-259	158	17	exhibit	exhibit	VERB
cana-259	158	18	ergodic	ergodic	ADJ
cana-259	158	19	behavior	behavior	NOUN
cana-259	158	20	[	[	X
cana-259	158	21	45	45	NUM
cana-259	158	22	]	]	PUNCT
cana-259	158	23	,	,	PUNCT
cana-259	158	24	the	the	DET
cana-259	158	25	following	follow	VERB
cana-259	158	26	is	be	AUX
cana-259	158	27	an	an	DET
cana-259	158	28	expression	expression	NOUN
cana-259	158	29	for	for	ADP
cana-259	158	30	the	the	DET
cana-259	158	31	spatial	spatial	ADJ
cana-259	158	32	association	association	NOUN
cana-259	158	33	value	value	NOUN
cana-259	158	34	:	:	PUNCT
cana-259	158	35	the	the	DET
cana-259	158	36	mercer	mercer	PROPN
cana-259	158	37	theorem	theorem	VERB
cana-259	158	38	[	[	X
cana-259	158	39	46	46	NUM
cana-259	158	40	]	]	PUNCT
cana-259	158	41	states	state	VERB
cana-259	158	42	that	that	SCONJ
cana-259	158	43	r(z	r(z	NOUN
cana-259	158	44	,	,	PUNCT
cana-259	158	45	ξ	ξ	X
cana-259	158	46	)	)	PUNCT
cana-259	158	47	possesses	possess	VERB
cana-259	158	48	a	a	DET
cana-259	158	49	characteristic	characteristic	NOUN
cana-259	158	50	that	that	SCONJ
cana-259	158	51	where	where	SCONJ
cana-259	158	52	the	the	DET
cana-259	158	53	orthogonal	orthogonal	ADJ
cana-259	158	54	eigenfunctions	eigenfunction	NOUN
cana-259	158	55	of	of	ADP
cana-259	158	56	r(z	r(z	PROPN
cana-259	158	57	,	,	PUNCT
cana-259	158	58	ξ	ξ	X
cana-259	158	59	)	)	PUNCT
cana-259	158	60	are	be	AUX
cana-259	158	61	represented	represent	VERB
cana-259	158	62	by	by	ADP
cana-259	158	63	φi(z	φi(z	NOUN
cana-259	158	64	)	)	PUNCT
cana-259	158	65	while	while	SCONJ
cana-259	158	66	the	the	DET
cana-259	158	67	positive	positive	ADJ
cana-259	158	68	eigenvalues	eigenvalue	NOUN
cana-259	158	69	by	by	ADP
cana-259	158	70	λi	λi	INTJ
cana-259	158	71	.	.	NOUN
cana-259	158	72	taking	take	VERB
cana-259	158	73	into	into	ADP
cana-259	158	74	account	account	NOUN
cana-259	158	75	the	the	DET
cana-259	158	76	subsequent	subsequent	ADJ
cana-259	158	77	integral	integral	ADJ
cana-259	158	78	and	and	CCONJ
cana-259	158	79	employing	employ	VERB
cana-259	158	80	(	(	PUNCT
cana-259	158	81	6	6	NUM
cana-259	158	82	)	)	PUNCT
cana-259	158	83	,	,	PUNCT
cana-259	158	84	we	we	PRON
cana-259	158	85	've	have	AUX
cana-259	158	86	communications	communication	NOUN
cana-259	158	87	on	on	ADP
cana-259	158	88	applied	apply	VERB
cana-259	158	89	nonlinear	nonlinear	ADJ
cana-259	158	90	analysis	analysis	NOUN
cana-259	158	91	issn	issn	NOUN
cana-259	158	92	:	:	PUNCT
cana-259	158	93	1074	1074	NUM
cana-259	158	94	-	-	PUNCT
cana-259	158	95	133x	133x	NUM
cana-259	158	96	vol	vol	NOUN
cana-259	158	97	30	30	NUM
cana-259	159	1	no	no	NOUN
cana-259	159	2	.	.	NOUN
cana-259	159	3	2	2	NUM
cana-259	159	4	(	(	PUNCT
cana-259	159	5	2023	2023	NUM
cana-259	159	6	)	)	PUNCT
cana-259	159	7	7	7	NUM
cana-259	159	8	https://internationalpubls.com	https://internationalpubls.com	X
cana-259	159	9	where	where	SCONJ
cana-259	159	10	,	,	PUNCT
cana-259	159	11	αji	αji	NOUN
cana-259	159	12	=	=	PUNCT
cana-259	159	13	λ−i	λ−i	NOUN
cana-259	159	14	1ϑj	1ϑj	ADJ
cana-259	159	15	.	.	PUNCT
cana-259	160	1	observe	observe	VERB
cana-259	160	2	that	that	SCONJ
cana-259	160	3	the	the	DET
cana-259	160	4	eefs	eef	NOUN
cana-259	160	5	{	{	PUNCT
cana-259	160	6	\i(z	\i(z	ADV
cana-259	160	7	)	)	PUNCT
cana-259	160	8	}	}	PUNCT
cana-259	160	9	are	be	AUX
cana-259	160	10	merely	merely	ADV
cana-259	160	11	linear	linear	ADJ
cana-259	160	12	mixtures	mixture	NOUN
cana-259	160	13	of	of	ADP
cana-259	160	14	snapshots	snapshot	NOUN
cana-259	160	15	{	{	PUNCT
cana-259	160	16	yi(z	yi(z	NOUN
cana-259	160	17	)	)	PUNCT
cana-259	160	18	}	}	PUNCT
cana-259	160	19	;	;	PUNCT
cana-259	160	20	hence	hence	ADV
cana-259	160	21	,	,	PUNCT
cana-259	160	22	the	the	DET
cana-259	160	23	computation	computation	NOUN
cana-259	160	24	of	of	ADP
cana-259	160	25	the	the	DET
cana-259	160	26	coefficients	coefficient	NOUN
cana-259	160	27	is	be	AUX
cana-259	160	28	all	all	PRON
cana-259	160	29	that	that	PRON
cana-259	160	30	is	be	AUX
cana-259	160	31	needed	need	VERB
cana-259	160	32	to	to	PART
cana-259	160	33	compute	compute	VERB
cana-259	160	34	the	the	DET
cana-259	160	35	eefs	eef	NOUN
cana-259	160	36	.	.	PUNCT
cana-259	161	1	[	[	X
cana-259	161	2	α1	α1	PROPN
cana-259	161	3	·	·	SYM
cana-259	161	4	·	·	SYM
cana-259	161	5	·	·	SYM
cana-259	161	6	α1i	α1i	NOUN
cana-259	161	7	<	<	X
cana-259	161	8	ami	ami	NOUN
cana-259	161	9	]	]	PUNCT
cana-259	161	10	=	=	SYM
cana-259	161	11	δt	δt	X
cana-259	161	12	.	.	PUNCT
cana-259	162	1	reorganizing	reorganize	VERB
cana-259	162	2	(	(	PUNCT
cana-259	162	3	7	7	NUM
cana-259	162	4	)	)	PUNCT
cana-259	162	5	and	and	CCONJ
cana-259	162	6	putting	put	VERB
cana-259	162	7	(	(	PUNCT
cana-259	162	8	6	6	NUM
cana-259	162	9	)	)	PUNCT
cana-259	162	10	and	and	CCONJ
cana-259	162	11	(	(	PUNCT
cana-259	162	12	9	9	NUM
cana-259	162	13	)	)	PUNCT
cana-259	162	14	into	into	ADP
cana-259	162	15	(	(	PUNCT
cana-259	162	16	7	7	X
cana-259	162	17	)	)	PUNCT
cana-259	162	18	produce	produce	VERB
cana-259	162	19	y	y	PROPN
cana-259	162	20	(	(	PUNCT
cana-259	162	21	z	z	NOUN
cana-259	162	22	)	)	PUNCT
cana-259	162	23	(	(	PUNCT
cana-259	162	24	cαi	cαi	PROPN
cana-259	162	25	)	)	PUNCT
cana-259	162	26	=	=	SYM
cana-259	162	27	y	y	PROPN
cana-259	162	28	(	(	PUNCT
cana-259	162	29	z	z	NOUN
cana-259	162	30	)	)	PUNCT
cana-259	162	31	(	(	PUNCT
cana-259	162	32	λiαi	λiαi	ADV
cana-259	162	33	)	)	PUNCT
cana-259	162	34	(	(	PUNCT
cana-259	162	35	10	10	NUM
cana-259	162	36	)	)	PUNCT
cana-259	162	37	the	the	DET
cana-259	162	38	conventional	conventional	ADJ
cana-259	162	39	method	method	NOUN
cana-259	162	40	of	of	ADP
cana-259	162	41	evaluation	evaluation	NOUN
cana-259	162	42	deconstruction	deconstruction	NOUN
cana-259	162	43	can	can	AUX
cana-259	162	44	be	be	AUX
cana-259	162	45	used	use	VERB
cana-259	162	46	to	to	PART
cana-259	162	47	calculate	calculate	VERB
cana-259	162	48	all	all	DET
cana-259	162	49	eigenvectors	eigenvector	NOUN
cana-259	162	50	are	be	AUX
cana-259	162	51	{	{	PUNCT
cana-259	162	52	αi	αi	NOUN
cana-259	162	53	}	}	PUNCT
cana-259	162	54	and	and	CCONJ
cana-259	162	55	related	relate	VERB
cana-259	162	56	eigenvalues	eigenvalue	NOUN
cana-259	162	57	{	{	PUNCT
cana-259	162	58	λi	λi	NOUN
cana-259	162	59	}	}	PUNCT
cana-259	162	60	for	for	ADP
cana-259	162	61	the	the	DET
cana-259	162	62	subsequent	subsequent	ADJ
cana-259	162	63	eigenvalue	eigenvalue	PROPN
cana-259	162	64	issues	issue	NOUN
cana-259	162	65	include	include	VERB
cana-259	162	66	cαi	cαi	NOUN
cana-259	162	67	=	=	SYM
cana-259	162	68	λiαi	λiαi	ADV
cana-259	162	69	,	,	PUNCT
cana-259	162	70	assumes	assume	VERB
cana-259	162	71	linear	linear	ADJ
cana-259	162	72	independence	independence	NOUN
cana-259	162	73	of	of	ADP
cana-259	162	74	the	the	DET
cana-259	162	75	set	set	NOUN
cana-259	162	76	{	{	PUNCT
cana-259	162	77	yi(z	yi(z	NOUN
cana-259	162	78	)	)	PUNCT
cana-259	162	79	}	}	PUNCT
cana-259	162	80	.	.	PUNCT
cana-259	163	1	after	after	ADP
cana-259	163	2	standardising	standardise	VERB
cana-259	163	3	the	the	DET
cana-259	163	4	eigenvector	eigenvector	NOUN
cana-259	163	5	αi	αi	NOUN
cana-259	163	6	to	to	PART
cana-259	163	7	meet	meet	VERB
cana-259	163	8	αi	αi	PRON
cana-259	163	9	,	,	PUNCT
cana-259	163	10	αi	αi	PROPN
cana-259	163	11	rm	rm	NOUN
cana-259	163	12	=	=	PUNCT
cana-259	163	13	1/(m	1/(m	PROPN
cana-259	163	14	λi	λi	NOUN
cana-259	163	15	)	)	PUNCT
cana-259	163	16	,	,	PUNCT
cana-259	163	17	eefs	eef	NOUN
cana-259	163	18	can	can	AUX
cana-259	163	19	be	be	AUX
cana-259	163	20	globally	globally	ADV
cana-259	163	21	orthogonal	orthogonal	ADJ
cana-259	163	22	.	.	PUNCT
cana-259	164	1	next	next	ADJ
cana-259	164	2	,	,	PUNCT
cana-259	164	3	using	use	VERB
cana-259	164	4	(	(	PUNCT
cana-259	164	5	9	9	NUM
cana-259	164	6	)	)	PUNCT
cana-259	164	7	,	,	PUNCT
cana-259	164	8	all	all	DET
cana-259	164	9	eefs	eef	NOUN
cana-259	164	10	φi(z	φi(z	NOUN
cana-259	164	11	)	)	PUNCT
cana-259	164	12	are	be	AUX
cana-259	164	13	obtained	obtain	VERB
cana-259	164	14	directly	directly	ADV
cana-259	164	15	.	.	PUNCT
cana-259	165	1	remark	remark	NOUN
cana-259	165	2	1	1	NUM
cana-259	165	3	:	:	PUNCT
cana-259	165	4	it	it	PRON
cana-259	165	5	is	be	AUX
cana-259	165	6	important	important	ADJ
cana-259	165	7	to	to	PART
cana-259	165	8	note	note	VERB
cana-259	165	9	because	because	SCONJ
cana-259	165	10	in	in	ADP
cana-259	165	11	the	the	DET
cana-259	165	12	pde	pde	NOUN
cana-259	165	13	system	system	NOUN
cana-259	165	14	(	(	PUNCT
cana-259	165	15	5	5	NUM
cana-259	165	16	)	)	PUNCT
cana-259	165	17	,	,	PUNCT
cana-259	165	18	i.e.	i.e.	X
cana-259	165	19	,	,	PUNCT
cana-259	165	20	(	(	PUNCT
cana-259	165	21	φi(z	φi(z	NOUN
cana-259	165	22	)	)	PUNCT
cana-259	165	23	)	)	PUNCT
cana-259	166	1	=	=	PUNCT
cana-259	166	2	λiφi(z	λiφi(z	PROPN
cana-259	166	3	)	)	PUNCT
cana-259	166	4	,	,	PUNCT
cana-259	166	5	the	the	DET
cana-259	166	6	eigen	eigen	PROPN
cana-259	166	7	functions	function	NOUN
cana-259	166	8	and	and	CCONJ
cana-259	166	9	eigenvalues	eigenvalue	NOUN
cana-259	166	10	of	of	ADP
cana-259	166	11	the	the	DET
cana-259	166	12	operator	operator	NOUN
cana-259	166	13	(	(	PUNCT
cana-259	166	14	y	y	NOUN
cana-259	166	15	)	)	PUNCT
cana-259	166	16	are	be	AUX
cana-259	166	17	not	not	PART
cana-259	166	18	the	the	DET
cana-259	166	19	eefs	eef	NOUN
cana-259	166	20	and	and	CCONJ
cana-259	166	21	their	their	PRON
cana-259	166	22	corresponding	corresponding	ADJ
cana-259	166	23	eigenvalues	eigenvalue	NOUN
cana-259	166	24	.	.	PUNCT
cana-259	167	1	the	the	DET
cana-259	167	2	amplitude	amplitude	NOUN
cana-259	167	3	of	of	ADP
cana-259	167	4	an	an	DET
cana-259	167	5	eef	eef	PROPN
cana-259	167	6	,	,	PUNCT
cana-259	167	7	which	which	PRON
cana-259	167	8	stands	stand	VERB
cana-259	167	9	for	for	ADP
cana-259	167	10	the	the	DET
cana-259	167	11	"	"	PUNCT
cana-259	167	12	architecture	architecture	NOUN
cana-259	167	13	"	"	PUNCT
cana-259	167	14	that	that	PRON
cana-259	167	15	symbolizes	symbolize	VERB
cana-259	167	16	the	the	DET
cana-259	167	17	cohesion	cohesion	NOUN
cana-259	167	18	of	of	ADP
cana-259	167	19	the	the	DET
cana-259	167	20	outfit	outfit	NOUN
cana-259	167	21	,	,	PUNCT
cana-259	167	22	which	which	PRON
cana-259	167	23	consisted	consist	VERB
cana-259	167	24	is	be	AUX
cana-259	167	25	the	the	DET
cana-259	167	26	matching	match	VERB
cana-259	167	27	force	force	NOUN
cana-259	167	28	that	that	PRON
cana-259	167	29	is	be	AUX
cana-259	167	30	recorded	record	VERB
cana-259	167	31	.	.	PUNCT
cana-259	168	1	b.	b.	PROPN
cana-259	168	2	using	use	VERB
cana-259	168	3	sp	sp	ADP
cana-259	168	4	methodology	methodology	NOUN
cana-259	168	5	to	to	PART
cana-259	168	6	derive	derive	VERB
cana-259	168	7	reduced	reduce	VERB
cana-259	168	8	-	-	PUNCT
cana-259	168	9	order	order	NOUN
cana-259	168	10	ode	ode	NOUN
cana-259	168	11	modeling	modeling	NOUN
cana-259	168	12	the	the	DET
cana-259	168	13	primary	primary	ADJ
cana-259	168	14	characteristic	characteristic	NOUN
cana-259	168	15	of	of	ADP
cana-259	168	16	parabolic	parabolic	ADJ
cana-259	168	17	pde	pde	NOUN
cana-259	168	18	systems	system	NOUN
cana-259	168	19	,	,	PUNCT
cana-259	168	20	which	which	PRON
cana-259	168	21	are	be	AUX
cana-259	168	22	very	very	ADV
cana-259	168	23	dissipative	dissipative	ADJ
cana-259	168	24	,	,	PUNCT
cana-259	168	25	is	be	AUX
cana-259	168	26	the	the	DET
cana-259	168	27	ability	ability	NOUN
cana-259	168	28	to	to	PART
cana-259	168	29	divide	divide	VERB
cana-259	168	30	the	the	DET
cana-259	168	31	sdo	sdo	NOUN
cana-259	168	32	's	's	PART
cana-259	168	33	eigen	eigen	PROPN
cana-259	168	34	spectrum	spectrum	NOUN
cana-259	168	35	into	into	ADP
cana-259	168	36	a	a	DET
cana-259	168	37	stable	stable	ADJ
cana-259	168	38	fast	fast	ADJ
cana-259	168	39	complement	complement	NOUN
cana-259	168	40	and	and	CCONJ
cana-259	168	41	a	a	DET
cana-259	168	42	finite	finite	ADJ
cana-259	168	43	-	-	ADJ
cana-259	168	44	dimensional	dimensional	ADJ
cana-259	168	45	slow	slow	ADJ
cana-259	168	46	one	one	NUM
cana-259	168	47	.	.	PUNCT
cana-259	169	1	this	this	PRON
cana-259	169	2	suggests	suggest	VERB
cana-259	169	3	that	that	SCONJ
cana-259	169	4	finite	finite	ADJ
cana-259	169	5	-	-	ADJ
cana-259	169	6	dimensional	dimensional	ADJ
cana-259	169	7	slow	slow	ADJ
cana-259	169	8	systems	system	NOUN
cana-259	169	9	can	can	AUX
cana-259	169	10	adequately	adequately	ADV
cana-259	169	11	explain	explain	VERB
cana-259	169	12	the	the	DET
cana-259	169	13	prevailing	prevail	VERB
cana-259	169	14	dynamic	dynamic	ADJ
cana-259	169	15	behavior	behavior	NOUN
cana-259	169	16	of	of	ADP
cana-259	169	17	such	such	ADJ
cana-259	169	18	systems	system	NOUN
cana-259	169	19	[	[	X
cana-259	169	20	20	20	NUM
cana-259	169	21	]	]	PUNCT
cana-259	169	22	,	,	PUNCT
cana-259	169	23	[	[	X
cana-259	169	24	21	21	NUM
cana-259	169	25	]	]	PUNCT
cana-259	169	26	,	,	PUNCT
cana-259	169	27	[	[	X
cana-259	169	28	48	48	NUM
cana-259	169	29	]	]	PUNCT
cana-259	169	30	.	.	PUNCT
cana-259	170	1	nevertheless	nevertheless	ADV
cana-259	170	2	,	,	PUNCT
cana-259	170	3	it	it	PRON
cana-259	170	4	is	be	AUX
cana-259	170	5	frequently	frequently	ADV
cana-259	170	6	impossible	impossible	ADJ
cana-259	170	7	to	to	PART
cana-259	170	8	obtain	obtain	VERB
cana-259	170	9	the	the	DET
cana-259	170	10	nonlinear	nonlinear	ADJ
cana-259	170	11	sdo	sdo	NOUN
cana-259	170	12	's	's	PART
cana-259	170	13	eigen	eigen	PROPN
cana-259	170	14	spectrum	spectrum	NOUN
cana-259	170	15	.	.	PUNCT
cana-259	171	1	the	the	DET
cana-259	171	2	division	division	NOUN
cana-259	171	3	of	of	ADP
cana-259	171	4	the	the	DET
cana-259	171	5	pde	pde	NOUN
cana-259	171	6	system	system	NOUN
cana-259	171	7	using	use	VERB
cana-259	171	8	eefs	eef	NOUN
cana-259	171	9	is	be	AUX
cana-259	171	10	essentially	essentially	ADV
cana-259	171	11	not	not	PART
cana-259	171	12	distinctive	distinctive	ADJ
cana-259	171	13	from	from	ADP
cana-259	171	14	using	use	VERB
cana-259	171	15	other	other	ADJ
cana-259	171	16	conventional	conventional	ADJ
cana-259	171	17	basis	basis	NOUN
cana-259	171	18	functions	function	NOUN
cana-259	171	19	sets	set	NOUN
cana-259	171	20	,	,	PUNCT
cana-259	171	21	such	such	ADJ
cana-259	171	22	as	as	ADP
cana-259	171	23	the	the	DET
cana-259	171	24	legendary	legendary	ADJ
cana-259	171	25	equations	equation	NOUN
cana-259	171	26	and	and	CCONJ
cana-259	171	27	sine	sine	NOUN
cana-259	171	28	and	and	CCONJ
cana-259	171	29	cosine	cosine	NOUN
cana-259	171	30	functions	function	NOUN
cana-259	171	31	.	.	PUNCT
cana-259	172	1	if	if	SCONJ
cana-259	172	2	the	the	DET
cana-259	172	3	collection	collection	NOUN
cana-259	172	4	of	of	ADP
cana-259	172	5	pictures	picture	NOUN
cana-259	172	6	is	be	AUX
cana-259	172	7	sufficiently	sufficiently	ADV
cana-259	172	8	vast	vast	ADJ
cana-259	172	9	and	and	CCONJ
cana-259	172	10	includes	include	VERB
cana-259	172	11	sufficient	sufficient	ADJ
cana-259	172	12	data	datum	NOUN
cana-259	172	13	on	on	ADP
cana-259	172	14	the	the	DET
cana-259	172	15	pde	pde	NOUN
cana-259	172	16	system	system	NOUN
cana-259	172	17	's	's	PART
cana-259	172	18	worldwide	worldwide	ADJ
cana-259	172	19	fluctuations	fluctuation	NOUN
cana-259	172	20	[	[	X
cana-259	172	21	21	21	NUM
cana-259	172	22	]	]	PUNCT
cana-259	172	23	.	.	PUNCT
cana-259	173	1	by	by	ADP
cana-259	173	2	omitting	omit	VERB
cana-259	173	3	the	the	DET
cana-259	173	4	fast	fast	ADJ
cana-259	173	5	modes	mode	NOUN
cana-259	173	6	outright	outright	ADV
cana-259	173	7	,	,	PUNCT
cana-259	173	8	galerkin	galerkin	PROPN
cana-259	173	9	's	's	PART
cana-259	173	10	technique	technique	NOUN
cana-259	173	11	was	be	AUX
cana-259	173	12	used	use	VERB
cana-259	173	13	in	in	ADP
cana-259	173	14	[	[	X
cana-259	173	15	17]–[19	17]–[19	NUM
cana-259	173	16	]	]	X
cana-259	173	17	,	,	PUNCT
cana-259	173	18	[	[	X
cana-259	173	19	21	21	NUM
cana-259	173	20	]	]	PUNCT
cana-259	173	21	,	,	PUNCT
cana-259	173	22	and	and	CCONJ
cana-259	173	23	[	[	X
cana-259	173	24	22	22	NUM
cana-259	173	25	]	]	PUNCT
cana-259	173	26	to	to	PART
cana-259	173	27	develop	develop	VERB
cana-259	173	28	an	an	DET
cana-259	173	29	eef	eef	PROPN
cana-259	173	30	-	-	PUNCT
cana-259	173	31	based	base	VERB
cana-259	173	32	finite	finite	ADJ
cana-259	173	33	-	-	ADJ
cana-259	173	34	dimensional	dimensional	ADJ
cana-259	173	35	ode	ode	ADJ
cana-259	173	36	model	model	NOUN
cana-259	173	37	.	.	PUNCT
cana-259	174	1	in	in	ADP
cana-259	174	2	this	this	DET
cana-259	174	3	part	part	NOUN
cana-259	174	4	,	,	PUNCT
cana-259	174	5	we	we	PRON
cana-259	174	6	apply	apply	VERB
cana-259	174	7	the	the	DET
cana-259	174	8	sp	sp	NOUN
cana-259	174	9	technique	technique	NOUN
cana-259	174	10	—	—	PUNCT
cana-259	174	11	basically	basically	ADV
cana-259	174	12	a	a	DET
cana-259	174	13	multitime	multitime	ADJ
cana-259	174	14	-	-	PUNCT
cana-259	174	15	scale	scale	NOUN
cana-259	174	16	approach	approach	NOUN
cana-259	174	17	—	—	PUNCT
cana-259	174	18	to	to	PART
cana-259	174	19	derive	derive	VERB
cana-259	174	20	a	a	DET
cana-259	174	21	rom	rom	NOUN
cana-259	174	22	based	base	VERB
cana-259	174	23	on	on	ADP
cana-259	174	24	eefs	eef	NOUN
cana-259	174	25	.	.	PUNCT
cana-259	175	1	for	for	ADP
cana-259	175	2	an	an	DET
cana-259	175	3	estimate	estimate	NOUN
cana-259	175	4	of	of	ADP
cana-259	175	5	your	your	PRON
cana-259	175	6	the	the	DET
cana-259	175	7	pde	pde	NOUN
cana-259	175	8	system	system	NOUN
cana-259	175	9	,	,	PUNCT
cana-259	175	10	we	we	PRON
cana-259	175	11	first	first	ADV
cana-259	175	12	employ	employ	VERB
cana-259	175	13	a	a	DET
cana-259	175	14	high	high	ADJ
cana-259	175	15	-	-	PUNCT
cana-259	175	16	order	order	NOUN
cana-259	175	17	ode	ode	NOUN
cana-259	175	18	model	model	NOUN
cana-259	175	19	based	base	VERB
cana-259	175	20	on	on	ADP
cana-259	175	21	eefs	eef	NOUN
cana-259	175	22	(	(	PUNCT
cana-259	175	23	5	5	NUM
cana-259	175	24	)	)	PUNCT
cana-259	175	25	.	.	PUNCT
cana-259	176	1	to	to	PART
cana-259	176	2	further	far	ADV
cana-259	176	3	minimise	minimise	VERB
cana-259	176	4	its	its	PRON
cana-259	176	5	size	size	NOUN
cana-259	176	6	,	,	PUNCT
cana-259	176	7	an	an	DET
cana-259	176	8	sp	sp	NOUN
cana-259	176	9	model	model	NOUN
cana-259	176	10	of	of	ADP
cana-259	176	11	a	a	DET
cana-259	176	12	linked	link	VERB
cana-259	176	13	fast	fast	ADJ
cana-259	176	14	/	/	SYM
cana-259	176	15	slow	slow	ADJ
cana-259	176	16	ode	ode	NOUN
cana-259	176	17	systems	system	NOUN
cana-259	176	18	is	be	AUX
cana-259	176	19	built	build	VERB
cana-259	176	20	,	,	PUNCT
cana-259	176	21	and	and	CCONJ
cana-259	176	22	a	a	DET
cana-259	176	23	fast	fast	ADJ
cana-259	176	24	moments	moment	NOUN
cana-259	176	25	scale	scale	NOUN
cana-259	176	26	is	be	AUX
cana-259	176	27	added	add	VERB
cana-259	176	28	to	to	PART
cana-259	176	29	achieve	achieve	VERB
cana-259	176	30	a	a	DET
cana-259	176	31	rom	rom	NOUN
cana-259	176	32	.	.	PUNCT
cana-259	177	1	the	the	DET
cana-259	177	2	eigenvalues	eigenvalue	NOUN
cana-259	177	3	of	of	ADP
cana-259	177	4	matrix	matrix	NOUN
cana-259	177	5	c	c	NOUN
cana-259	177	6	are	be	AUX
cana-259	177	7	represented	represent	VERB
cana-259	177	8	by	by	ADP
cana-259	177	9	{	{	PUNCT
cana-259	177	10	λi	λi	NOUN
cana-259	177	11	}	}	PUNCT
cana-259	177	12	,	,	PUNCT
cana-259	177	13	and	and	CCONJ
cana-259	177	14	the	the	DET
cana-259	177	15	equivalent	equivalent	ADJ
cana-259	177	16	eefs	eef	NOUN
cana-259	177	17	in	in	ADP
cana-259	177	18	kld	kld	PROPN
cana-259	177	19	are	be	AUX
cana-259	177	20	represented	represent	VERB
cana-259	177	21	by	by	ADP
cana-259	177	22	{	{	PUNCT
cana-259	177	23	φi(z	φi(z	NOUN
cana-259	177	24	)	)	PUNCT
cana-259	177	25	}	}	PUNCT
cana-259	177	26	,	,	PUNCT
cana-259	177	27	as	as	SCONJ
cana-259	177	28	demonstrated	demonstrate	VERB
cana-259	177	29	in	in	ADP
cana-259	177	30	subsection	subsection	NOUN
cana-259	177	31	iii	iii	NOUN
cana-259	177	32	-	-	NOUN
cana-259	177	33	a.	a.	NOUN
cana-259	177	34	when	when	SCONJ
cana-259	177	35	{	{	PUNCT
cana-259	177	36	λi	λi	NOUN
cana-259	177	37	}	}	PUNCT
cana-259	177	38	and	and	CCONJ
cana-259	177	39	{	{	PUNCT
cana-259	177	40	φi(z	φi(z	NOUN
cana-259	177	41	)	)	PUNCT
cana-259	177	42	}	}	PUNCT
cana-259	177	43	are	be	AUX
cana-259	177	44	sorted	sort	VERB
cana-259	177	45	according	accord	VERB
cana-259	177	46	to	to	ADP
cana-259	177	47	{	{	PUNCT
cana-259	177	48	λi	λi	ADP
cana-259	177	49	}	}	PUNCT
cana-259	177	50	in	in	ADP
cana-259	177	51	a	a	DET
cana-259	177	52	decreasing	decrease	VERB
cana-259	177	53	order	order	NOUN
cana-259	177	54	,	,	PUNCT
cana-259	177	55	that	that	ADV
cana-259	177	56	is	is	ADV
cana-259	177	57	,	,	PUNCT
cana-259	177	58	λ1	λ1	ADJ
cana-259	177	59	≥	≥	NUM
cana-259	177	60	λ	λ	PROPN
cana-259	177	61	2	2	NUM
cana-259	177	62	≥	≥	NOUN
cana-259	177	63	·	·	PUNCT
cana-259	177	64	·	·	PUNCT
cana-259	177	65	·	·	PUNCT
cana-259	177	66	≥	≥	NUM
cana-259	177	67	λm	λm	ADP
cana-259	177	68	,	,	PUNCT
cana-259	177	69	the	the	DET
cana-259	177	70	pde	pde	NOUN
cana-259	177	71	equation	equation	NOUN
cana-259	177	72	(	(	PUNCT
cana-259	177	73	5	5	NUM
cana-259	177	74	)	)	PUNCT
cana-259	177	75	's	's	PART
cana-259	177	76	resolution	resolution	NOUN
cana-259	177	77	y(z	y(z	PROPN
cana-259	177	78	,	,	PUNCT
cana-259	177	79	t	t	PROPN
cana-259	177	80	)	)	PUNCT
cana-259	177	81	can	can	AUX
cana-259	177	82	be	be	AUX
cana-259	177	83	roughly	roughly	ADV
cana-259	177	84	expressed	express	VERB
cana-259	177	85	as	as	ADP
cana-259	177	86	an	an	DET
cana-259	177	87	m	m	ADV
cana-259	177	88	-	-	ADJ
cana-259	177	89	dimensional	dimensional	ADJ
cana-259	177	90	ode	ode	ADJ
cana-259	177	91	system	system	NOUN
cana-259	177	92	is	be	AUX
cana-259	177	93	obtained	obtain	VERB
cana-259	177	94	by	by	ADP
cana-259	177	95	substituting	substitute	VERB
cana-259	177	96	(	(	PUNCT
cana-259	177	97	11	11	NUM
cana-259	177	98	)	)	PUNCT
cana-259	177	99	for	for	ADP
cana-259	177	100	y(z	y(z	PROPN
cana-259	177	101	,	,	PUNCT
cana-259	177	102	t	t	PROPN
cana-259	177	103	)	)	PUNCT
cana-259	177	104	in	in	ADP
cana-259	177	105	equation	equation	NOUN
cana-259	177	106	(	(	PUNCT
cana-259	177	107	5	5	NUM
cana-259	177	108	)	)	PUNCT
cana-259	177	109	and	and	CCONJ
cana-259	177	110	applying	apply	VERB
cana-259	177	111	eefs	eef	NOUN
cana-259	177	112	to	to	ADP
cana-259	177	113	both	both	DET
cana-259	177	114	sides	side	NOUN
cana-259	177	115	for	for	ADP
cana-259	177	116	the	the	DET
cana-259	177	117	expression	expression	NOUN
cana-259	177	118	to	to	PART
cana-259	177	119	accomplish	accomplish	VERB
cana-259	177	120	the	the	DET
cana-259	177	121	center	center	NOUN
cana-259	177	122	composition	composition	NOUN
cana-259	177	123	.	.	PUNCT
cana-259	178	1	communications	communication	NOUN
cana-259	178	2	on	on	ADP
cana-259	178	3	applied	apply	VERB
cana-259	178	4	nonlinear	nonlinear	ADJ
cana-259	178	5	analysis	analysis	NOUN
cana-259	178	6	issn	issn	NOUN
cana-259	178	7	:	:	PUNCT
cana-259	178	8	1074	1074	NUM
cana-259	178	9	-	-	PUNCT
cana-259	178	10	133x	133x	NUM
cana-259	178	11	vol	vol	NOUN
cana-259	178	12	30	30	NUM
cana-259	178	13	no	no	NOUN
cana-259	178	14	.	.	NOUN
cana-259	178	15	2	2	NUM
cana-259	178	16	(	(	PUNCT
cana-259	178	17	2023	2023	NUM
cana-259	178	18	)	)	PUNCT
cana-259	178	19	8	8	NUM
cana-259	178	20	https://internationalpubls.com	https://internationalpubls.com	X
cana-259	178	21	the	the	DET
cana-259	178	22	disparity	disparity	NOUN
cana-259	178	23	among	among	ADP
cana-259	178	24	the	the	DET
cana-259	178	25	pde	pde	NOUN
cana-259	178	26	equation	equation	NOUN
cana-259	178	27	(	(	PUNCT
cana-259	178	28	5	5	NUM
cana-259	178	29	)	)	PUNCT
cana-259	178	30	's	's	PART
cana-259	178	31	resolution	resolution	NOUN
cana-259	178	32	y(z	y(z	PROPN
cana-259	178	33	,	,	PUNCT
cana-259	178	34	t	t	PROPN
cana-259	178	35	)	)	PUNCT
cana-259	178	36	furthermore	furthermore	ADV
cana-259	178	37	it	it	PRON
cana-259	178	38	is	be	AUX
cana-259	178	39	demonstrated	demonstrate	VERB
cana-259	178	40	that	that	SCONJ
cana-259	178	41	the	the	DET
cana-259	178	42	solution	solution	NOUN
cana-259	178	43	yˆ(z	yˆ(z	NOUN
cana-259	178	44	,	,	PUNCT
cana-259	178	45	t	t	PROPN
cana-259	178	46	)	)	PUNCT
cana-259	179	1	[	[	X
cana-259	179	2	derived	derive	VERB
cana-259	179	3	by	by	ADP
cana-259	179	4	(	(	PUNCT
cana-259	179	5	11	11	NUM
cana-259	179	6	)	)	PUNCT
cana-259	179	7	and	and	CCONJ
cana-259	179	8	(	(	PUNCT
cana-259	179	9	12	12	NUM
cana-259	179	10	)	)	PUNCT
cana-259	179	11	]	]	PUNCT
cana-259	179	12	satisfies	satisfie	NOUN
cana-259	179	13	ρy(z	ρy(z	ADP
cana-259	179	14	,	,	PUNCT
cana-259	179	15	t	t	PROPN
cana-259	179	16	)	)	PUNCT
cana-259	179	17	−	−	NOUN
cana-259	179	18	yʆ(z	yʆ(z	NOUN
cana-259	179	19	,	,	PUNCT
cana-259	179	20	t)ρ2	t)ρ2	NOUN
cana-259	179	21	=	=	SYM
cana-259	179	22	μ(m	μ(m	PROPN
cana-259	179	23	)	)	PUNCT
cana-259	179	24	,	,	PUNCT
cana-259	179	25	where	where	SCONJ
cana-259	179	26	μ(m	μ(m	VERB
cana-259	179	27	)	)	PUNCT
cana-259	179	28	)	)	PUNCT
cana-259	179	29	is	be	AUX
cana-259	179	30	a	a	DET
cana-259	179	31	small	small	ADJ
cana-259	179	32	optimistic	optimistic	ADJ
cana-259	179	33	actual	actual	ADJ
cana-259	179	34	number	number	NOUN
cana-259	179	35	that	that	PRON
cana-259	179	36	depends	depend	VERB
cana-259	179	37	on	on	ADP
cana-259	179	38	m.	m.	NOUN
cana-259	179	39	additionally	additionally	ADV
cana-259	179	40	limm→∞	limm→∞	PROPN
cana-259	179	41	μ(m	μ(m	X
cana-259	179	42	)	)	PUNCT
cana-259	180	1	=	=	PUNCT
cana-259	180	2	0	0	X
cana-259	180	3	.	.	PUNCT
cana-259	181	1	this	this	PRON
cana-259	181	2	can	can	AUX
cana-259	181	3	be	be	AUX
cana-259	181	4	shown	show	VERB
cana-259	181	5	from	from	ADP
cana-259	181	6	[	[	X
cana-259	181	7	20	20	NUM
cana-259	181	8	,	,	PUNCT
cana-259	181	9	claim	claim	VERB
cana-259	181	10	1	1	NUM
cana-259	181	11	]	]	PUNCT
cana-259	181	12	.	.	PUNCT
cana-259	182	1	owing	owe	VERB
cana-259	182	2	to	to	ADP
cana-259	182	3	the	the	DET
cana-259	182	4	ode	ode	ADJ
cana-259	182	5	technique	technique	NOUN
cana-259	182	6	's	's	PART
cana-259	182	7	(	(	PUNCT
cana-259	182	8	12	12	NUM
cana-259	182	9	)	)	PUNCT
cana-259	182	10	large	large	ADJ
cana-259	182	11	dimension	dimension	NOUN
cana-259	182	12	,	,	PUNCT
cana-259	182	13	a	a	DET
cana-259	182	14	greater	great	ADJ
cana-259	182	15	dimension	dimension	NOUN
cana-259	182	16	lowering	lower	VERB
cana-259	182	17	is	be	AUX
cana-259	182	18	necessary	necessary	ADJ
cana-259	182	19	.	.	PUNCT
cana-259	183	1	at	at	ADP
cana-259	183	2	this	this	DET
cana-259	183	3	equilibrium	equilibrium	NOUN
cana-259	183	4	point	point	NOUN
cana-259	183	5	,	,	PUNCT
cana-259	183	6	or	or	CCONJ
cana-259	183	7	origin	origin	NOUN
cana-259	183	8	,	,	PUNCT
cana-259	183	9	of	of	ADP
cana-259	183	10	interest	interest	NOUN
cana-259	183	11	,	,	PUNCT
cana-259	183	12	a	a	DET
cana-259	183	13	linearization	linearization	NOUN
cana-259	183	14	is	be	AUX
cana-259	183	15	performed	perform	VERB
cana-259	183	16	for	for	ADP
cana-259	183	17	(	(	PUNCT
cana-259	183	18	12	12	NUM
cana-259	183	19	)	)	PUNCT
cana-259	183	20	.	.	PUNCT
cana-259	184	1	after	after	ADP
cana-259	184	2	that	that	PRON
cana-259	184	3	,	,	PUNCT
cana-259	184	4	(	(	PUNCT
cana-259	184	5	12	12	NUM
cana-259	184	6	)	)	PUNCT
cana-259	184	7	is	be	AUX
cana-259	184	8	the	the	DET
cana-259	184	9	same	same	ADJ
cana-259	184	10	recast	recast	NOUN
cana-259	184	11	as	as	ADP
cana-259	184	12	in	in	ADP
cana-259	184	13	this	this	DET
cana-259	184	14	instance	instance	NOUN
cana-259	184	15	,	,	PUNCT
cana-259	184	16	we	we	PRON
cana-259	184	17	recast	recast	VERB
cana-259	184	18	(	(	PUNCT
cana-259	184	19	13	13	NUM
cana-259	184	20	)	)	PUNCT
cana-259	184	21	as	as	ADP
cana-259	184	22	a	a	DET
cana-259	184	23	connected	connected	ADJ
cana-259	184	24	ode	ode	ADJ
cana-259	184	25	systems	system	NOUN
cana-259	184	26	with	with	ADP
cana-259	184	27	slow	slow	ADJ
cana-259	184	28	and	and	CCONJ
cana-259	184	29	fast	fast	ADJ
cana-259	184	30	subsystems	subsystem	NOUN
cana-259	184	31	and	and	CCONJ
cana-259	184	32	matching	matching	NOUN
cana-259	184	33	measures	measure	NOUN
cana-259	184	34	of	of	ADP
cana-259	184	35	n	n	PRON
cana-259	184	36	and	and	CCONJ
cana-259	184	37	m	m	PROPN
cana-259	184	38	n.	n.	ADJ
cana-259	184	39	suitable	suitable	ADJ
cana-259	184	40	proportions	proportion	NOUN
cana-259	184	41	that	that	PRON
cana-259	184	42	fulfil	fulfil	VERB
cana-259	184	43	the	the	DET
cana-259	184	44	xs	xs	PROPN
cana-259	184	45	subsystem	subsystem	NOUN
cana-259	184	46	's	's	PART
cana-259	184	47	depth	depth	NOUN
cana-259	184	48	,	,	PUNCT
cana-259	184	49	or	or	CCONJ
cana-259	184	50	n	n	CCONJ
cana-259	184	51	,	,	PUNCT
cana-259	184	52	needs	need	VERB
cana-259	184	53	to	to	PART
cana-259	184	54	be	be	AUX
cana-259	184	55	selected	select	VERB
cana-259	184	56	so	so	SCONJ
cana-259	184	57	that	that	SCONJ
cana-259	184	58	it	it	PRON
cana-259	184	59	fulfils	fulfil	VERB
cana-259	184	60	communications	communication	NOUN
cana-259	184	61	on	on	ADP
cana-259	184	62	applied	apply	VERB
cana-259	184	63	nonlinear	nonlinear	ADJ
cana-259	184	64	analysis	analysis	NOUN
cana-259	184	65	issn	issn	NOUN
cana-259	184	66	:	:	PUNCT
cana-259	184	67	1074	1074	NUM
cana-259	184	68	-	-	PUNCT
cana-259	184	69	133x	133x	NUM
cana-259	184	70	vol	vol	NOUN
cana-259	184	71	30	30	NUM
cana-259	184	72	no	no	NOUN
cana-259	184	73	.	.	NOUN
cana-259	184	74	2	2	NUM
cana-259	184	75	(	(	PUNCT
cana-259	184	76	2023	2023	NUM
cana-259	184	77	)	)	PUNCT
cana-259	184	78	9	9	NUM
cana-259	184	79	https://internationalpubls.com	https://internationalpubls.com	X
cana-259	184	80	regarding	regard	VERB
cana-259	184	81	a	a	DET
cana-259	184	82	modest	modest	ADJ
cana-259	184	83	positive	positive	ADJ
cana-259	184	84	real	real	ADJ
cana-259	184	85	number	number	NOUN
cana-259	184	86	ζ	ζ	NOUN
cana-259	184	87	.	.	PUNCT
cana-259	185	1	assume	assume	VERB
cana-259	185	2	that	that	SCONJ
cana-259	185	3	σ(as	σ(as	X
cana-259	185	4	)	)	PUNCT
cana-259	185	5	=	=	PRON
cana-259	185	6	{	{	PUNCT
cana-259	185	7	1	1	NUM
cana-259	185	8	,	,	PUNCT
cana-259	185	9	2	2	NUM
cana-259	185	10	,	,	PUNCT
cana-259	185	11	...	...	PUNCT
cana-259	185	12	,	,	PUNCT
cana-259	185	13	n	n	CCONJ
cana-259	185	14	}	}	PUNCT
cana-259	185	15	symbolises	symbolise	VERB
cana-259	185	16	as	as	SCONJ
cana-259	185	17	's	's	PART
cana-259	185	18	ganz	ganz	ADJ
cana-259	185	19	range	range	NOUN
cana-259	185	20	,	,	PUNCT
cana-259	185	21	while	while	SCONJ
cana-259	185	22	σ(af	σ(af	PROPN
cana-259	185	23	)	)	PUNCT
cana-259	185	24	=	=	SYM
cana-259	185	25	1	1	NUM
cana-259	185	26	,	,	PUNCT
cana-259	185	27	2	2	NUM
cana-259	185	28	,	,	PUNCT
cana-259	185	29	...	...	PUNCT
cana-259	185	30	,	,	PUNCT
cana-259	186	1	m	m	VERB
cana-259	186	2	−n	−n	ADJ
cana-259	186	3	represents	represent	VERB
cana-259	186	4	the	the	DET
cana-259	186	5	eigen	eigen	PROPN
cana-259	186	6	spectrum	spectrum	NOUN
cana-259	186	7	of	of	ADP
cana-259	186	8	af	af	PROPN
cana-259	186	9	.	.	PUNCT
cana-259	187	1	then	then	ADV
cana-259	187	2	,	,	PUNCT
cana-259	187	3	our	our	PRON
cana-259	187	4	theories	theory	NOUN
cana-259	187	5	regarding	regard	VERB
cana-259	187	6	the	the	DET
cana-259	187	7	distinct	distinct	ADJ
cana-259	187	8	attribute	attribute	NOUN
cana-259	187	9	of	of	ADP
cana-259	187	10	(	(	PUNCT
cana-259	187	11	14	14	NUM
cana-259	187	12	)	)	PUNCT
cana-259	187	13	are	be	AUX
cana-259	187	14	stated	state	VERB
cana-259	187	15	in	in	ADP
cana-259	187	16	our	our	PRON
cana-259	187	17	presumption	presumption	NOUN
cana-259	187	18	that	that	PRON
cana-259	187	19	follows	follow	VERB
cana-259	187	20	.	.	PUNCT
cana-259	188	1	addressing	address	VERB
cana-259	188	2	{	{	PUNCT
cana-259	188	3	˜1	˜1	PROPN
cana-259	188	4	}	}	PUNCT
cana-259	188	5	≥	≥	NOUN
cana-259	188	6	re{2	re{2	NUM
cana-259	188	7	}	}	PUNCT
cana-259	188	8	≥	≥	X
cana-259	188	9	·	·	PUNCT
cana-259	188	10	·	·	PUNCT
cana-259	188	11	·	·	PUNCT
cana-259	188	12	≥	≥	NUM
cana-259	188	13	re{n	re{n	NOUN
cana-259	188	14	}	}	PUNCT
cana-259	188	15	and	and	CCONJ
cana-259	188	16	which{1	which{1	PROPN
cana-259	188	17	}	}	PUNCT
cana-259	188	18	≥	≥	NOUN
cana-259	188	19	which{2	which{2	PROPN
cana-259	188	20	}	}	PUNCT
cana-259	188	21	≥	≥	X
cana-259	188	22	·	·	PUNCT
cana-259	188	23	·	·	PUNCT
cana-259	188	24	·	·	PUNCT
cana-259	188	25	≥	≥	X
cana-259	188	26	re{ˆm	re{ˆm	VERB
cana-259	188	27	−n	−n	NOUN
cana-259	188	28	}	}	PUNCT
cana-259	188	29	,	,	PUNCT
cana-259	188	30	where	where	SCONJ
cana-259	188	31	\j	\j	NOUN
cana-259	188	32	is	be	AUX
cana-259	188	33	the	the	DET
cana-259	188	34	imaginary	imaginary	ADJ
cana-259	188	35	part	part	NOUN
cana-259	188	36	.	.	PUNCT
cana-259	189	1	this	this	PRON
cana-259	189	2	is	be	AUX
cana-259	189	3	the	the	DET
cana-259	189	4	first	first	ADJ
cana-259	189	5	postulate	postulate	NOUN
cana-259	189	6	.	.	PUNCT
cana-259	190	1	a	a	DET
cana-259	190	2	tiny	tiny	ADJ
cana-259	190	3	positive	positive	ADJ
cana-259	190	4	value	value	NOUN
cana-259	190	5	,	,	PUNCT
cana-259	190	6	ε	ε	PROPN
cana-259	190	7	=	=	SYM
cana-259	190	8	|re{\1}|/|re{\1}|	|re{\1}|/|re{\1}|	PROPN
cana-259	190	9	<	<	X
cana-259	190	10	1	1	NUM
cana-259	190	11	,	,	PUNCT
cana-259	190	12	is	be	AUX
cana-259	190	13	present	present	ADJ
cana-259	190	14	.	.	PUNCT
cana-259	191	1	the	the	DET
cana-259	191	2	order	order	NOUN
cana-259	191	3	-	-	PUNCT
cana-259	191	4	of	of	ADP
cana-259	191	5	-	-	PUNCT
cana-259	191	6	magnitude	magnitude	NOUN
cana-259	191	7	nomenclature	nomenclature	NOUN
cana-259	191	8	in	in	ADP
cana-259	191	9	this	this	DET
cana-259	191	10	case	case	NOUN
cana-259	191	11	is	be	AUX
cana-259	191	12	o(ε	o(ε	PROPN
cana-259	191	13	)	)	PUNCT
cana-259	192	1	[	[	X
cana-259	192	2	47	47	NUM
cana-259	192	3	]	]	PUNCT
cana-259	192	4	;	;	PUNCT
cana-259	192	5	which	which	PRON
cana-259	192	6	means	mean	VERB
cana-259	192	7	that	that	SCONJ
cana-259	192	8	ς(ε	ς(ε	NOUN
cana-259	192	9	)	)	PUNCT
cana-259	192	10	=	=	SYM
cana-259	192	11	o(ε	o(ε	PROPN
cana-259	192	12	)	)	PUNCT
cana-259	192	13	if	if	SCONJ
cana-259	192	14	the	the	DET
cana-259	192	15	real	real	ADJ
cana-259	192	16	numbers	number	NOUN
cana-259	192	17	k1	k1	NOUN
cana-259	192	18	and	and	CCONJ
cana-259	192	19	k2	k2	PROPN
cana-259	192	20	exist	exist	VERB
cana-259	192	21	with	with	ADP
cana-259	192	22	respect	respect	NOUN
cana-259	192	23	to	to	ADP
cana-259	192	24	ς(ε)<k1	ς(ε)<k1	PROPN
cana-259	192	25	ε	ε	PROPN
cana-259	192	26	,	,	PUNCT
cana-259	192	27	ε	ε	PROPN
cana-259	192	28	<	<	X
cana-259	192	29	k2	k2	PROPN
cana-259	192	30	)	)	PUNCT
cana-259	192	31	.	.	PUNCT
cana-259	193	1	regarding	regard	VERB
cana-259	193	2	a	a	DET
cana-259	193	3	modest	modest	ADJ
cana-259	193	4	positive	positive	ADJ
cana-259	193	5	real	real	ADJ
cana-259	193	6	number	number	NOUN
cana-259	193	7	ζ	ζ	NOUN
cana-259	193	8	.	.	PUNCT
cana-259	193	9	assume	assume	VERB
cana-259	193	10	that	that	SCONJ
cana-259	193	11	σ(as	σ(as	X
cana-259	193	12	)	)	PUNCT
cana-259	193	13	=	=	PRON
cana-259	193	14	{	{	PUNCT
cana-259	193	15	1	1	NUM
cana-259	193	16	,	,	PUNCT
cana-259	193	17	2	2	NUM
cana-259	193	18	,	,	PUNCT
cana-259	193	19	...	...	PUNCT
cana-259	193	20	,	,	PUNCT
cana-259	193	21	n	n	CCONJ
cana-259	193	22	}	}	PUNCT
cana-259	193	23	represents	represent	VERB
cana-259	193	24	the	the	DET
cana-259	193	25	eigen	eigen	PROPN
cana-259	193	26	spectrum	spectrum	NOUN
cana-259	193	27	associated	associate	VERB
cana-259	193	28	with	with	ADP
cana-259	193	29	as	as	ADP
cana-259	193	30	,	,	PUNCT
cana-259	193	31	while	while	SCONJ
cana-259	193	32	σ(af	σ(af	PROPN
cana-259	193	33	)	)	PUNCT
cana-259	193	34	=	=	SYM
cana-259	194	1	1	1	NUM
cana-259	194	2	,	,	PUNCT
cana-259	194	3	2	2	NUM
cana-259	194	4	,	,	PUNCT
cana-259	194	5	...	...	PUNCT
cana-259	194	6	,	,	PUNCT
cana-259	194	7	m	m	VERB
cana-259	194	8	−n	−n	ADJ
cana-259	194	9	represents	represent	VERB
cana-259	194	10	the	the	DET
cana-259	194	11	eigen	eigen	PROPN
cana-259	194	12	rainbow	rainbow	PROPN
cana-259	194	13	of	of	ADP
cana-259	194	14	af	af	PROPN
cana-259	194	15	.	.	PUNCT
cana-259	195	1	then	then	ADV
cana-259	195	2	,	,	PUNCT
cana-259	195	3	our	our	PRON
cana-259	195	4	theories	theory	NOUN
cana-259	195	5	regarding	regard	VERB
cana-259	195	6	the	the	DET
cana-259	195	7	distinct	distinct	ADJ
cana-259	195	8	attribute	attribute	NOUN
cana-259	195	9	of	of	ADP
cana-259	195	10	(	(	PUNCT
cana-259	195	11	14	14	NUM
cana-259	195	12	)	)	PUNCT
cana-259	195	13	are	be	AUX
cana-259	195	14	stated	state	VERB
cana-259	195	15	in	in	ADP
cana-259	195	16	the	the	DET
cana-259	195	17	presumption	presumption	NOUN
cana-259	195	18	that	that	PRON
cana-259	195	19	follows	follow	VERB
cana-259	195	20	.	.	PUNCT
cana-259	196	1	a	a	DET
cana-259	196	2	tiny	tiny	ADJ
cana-259	196	3	positive	positive	ADJ
cana-259	196	4	value	value	NOUN
cana-259	196	5	,	,	PUNCT
cana-259	196	6	ε	ε	PROPN
cana-259	196	7	=	=	SYM
cana-259	196	8	|re{\1}|/|re{\1}|	|re{\1}|/|re{\1}|	PROPN
cana-259	196	9	<	<	X
cana-259	196	10	1	1	NUM
cana-259	196	11	,	,	PUNCT
cana-259	196	12	is	be	AUX
cana-259	196	13	present	present	ADJ
cana-259	196	14	.	.	PUNCT
cana-259	197	1	the	the	DET
cana-259	197	2	order	order	NOUN
cana-259	197	3	-	-	PUNCT
cana-259	197	4	of	of	ADP
cana-259	197	5	-	-	PUNCT
cana-259	197	6	magnitude	magnitude	NOUN
cana-259	197	7	designation	designation	NOUN
cana-259	197	8	in	in	ADP
cana-259	197	9	this	this	DET
cana-259	197	10	case	case	NOUN
cana-259	197	11	is	be	AUX
cana-259	197	12	o(ε	o(ε	PROPN
cana-259	197	13	)	)	PUNCT
cana-259	198	1	[	[	X
cana-259	198	2	47	47	NUM
cana-259	198	3	]	]	PUNCT
cana-259	198	4	;	;	PUNCT
cana-259	198	5	namely	namely	ADV
cana-259	198	6	,	,	PUNCT
cana-259	198	7	ς(ε	ς(ε	NOUN
cana-259	198	8	)	)	PUNCT
cana-259	198	9	=	=	SYM
cana-259	198	10	o(ε	o(ε	PROPN
cana-259	198	11	)	)	PUNCT
cana-259	198	12	if	if	SCONJ
cana-259	198	13	positive	positive	ADJ
cana-259	198	14	real	real	ADJ
cana-259	198	15	numbers	number	NOUN
cana-259	198	16	k1	k1	NOUN
cana-259	198	17	and	and	CCONJ
cana-259	198	18	k2	k2	PROPN
cana-259	198	19	exist	exist	VERB
cana-259	198	20	with	with	ADP
cana-259	198	21	respect	respect	NOUN
cana-259	198	22	to	to	ADP
cana-259	198	23	ς(ε)<k1	ς(ε)<k1	PROPN
cana-259	198	24	ε	ε	PROPN
cana-259	198	25	,	,	PUNCT
cana-259	198	26	ε	ε	PROPN
cana-259	198	27	<	<	X
cana-259	198	28	k2	k2	PROPN
cana-259	198	29	)	)	PUNCT
cana-259	198	30	.	.	PUNCT
cana-259	199	1	remark	remark	NOUN
cana-259	199	2	2	2	NUM
cana-259	199	3	:	:	PUNCT
cana-259	199	4	the	the	DET
cana-259	199	5	parabolic	parabolic	ADJ
cana-259	199	6	pde	pde	NOUN
cana-259	199	7	systems	system	NOUN
cana-259	199	8	with	with	ADP
cana-259	199	9	nonlinear	nonlinear	ADJ
cana-259	199	10	sdos	sdo	NOUN
cana-259	199	11	have	have	VERB
cana-259	199	12	the	the	DET
cana-259	199	13	fast	fast	ADJ
cana-259	199	14	/	/	SYM
cana-259	199	15	slow	slow	ADJ
cana-259	199	16	dissolution	dissolution	NOUN
cana-259	199	17	feature	feature	NOUN
cana-259	199	18	.	.	PUNCT
cana-259	200	1	[	[	X
cana-259	200	2	20	20	NUM
cana-259	200	3	]	]	PUNCT
cana-259	200	4	,	,	PUNCT
cana-259	200	5	[	[	X
cana-259	200	6	21	21	NUM
cana-259	200	7	]	]	PUNCT
cana-259	200	8	,	,	PUNCT
cana-259	200	9	and	and	CCONJ
cana-259	200	10	basic	basic	ADJ
cana-259	200	11	sdos	sdo	NOUN
cana-259	200	12	[	[	X
cana-259	200	13	48	48	NUM
cana-259	200	14	]	]	PUNCT
cana-259	200	15	.	.	PUNCT
cana-259	201	1	this	this	DET
cana-259	201	2	characteristic	characteristic	NOUN
cana-259	201	3	is	be	AUX
cana-259	201	4	stated	state	VERB
cana-259	201	5	using	use	VERB
cana-259	201	6	assumption	assumption	NOUN
cana-259	201	7	1	1	NUM
cana-259	201	8	,	,	PUNCT
cana-259	201	9	which	which	PRON
cana-259	201	10	is	be	AUX
cana-259	201	11	shown	show	VERB
cana-259	201	12	here	here	ADV
cana-259	201	13	.	.	PUNCT
cana-259	202	1	for	for	ADP
cana-259	202	2	hyperbolic	hyperbolic	ADJ
cana-259	202	3	pde	pde	NOUN
cana-259	202	4	frameworks	framework	NOUN
cana-259	202	5	,	,	PUNCT
cana-259	202	6	the	the	DET
cana-259	202	7	criteria	criterion	NOUN
cana-259	202	8	in	in	ADP
cana-259	202	9	assumption	assumption	NOUN
cana-259	202	10	1	1	NUM
cana-259	202	11	are	be	AUX
cana-259	202	12	frequently	frequently	ADV
cana-259	202	13	met	meet	VERB
cana-259	202	14	by	by	ADP
cana-259	202	15	appropriately	appropriately	ADV
cana-259	202	16	selecting	select	VERB
cana-259	202	17	constants	constant	NOUN
cana-259	202	18	n	n	CCONJ
cana-259	202	19	and	and	CCONJ
cana-259	202	20	m.	m.	NOUN
cana-259	202	21	a	a	DET
cana-259	202	22	typical	typical	ADJ
cana-259	202	23	sp	sp	ADP
cana-259	202	24	counterpart	counterpart	NOUN
cana-259	202	25	of	of	ADP
cana-259	202	26	the	the	DET
cana-259	202	27	xf	xf	PROPN
cana-259	202	28	module	module	NOUN
cana-259	202	29	may	may	AUX
cana-259	202	30	be	be	AUX
cana-259	202	31	obtained	obtain	VERB
cana-259	202	32	by	by	ADP
cana-259	202	33	multiplying	multiply	VERB
cana-259	202	34	both	both	DET
cana-259	202	35	sides	side	NOUN
cana-259	202	36	by	by	ADP
cana-259	202	37	ε	ε	PROPN
cana-259	202	38	(	(	PUNCT
cana-259	202	39	14	14	NUM
cana-259	202	40	)	)	PUNCT
cana-259	202	41	that	that	PRON
cana-259	202	42	is	be	AUX
cana-259	202	43	equal	equal	ADJ
cana-259	202	44	to	to	ADP
cana-259	202	45	what	what	PRON
cana-259	202	46	is	be	AUX
cana-259	202	47	presented	present	VERB
cana-259	202	48	in	in	ADP
cana-259	202	49	proposition	proposition	NOUN
cana-259	202	50	1	1	NUM
cana-259	202	51	.	.	PUNCT
cana-259	203	1	communications	communication	NOUN
cana-259	203	2	on	on	ADP
cana-259	203	3	applied	apply	VERB
cana-259	203	4	nonlinear	nonlinear	ADJ
cana-259	203	5	analysis	analysis	NOUN
cana-259	203	6	issn	issn	NOUN
cana-259	203	7	:	:	PUNCT
cana-259	203	8	1074	1074	NUM
cana-259	203	9	-	-	PUNCT
cana-259	203	10	133x	133x	NUM
cana-259	203	11	vol	vol	NOUN
cana-259	203	12	30	30	NUM
cana-259	203	13	no	no	NOUN
cana-259	203	14	.	.	NOUN
cana-259	203	15	2	2	NUM
cana-259	203	16	(	(	PUNCT
cana-259	203	17	2023	2023	NUM
cana-259	203	18	)	)	PUNCT
cana-259	203	19	10	10	NUM
cana-259	203	20	https://internationalpubls.com	https://internationalpubls.com	X
cana-259	203	21	system	system	NOUN
cana-259	203	22	(	(	PUNCT
cana-259	203	23	17	17	NUM
cana-259	203	24	)	)	PUNCT
cana-259	203	25	is	be	AUX
cana-259	203	26	globally	globally	ADV
cana-259	203	27	exponentially	exponentially	ADV
cana-259	203	28	stable	stable	ADJ
cana-259	203	29	based	base	VERB
cana-259	203	30	on	on	ADP
cana-259	203	31	the	the	DET
cana-259	203	32	concept	concept	NOUN
cana-259	203	33	of	of	ADP
cana-259	203	34	ε	ε	PROPN
cana-259	203	35	and	and	CCONJ
cana-259	203	36	the	the	DET
cana-259	203	37	fact	fact	NOUN
cana-259	203	38	that	that	SCONJ
cana-259	203	39	re	re	VERB
cana-259	203	40	1	1	NUM
cana-259	203	41	<	<	X
cana-259	203	42	0	0	NUM
cana-259	203	43	.	.	PUNCT
cana-259	204	1	consequently	consequently	ADV
cana-259	204	2	,	,	PUNCT
cana-259	204	3	xf	xf	PROPN
cana-259	204	4	=	=	PROPN
cana-259	204	5	0	0	PROPN
cana-259	204	6	.	.	PUNCT
cana-259	205	1	the	the	DET
cana-259	205	2	rom	rom	NOUN
cana-259	205	3	is	be	AUX
cana-259	205	4	obtained	obtain	VERB
cana-259	205	5	as	as	ADP
cana-259	205	6	(	(	PUNCT
cana-259	205	7	16	16	NUM
cana-259	205	8	)	)	PUNCT
cana-259	205	9	.	.	PUNCT
cana-259	206	1	in	in	ADP
cana-259	206	2	which	which	DET
cana-259	206	3	case	case	NOUN
cana-259	206	4	gs	gs	X
cana-259	206	5	(	(	PUNCT
cana-259	206	6	xs	xs	PROPN
cana-259	206	7	)	)	PUNCT
cana-259	207	1	=	=	PRON
cana-259	207	2	gs	gs	PROPN
cana-259	207	3	(	(	PUNCT
cana-259	207	4	xs	xs	PROPN
cana-259	207	5	,	,	PUNCT
cana-259	207	6	0	0	NUM
cana-259	207	7	)	)	PUNCT
cana-259	207	8	.	.	PUNCT
cana-259	208	1	remark	remark	VERB
cana-259	208	2	3	3	NUM
cana-259	208	3	:	:	PUNCT
cana-259	208	4	the	the	DET
cana-259	208	5	approach	approach	NOUN
cana-259	208	6	used	use	VERB
cana-259	208	7	to	to	PART
cana-259	208	8	get	get	VERB
cana-259	208	9	the	the	DET
cana-259	208	10	rom	rom	NOUN
cana-259	208	11	here	here	ADV
cana-259	208	12	differs	differ	VERB
cana-259	208	13	from	from	ADP
cana-259	208	14	the	the	DET
cana-259	208	15	approach	approach	NOUN
cana-259	208	16	described	describe	VERB
cana-259	208	17	in	in	ADP
cana-259	208	18	[	[	X
cana-259	208	19	20	20	NUM
cana-259	208	20	]	]	PUNCT
cana-259	208	21	.	.	PUNCT
cana-259	209	1	the	the	DET
cana-259	209	2	linked	link	VERB
cana-259	209	3	fast	fast	ADJ
cana-259	209	4	/	/	SYM
cana-259	209	5	slow	slow	ADJ
cana-259	209	6	ode	ode	ADJ
cana-259	209	7	structure	structure	NOUN
cana-259	209	8	(	(	PUNCT
cana-259	209	9	14	14	NUM
cana-259	209	10	)	)	PUNCT
cana-259	209	11	is	be	AUX
cana-259	209	12	derived	derive	VERB
cana-259	209	13	in	in	ADP
cana-259	209	14	[	[	X
cana-259	209	15	20	20	NUM
cana-259	209	16	]	]	PUNCT
cana-259	209	17	via	via	ADP
cana-259	209	18	the	the	DET
cana-259	209	19	coordinate	coordinate	NOUN
cana-259	209	20	change	change	NOUN
cana-259	209	21	,	,	PUNCT
cana-259	209	22	where	where	SCONJ
cana-259	209	23	as	as	ADP
cana-259	209	24	and	and	CCONJ
cana-259	209	25	af	af	PROPN
cana-259	209	26	are	be	AUX
cana-259	209	27	orthogonal	orthogonal	ADJ
cana-259	209	28	matrices	matrix	NOUN
cana-259	209	29	and	and	CCONJ
cana-259	209	30	the	the	DET
cana-259	209	31	terms	term	NOUN
cana-259	209	32	asf	asf	PROPN
cana-259	209	33	xf	xf	PROPN
cana-259	209	34	and	and	CCONJ
cana-259	209	35	afsxs	afsx	NOUN
cana-259	209	36	are	be	AUX
cana-259	209	37	miss	miss	ADV
cana-259	209	38	-	-	PUNCT
cana-259	209	39	identified	identify	VERB
cana-259	209	40	.	.	PUNCT
cana-259	210	1	iv	iv	X
cana-259	210	2	.	.	PUNCT
cana-259	210	3	synthesis	synthesis	NOUN
cana-259	210	4	of	of	ADP
cana-259	210	5	approximate	approximate	ADJ
cana-259	210	6	optimal	optimal	ADJ
cana-259	210	7	controller	controller	NOUN
cana-259	210	8	this	this	DET
cana-259	210	9	section	section	NOUN
cana-259	210	10	will	will	AUX
cana-259	210	11	create	create	VERB
cana-259	210	12	an	an	DET
cana-259	210	13	estimated	estimate	VERB
cana-259	210	14	optimum	optimum	ADJ
cana-259	210	15	controller	controller	NOUN
cana-259	210	16	using	use	VERB
cana-259	210	17	nn	nn	PROPN
cana-259	210	18	for	for	ADP
cana-259	210	19	the	the	DET
cana-259	210	20	pde	pde	NOUN
cana-259	210	21	system	system	NOUN
cana-259	210	22	(	(	PUNCT
cana-259	210	23	5	5	X
cana-259	210	24	)	)	PUNCT
cana-259	210	25	using	use	VERB
cana-259	210	26	the	the	DET
cana-259	210	27	hjb	hjb	NOUN
cana-259	210	28	theoretical	theoretical	ADJ
cana-259	210	29	structure	structure	NOUN
cana-259	210	30	,	,	PUNCT
cana-259	210	31	based	base	VERB
cana-259	210	32	around	around	ADP
cana-259	210	33	the	the	DET
cana-259	210	34	rom	rom	NOUN
cana-259	210	35	(	(	PUNCT
cana-259	210	36	18	18	NUM
cana-259	210	37	)	)	PUNCT
cana-259	210	38	.	.	PUNCT
cana-259	211	1	a.	a.	NOUN
cana-259	211	2	hjb	hjb	PROPN
cana-259	211	3	approach	approach	NOUN
cana-259	211	4	to	to	ADP
cana-259	211	5	optimal	optimal	ADJ
cana-259	211	6	controller	controller	NOUN
cana-259	211	7	synthesis	synthesis	NOUN
cana-259	211	8	now	now	ADV
cana-259	211	9	,	,	PUNCT
cana-259	211	10	let	let	VERB
cana-259	211	11	's	us	PRON
cana-259	211	12	examine	examine	VERB
cana-259	211	13	a	a	DET
cana-259	211	14	generic	generic	ADJ
cana-259	211	15	effectiveness	effectiveness	NOUN
cana-259	211	16	functionality	functionality	NOUN
cana-259	211	17	.	.	PUNCT
cana-259	212	1	in	in	ADP
cana-259	212	2	this	this	DET
cana-259	212	3	case	case	NOUN
cana-259	212	4	,	,	PUNCT
cana-259	212	5	q	q	X
cana-259	212	6	(	(	PUNCT
cana-259	212	7	xs	xs	PROPN
cana-259	212	8	)	)	PUNCT
cana-259	212	9	is	be	AUX
cana-259	212	10	a	a	DET
cana-259	212	11	positive	positive	ADJ
cana-259	212	12	definite	definite	ADJ
cana-259	212	13	function	function	NOUN
cana-259	212	14	;	;	PUNCT
cana-259	212	15	that	that	PRON
cana-259	212	16	is	is	ADV
cana-259	212	17	,	,	PUNCT
cana-259	212	18	if	if	SCONJ
cana-259	212	19	xs	xs	PROPN
cana-259	212	20	=	=	SYM
cana-259	212	21	0	0	PROPN
cana-259	212	22	,	,	PUNCT
cana-259	212	23	then	then	ADV
cana-259	212	24	q	q	PROPN
cana-259	212	25	(	(	PUNCT
cana-259	212	26	xs	xs	PROPN
cana-259	212	27	)	)	PUNCT
cana-259	212	28	>	>	X
cana-259	212	29	0	0	NUM
cana-259	212	30	;	;	PUNCT
cana-259	212	31	q	q	X
cana-259	212	32	(	(	PUNCT
cana-259	212	33	xs	xs	NOUN
cana-259	212	34	)	)	PUNCT
cana-259	212	35	=	=	PUNCT
cana-259	212	36	0	0	PUNCT
cana-259	213	1	only	only	ADV
cana-259	213	2	in	in	ADP
cana-259	213	3	that	that	DET
cana-259	213	4	case	case	NOUN
cana-259	213	5	.	.	PUNCT
cana-259	214	1	r	r	NOUN
cana-259	214	2	is	be	AUX
cana-259	214	3	a	a	DET
cana-259	214	4	subset	subset	NOUN
cana-259	214	5	of	of	ADP
cana-259	214	6	rp×p	rp×p	PROPN
cana-259	214	7	.	.	PUNCT
cana-259	215	1	when	when	SCONJ
cana-259	215	2	∀xs	∀xs	PROPN
cana-259	215	3	=	=	SYM
cana-259	215	4	0	0	NUM
cana-259	215	5	,	,	PUNCT
cana-259	215	6	q	q	PROPN
cana-259	215	7	(	(	PUNCT
cana-259	215	8	xs	xs	PROPN
cana-259	215	9	)	)	PUNCT
cana-259	215	10	>	>	X
cana-259	216	1	0	0	NUM
cana-259	216	2	;	;	PUNCT
cana-259	216	3	q	q	X
cana-259	216	4	(	(	PUNCT
cana-259	216	5	xs	xs	NOUN
cana-259	216	6	)	)	PUNCT
cana-259	216	7	=	=	PUNCT
cana-259	216	8	0	0	PUNCT
cana-259	217	1	only	only	ADV
cana-259	217	2	when	when	SCONJ
cana-259	217	3	xs	xs	PROPN
cana-259	217	4	=	=	PROPN
cana-259	217	5	0	0	PROPN
cana-259	217	6	.	.	PUNCT
cana-259	217	7	here	here	ADV
cana-259	217	8	,	,	PUNCT
cana-259	217	9	q	q	PROPN
cana-259	217	10	(	(	PUNCT
cana-259	217	11	xs	xs	NOUN
cana-259	217	12	)	)	PUNCT
cana-259	217	13	is	be	AUX
cana-259	217	14	an	an	DET
cana-259	217	15	optimistic	optimistic	ADJ
cana-259	217	16	continuous	continuous	ADJ
cana-259	217	17	function	function	NOUN
cana-259	217	18	.	.	PUNCT
cana-259	218	1	a	a	DET
cana-259	218	2	positive	positive	ADJ
cana-259	218	3	definite	definite	ADJ
cana-259	218	4	matrix	matrix	NOUN
cana-259	218	5	is	be	AUX
cana-259	218	6	denoted	denote	VERB
cana-259	218	7	by	by	ADP
cana-259	218	8	r	r	PROPN
cana-259	218	9	∈	∈	PROPN
cana-259	218	10	rp×p	rp×p	PROPN
cana-259	218	11	.	.	PUNCT
cana-259	219	1	when	when	SCONJ
cana-259	219	2	xs	xs	PROPN
cana-259	219	3	=	=	SYM
cana-259	219	4	0	0	PROPN
cana-259	219	5	,	,	PUNCT
cana-259	219	6	v	v	PROPN
cana-259	219	7	(	(	PUNCT
cana-259	219	8	xs	xs	PROPN
cana-259	219	9	)	)	PUNCT
cana-259	219	10	>	>	X
cana-259	219	11	0	0	NUM
cana-259	219	12	;	;	PUNCT
cana-259	219	13	that	that	PRON
cana-259	219	14	is	be	AUX
cana-259	219	15	,	,	PUNCT
cana-259	219	16	v(xs	v(xs	X
cana-259	219	17	)	)	PUNCT
cana-259	220	1	=	=	PUNCT
cana-259	220	2	0	0	PUNCT
cana-259	221	1	only	only	ADV
cana-259	221	2	in	in	ADP
cana-259	221	3	the	the	DET
cana-259	221	4	event	event	NOUN
cana-259	221	5	xs	xs	PROPN
cana-259	221	6	=	=	PUNCT
cana-259	221	7	0	0	PROPN
cana-259	221	8	.	.	PUNCT
cana-259	222	1	for	for	ADP
cana-259	222	2	xs	xs	PROPN
cana-259	222	3	=	=	SYM
cana-259	222	4	ω	ω	PROPN
cana-259	222	5	−	−	PROPN
cana-259	222	6	rn	rn	PROPN
cana-259	222	7	,	,	PUNCT
cana-259	222	8	v	v	PROPN
cana-259	222	9	(	(	PUNCT
cana-259	222	10	xs	xs	PROPN
cana-259	222	11	)	)	PUNCT
cana-259	222	12	−	−	PROPN
cana-259	222	13	c1(ω	c1(ω	X
cana-259	222	14	)	)	PUNCT
cana-259	222	15	is	be	AUX
cana-259	222	16	a	a	DET
cana-259	222	17	positive	positive	ADJ
cana-259	222	18	definite	definite	ADJ
cana-259	222	19	function	function	NOUN
cana-259	222	20	.	.	PUNCT
cana-259	223	1	we	we	PRON
cana-259	223	2	present	present	VERB
cana-259	223	3	the	the	DET
cana-259	223	4	concept	concept	NOUN
cana-259	223	5	of	of	ADP
cana-259	223	6	acceptable	acceptable	ADJ
cana-259	223	7	control	control	NOUN
cana-259	223	8	as	as	SCONJ
cana-259	223	9	follows	follow	VERB
cana-259	223	10	.	.	PUNCT
cana-259	224	1	criterion	criterion	NOUN
cana-259	224	2	1[37	1[37	NUM
cana-259	224	3	]	]	PUNCT
cana-259	224	4	,	,	PUNCT
cana-259	224	5	[	[	X
cana-259	224	6	38	38	NUM
cana-259	224	7	]	]	PUNCT
cana-259	224	8	(	(	PUNCT
cana-259	224	9	acceptable	acceptable	ADJ
cana-259	224	10	control	control	NOUN
cana-259	224	11	):	):	PUNCT
cana-259	224	12	given	give	VERB
cana-259	224	13	system	system	NOUN
cana-259	224	14	(	(	PUNCT
cana-259	224	15	18	18	NUM
cana-259	224	16	)	)	PUNCT
cana-259	224	17	,	,	PUNCT
cana-259	224	18	with	with	ADP
cana-259	224	19	xs	xs	PROPN
cana-259	224	20	©	©	PROPN
cana-259	224	21	,	,	PUNCT
cana-259	224	22	a	a	DET
cana-259	224	23	control	control	NOUN
cana-259	224	24	variable	variable	NOUN
cana-259	224	25	u(xs	u(xs	ADV
cana-259	224	26	):	):	PUNCT
cana-259	224	27	ω	ω	PROPN
cana-259	224	28	·	·	PUNCT
cana-259	224	29	rp	rp	NOUN
cana-259	224	30	is	be	AUX
cana-259	224	31	determined	determine	VERB
cana-259	224	32	to	to	PART
cana-259	224	33	be	be	AUX
cana-259	224	34	acceptable	acceptable	ADJ
cana-259	224	35	with	with	ADP
cana-259	224	36	regard	regard	NOUN
cana-259	224	37	to	to	ADP
cana-259	224	38	(	(	PUNCT
cana-259	224	39	19	19	NUM
cana-259	224	40	)	)	PUNCT
cana-259	224	41	on	on	ADP
cana-259	224	42	ω	ω	PROPN
cana-259	224	43	,	,	PUNCT
cana-259	224	44	represented	represent	VERB
cana-259	224	45	by	by	ADP
cana-259	224	46	u(xs	u(x	NOUN
cana-259	224	47	)	)	PUNCT
cana-259	224	48	(	(	PUNCT
cana-259	224	49	ω	ω	NOUN
cana-259	224	50	)	)	PUNCT
cana-259	224	51	,	,	PUNCT
cana-259	224	52	provided	provide	VERB
cana-259	224	53	that	that	SCONJ
cana-259	224	54	the	the	DET
cana-259	224	55	following	follow	VERB
cana-259	224	56	requirements	requirement	NOUN
cana-259	224	57	are	be	AUX
cana-259	224	58	met	meet	VERB
cana-259	224	59	:	:	PUNCT
cana-259	224	60	first	first	ADV
cana-259	224	61	,	,	PUNCT
cana-259	224	62	u	u	NOUN
cana-259	224	63	is	be	AUX
cana-259	224	64	continual	continual	ADJ
cana-259	224	65	on	on	ADP
cana-259	224	66	ω	ω	PROPN
cana-259	224	67	;	;	PUNCT
cana-259	224	68	second	second	ADJ
cana-259	224	69	,	,	PUNCT
cana-259	224	70	u(0	u(0	NOUN
cana-259	224	71	)	)	PUNCT
cana-259	224	72	=	=	SYM
cana-259	225	1	0	0	NUM
cana-259	225	2	;	;	PUNCT
cana-259	225	3	third	third	ADJ
cana-259	225	4	,	,	PUNCT
cana-259	225	5	u(xs	u(x	NOUN
cana-259	225	6	)	)	PUNCT
cana-259	225	7	stabilises	stabilise	VERB
cana-259	225	8	the	the	DET
cana-259	225	9	system	system	NOUN
cana-259	225	10	(	(	PUNCT
cana-259	225	11	18	18	NUM
cana-259	225	12	)	)	PUNCT
cana-259	225	13	;	;	PUNCT
cana-259	225	14	and	and	CCONJ
cana-259	225	15	fourth	fourth	ADJ
cana-259	225	16	,	,	PUNCT
cana-259	225	17	v	v	PROPN
cana-259	225	18	(	(	PUNCT
cana-259	225	19	xs0	xs0	PROPN
cana-259	225	20	)	)	PUNCT
cana-259	225	21	<	<	X
cana-259	225	22	,	,	PUNCT
cana-259	225	23	xs0	xs0	PROPN
cana-259	225	24	`	`	PUNCT
cana-259	225	25	.	.	PUNCT
cana-259	226	1	our	our	PRON
cana-259	226	2	goal	goal	NOUN
cana-259	226	3	is	be	AUX
cana-259	226	4	to	to	PART
cana-259	226	5	minimise	minimise	VERB
cana-259	226	6	the	the	DET
cana-259	226	7	performance	performance	NOUN
cana-259	226	8	functional	functional	ADJ
cana-259	226	9	(	(	PUNCT
cana-259	226	10	19	19	NUM
cana-259	226	11	)	)	PUNCT
cana-259	226	12	in	in	ADP
cana-259	226	13	order	order	NOUN
cana-259	226	14	to	to	PART
cana-259	226	15	identify	identify	VERB
cana-259	226	16	an	an	DET
cana-259	226	17	acceptable	acceptable	ADJ
cana-259	226	18	control	control	NOUN
cana-259	226	19	u∗(xs	u∗(x	VERB
cana-259	226	20	)	)	PUNCT
cana-259	226	21	(	(	PUNCT
cana-259	226	22	ω	ω	NOUN
cana-259	226	23	)	)	PUNCT
cana-259	226	24	.	.	PUNCT
cana-259	227	1	it	it	PRON
cana-259	227	2	is	be	AUX
cana-259	227	3	widely	widely	ADV
cana-259	227	4	acknowledged	acknowledge	VERB
cana-259	227	5	that	that	SCONJ
cana-259	227	6	the	the	DET
cana-259	227	7	problems	problem	NOUN
cana-259	227	8	that	that	PRON
cana-259	227	9	follow	follow	VERB
cana-259	227	10	may	may	AUX
cana-259	227	11	be	be	AUX
cana-259	227	12	correspondingly	correspondingly	ADV
cana-259	227	13	solved	solve	VERB
cana-259	227	14	by	by	ADP
cana-259	227	15	solving	solve	VERB
cana-259	227	16	the	the	DET
cana-259	227	17	optimum	optimum	ADJ
cana-259	227	18	control	control	NOUN
cana-259	227	19	issue	issue	NOUN
cana-259	227	20	regarding	regard	VERB
cana-259	227	21	the	the	DET
cana-259	227	22	system	system	NOUN
cana-259	227	23	in	in	ADP
cana-259	227	24	question	question	NOUN
cana-259	227	25	.	.	PUNCT
cana-259	228	1	hjb	hjb	NOUN
cana-259	228	2	with	with	ADP
cana-259	228	3	the	the	DET
cana-259	228	4	bernoulli	bernoulli	PROPN
cana-259	228	5	component	component	NOUN
cana-259	228	6	denoted	denote	VERB
cana-259	228	7	by	by	ADP
cana-259	228	8	h(u	h(u	PROPN
cana-259	228	9	)	)	PUNCT
cana-259	228	10	.	.	PUNCT
cana-259	229	1	h	h	NOUN
cana-259	229	2	(	(	PUNCT
cana-259	229	3	u	u	NOUN
cana-259	229	4	)	)	PUNCT
cana-259	230	1	=	=	NOUN
cana-259	230	2	δ	δ	NOUN
cana-259	230	3	v	v	ADP
cana-259	230	4	∗	∗	X
cana-259	230	5	t	t	NOUN
cana-259	230	6	(	(	PUNCT
cana-259	230	7	a	a	PRON
cana-259	230	8	x	x	INTJ
cana-259	230	9	+	+	NUM
cana-259	230	10	b	b	X
cana-259	230	11	u	u	NOUN
cana-259	230	12	+	+	X
cana-259	230	13	g	g	NOUN
cana-259	230	14	)	)	PUNCT
cana-259	231	1	+	+	CCONJ
cana-259	231	2	q	q	PUNCT
cana-259	232	1	+	+	NUM
cana-259	232	2	utru	utru	NOUN
cana-259	232	3	in	in	ADP
cana-259	232	4	which	which	PRON
cana-259	232	5	the	the	DET
cana-259	232	6	partial	partial	ADJ
cana-259	232	7	derivative	derivative	NOUN
cana-259	232	8	exists	exist	VERB
cana-259	232	9	about	about	ADP
cana-259	232	10	x	x	AUX
cana-259	232	11	is	be	AUX
cana-259	232	12	indicated	indicate	VERB
cana-259	232	13	by	by	ADP
cana-259	232	14	the	the	DET
cana-259	232	15	exponent	exponent	PROPN
cana-259	232	16	xs	xs	PROPN
cana-259	232	17	,	,	PUNCT
cana-259	232	18	meaning	mean	VERB
cana-259	232	19	that	that	SCONJ
cana-259	232	20	v	v	ADP
cana-259	232	21	∗	∗	NOUN
cana-259	232	22	=	=	SYM
cana-259	232	23	δ	δ	PROPN
cana-259	232	24	∂v	∂v	PROPN
cana-259	232	25	∗/∂x	∗/∂x	NOUN
cana-259	232	26	,	,	PUNCT
cana-259	232	27	and	and	CCONJ
cana-259	232	28	v	v	NOUN
cana-259	232	29	∗	∗	NOUN
cana-259	232	30	is	be	AUX
cana-259	232	31	the	the	DET
cana-259	232	32	magnitude	magnitude	NOUN
cana-259	232	33	of	of	ADP
cana-259	232	34	the	the	DET
cana-259	232	35	variable	variable	NOUN
cana-259	232	36	.	.	PUNCT
cana-259	233	1	the	the	DET
cana-259	233	2	initial	initial	ADJ
cana-259	233	3	-	-	PUNCT
cana-259	233	4	order	order	NOUN
cana-259	233	5	required	require	VERB
cana-259	233	6	condition	condition	NOUN
cana-259	233	7	of	of	ADP
cana-259	233	8	optimality	optimality	NOUN
cana-259	233	9	,	,	PUNCT
cana-259	233	10	which	which	PRON
cana-259	233	11	is	be	AUX
cana-259	233	12	satisfied	satisfied	ADJ
cana-259	233	13	by	by	ADP
cana-259	233	14	the	the	DET
cana-259	233	15	best	good	ADJ
cana-259	233	16	possible	possible	ADJ
cana-259	233	17	control	control	NOUN
cana-259	233	18	u∗	u∗	NOUN
cana-259	233	19	,	,	PUNCT
cana-259	233	20	is	be	AUX
cana-259	233	21	∂h(u)/∂u	∂h(u)/∂u	NOUN
cana-259	233	22	u	u	NOUN
cana-259	233	23	=	=	NOUN
cana-259	233	24	u∗	u∗	ADJ
cana-259	233	25	=	=	NOUN
cana-259	233	26	0	0	X
cana-259	233	27	.	.	PUNCT
cana-259	234	1	as	as	ADP
cana-259	234	2	a	a	DET
cana-259	234	3	result	result	NOUN
cana-259	234	4	,	,	PUNCT
cana-259	234	5	we	we	PRON
cana-259	234	6	have	have	AUX
cana-259	234	7	since	since	SCONJ
cana-259	234	8	u∗	u∗	PROPN
cana-259	234	9	,	,	PUNCT
cana-259	234	10	the	the	DET
cana-259	234	11	best	good	ADJ
cana-259	234	12	command	command	NOUN
cana-259	234	13	,	,	PUNCT
cana-259	234	14	violates	violate	VERB
cana-259	234	15	∂h(u)/∂u	∂h(u)/∂u	PROPN
cana-259	234	16	u	u	NOUN
cana-259	234	17	=	=	NOUN
cana-259	234	18	u∗	u∗	ADJ
cana-259	234	19	=	=	SYM
cana-259	234	20	0	0	NUM
cana-259	234	21	,	,	PUNCT
cana-259	234	22	the	the	DET
cana-259	234	23	situation	situation	NOUN
cana-259	234	24	is	be	AUX
cana-259	234	25	communications	communication	NOUN
cana-259	234	26	on	on	ADP
cana-259	234	27	applied	apply	VERB
cana-259	234	28	nonlinear	nonlinear	ADJ
cana-259	234	29	analysis	analysis	NOUN
cana-259	234	30	issn	issn	NOUN
cana-259	234	31	:	:	PUNCT
cana-259	234	32	1074	1074	NUM
cana-259	234	33	-	-	PUNCT
cana-259	234	34	133x	133x	NUM
cana-259	234	35	vol	vol	NOUN
cana-259	234	36	30	30	NUM
cana-259	234	37	no	no	NOUN
cana-259	234	38	.	.	NOUN
cana-259	234	39	2	2	NUM
cana-259	234	40	(	(	PUNCT
cana-259	234	41	2023	2023	NUM
cana-259	234	42	)	)	PUNCT
cana-259	234	43	11	11	NUM
cana-259	234	44	https://internationalpubls.com	https://internationalpubls.com	X
cana-259	234	45	conversely	conversely	ADV
cana-259	234	46	,	,	PUNCT
cana-259	234	47	the	the	DET
cana-259	234	48	related	related	ADJ
cana-259	234	49	expense	expense	NOUN
cana-259	234	50	variable	variable	NOUN
cana-259	234	51	v	v	NOUN
cana-259	234	52	for	for	ADP
cana-259	234	53	an	an	DET
cana-259	234	54	uncontrolled	uncontrolled	ADJ
cana-259	234	55	parameter	parameter	NOUN
cana-259	234	56	u	u	PROPN
cana-259	234	57	(	(	PUNCT
cana-259	234	58	ω	ω	NOUN
cana-259	234	59	)	)	PUNCT
cana-259	234	60	satisfies	satisfy	VERB
cana-259	234	61	the	the	DET
cana-259	234	62	following	follow	VERB
cana-259	234	63	ghjb	ghjb	NOUN
cana-259	234	64	equation	equation	NOUN
cana-259	235	1	[	[	X
cana-259	235	2	37]–[39	37]–[39	PROPN
cana-259	235	3	]	]	PUNCT
cana-259	235	4	:	:	PUNCT
cana-259	235	5	substituting	substitute	VERB
cana-259	235	6	u∗	u∗	NOUN
cana-259	235	7	into	into	ADP
cana-259	235	8	(	(	PUNCT
cana-259	235	9	22	22	NUM
cana-259	235	10	)	)	PUNCT
cana-259	235	11	yields	yield	NOUN
cana-259	235	12	(	(	PUNCT
cana-259	235	13	18	18	NUM
cana-259	235	14	)	)	PUNCT
cana-259	235	15	selecting	select	VERB
cana-259	235	16	v	v	ADP
cana-259	235	17	∗	∗	NOUN
cana-259	235	18	as	as	ADP
cana-259	235	19	the	the	DET
cana-259	235	20	potential	potential	ADJ
cana-259	235	21	lyapunov	lyapunov	ADJ
cana-259	235	22	product	product	NOUN
cana-259	235	23	for	for	ADP
cana-259	235	24	the	the	DET
cana-259	235	25	system	system	NOUN
cana-259	235	26	as	as	ADP
cana-259	235	27	a	a	DET
cana-259	235	28	whole	whole	ADJ
cana-259	235	29	(	(	PUNCT
cana-259	235	30	18	18	NUM
cana-259	235	31	)	)	PUNCT
cana-259	235	32	,	,	PUNCT
cana-259	235	33	we	we	PRON
cana-259	235	34	are	be	AUX
cana-259	235	35	left	leave	VERB
cana-259	235	36	with	with	ADP
cana-259	235	37	this	this	PRON
cana-259	235	38	implies	imply	VERB
cana-259	235	39	that	that	SCONJ
cana-259	235	40	the	the	DET
cana-259	235	41	closed	closed	ADJ
cana-259	235	42	-	-	PUNCT
cana-259	235	43	loop	loop	NOUN
cana-259	235	44	system	system	NOUN
cana-259	235	45	of	of	ADP
cana-259	235	46	(	(	PUNCT
cana-259	235	47	18	18	NUM
cana-259	235	48	)	)	PUNCT
cana-259	235	49	with	with	ADP
cana-259	235	50	optimal	optimal	ADJ
cana-259	235	51	control	control	NOUN
cana-259	235	52	is	be	AUX
cana-259	235	53	differently	differently	ADV
cana-259	235	54	stable	stable	ADJ
cana-259	235	55	.	.	PUNCT
cana-259	236	1	u∗.	u∗.	PROPN
cana-259	236	2	the	the	DET
cana-259	236	3	hjb	hjb	NOUN
cana-259	236	4	equation	equation	NOUN
cana-259	236	5	(	(	PUNCT
cana-259	236	6	20	20	NUM
cana-259	236	7	)	)	PUNCT
cana-259	236	8	may	may	AUX
cana-259	236	9	be	be	AUX
cana-259	236	10	rewritten	rewrite	VERB
cana-259	236	11	as	as	SCONJ
cana-259	236	12	follows	follow	VERB
cana-259	236	13	from	from	ADP
cana-259	236	14	(	(	PUNCT
cana-259	236	15	21	21	NUM
cana-259	236	16	)	)	PUNCT
cana-259	236	17	and	and	CCONJ
cana-259	236	18	(	(	PUNCT
cana-259	236	19	23	23	NUM
cana-259	236	20	)	)	PUNCT
cana-259	236	21	.	.	PUNCT
cana-259	237	1	thus	thus	ADV
cana-259	237	2	,	,	PUNCT
cana-259	237	3	the	the	DET
cana-259	237	4	hjb	hjb	NOUN
cana-259	237	5	equation	equation	NOUN
cana-259	237	6	(	(	PUNCT
cana-259	237	7	25	25	NUM
cana-259	237	8	)	)	PUNCT
cana-259	237	9	for	for	ADP
cana-259	237	10	v	v	NOUN
cana-259	237	11	∗	∗	NOUN
cana-259	237	12	may	may	AUX
cana-259	237	13	be	be	AUX
cana-259	237	14	solved	solve	VERB
cana-259	237	15	by	by	ADP
cana-259	237	16	reducing	reduce	VERB
cana-259	237	17	the	the	DET
cana-259	237	18	issue	issue	NOUN
cana-259	237	19	of	of	ADP
cana-259	237	20	constructing	construct	VERB
cana-259	237	21	an	an	DET
cana-259	237	22	optimum	optimum	ADJ
cana-259	237	23	control	control	NOUN
cana-259	237	24	(	(	PUNCT
cana-259	237	25	21	21	NUM
cana-259	237	26	)	)	PUNCT
cana-259	237	27	to	to	ADP
cana-259	237	28	that	that	PRON
cana-259	237	29	of	of	ADP
cana-259	237	30	solving	solve	VERB
cana-259	237	31	it	it	PRON
cana-259	237	32	.	.	PUNCT
cana-259	238	1	the	the	DET
cana-259	238	2	two	two	NUM
cana-259	238	3	components	component	NOUN
cana-259	238	4	of	of	ADP
cana-259	238	5	the	the	DET
cana-259	238	6	dynamics	dynamic	NOUN
cana-259	238	7	of	of	ADP
cana-259	238	8	the	the	DET
cana-259	238	9	system	system	NOUN
cana-259	238	10	(	(	PUNCT
cana-259	238	11	18	18	NUM
cana-259	238	12	)	)	PUNCT
cana-259	238	13	are	be	AUX
cana-259	238	14	the	the	DET
cana-259	238	15	negative	negative	ADJ
cana-259	238	16	term	term	NOUN
cana-259	238	17	gs	gs	PROPN
cana-259	238	18	and	and	CCONJ
cana-259	238	19	the	the	DET
cana-259	238	20	linear	linear	ADJ
cana-259	238	21	portion	portion	NOUN
cana-259	238	22	asxs	asx	NOUN
cana-259	238	23	,	,	PUNCT
cana-259	238	24	as	as	SCONJ
cana-259	238	25	we	we	PRON
cana-259	238	26	can	can	AUX
cana-259	238	27	see	see	VERB
cana-259	238	28	.	.	PUNCT
cana-259	239	1	in	in	ADP
cana-259	239	2	this	this	DET
cana-259	239	3	research	research	NOUN
cana-259	239	4	,	,	PUNCT
cana-259	239	5	we	we	PRON
cana-259	239	6	suggest	suggest	VERB
cana-259	239	7	an	an	DET
cana-259	239	8	optimum	optimum	ADJ
cana-259	239	9	microcontroller	microcontroller	NOUN
cana-259	239	10	synthesizing	synthesize	VERB
cana-259	239	11	approach	approach	NOUN
cana-259	239	12	employing	employ	VERB
cana-259	239	13	the	the	DET
cana-259	239	14	following	follow	VERB
cana-259	239	15	modal	modal	ADJ
cana-259	239	16	feedback	feedback	NOUN
cana-259	239	17	control	control	NOUN
cana-259	239	18	rule	rule	NOUN
cana-259	239	19	to	to	PART
cana-259	239	20	fully	fully	ADV
cana-259	239	21	use	use	VERB
cana-259	239	22	the	the	DET
cana-259	239	23	quadratic	quadratic	ADJ
cana-259	239	24	part	part	NOUN
cana-259	239	25	:	:	PUNCT
cana-259	239	26	let	let	VERB
cana-259	239	27	us	we	PRON
cana-259	239	28	examine	examine	VERB
cana-259	239	29	a	a	DET
cana-259	239	30	few	few	ADJ
cana-259	239	31	different	different	ADJ
cana-259	239	32	versions	version	NOUN
cana-259	239	33	of	of	ADP
cana-259	239	34	the	the	DET
cana-259	239	35	monetary	monetary	ADJ
cana-259	239	36	value	value	NOUN
cana-259	239	37	v	v	NOUN
cana-259	239	38	(	(	PUNCT
cana-259	239	39	xs	xs	PROPN
cana-259	239	40	)	)	PUNCT
cana-259	239	41	and	and	CCONJ
cana-259	239	42	the	the	DET
cana-259	239	43	state	state	NOUN
cana-259	239	44	penalty	penalty	NOUN
cana-259	239	45	function	function	NOUN
cana-259	239	46	q(xs	q(x	NOUN
cana-259	239	47	):	):	PUNCT
cana-259	239	48	the	the	DET
cana-259	239	49	optimum	optimum	ADJ
cana-259	239	50	controller	controller	NOUN
cana-259	239	51	may	may	AUX
cana-259	239	52	be	be	AUX
cana-259	239	53	expressed	express	VERB
cana-259	239	54	similar	similar	ADJ
cana-259	239	55	as	as	ADP
cana-259	239	56	(	(	PUNCT
cana-259	239	57	28	28	NUM
cana-259	239	58	)	)	PUNCT
cana-259	239	59	+	+	CCONJ
cana-259	239	60	(	(	PUNCT
cana-259	239	61	21	21	NUM
cana-259	239	62	)	)	PUNCT
cana-259	239	63	,	,	PUNCT
cana-259	239	64	where	where	SCONJ
cana-259	239	65	communications	communication	NOUN
cana-259	239	66	on	on	ADP
cana-259	239	67	applied	apply	VERB
cana-259	239	68	nonlinear	nonlinear	ADJ
cana-259	239	69	analysis	analysis	NOUN
cana-259	239	70	issn	issn	NOUN
cana-259	239	71	:	:	PUNCT
cana-259	239	72	1074	1074	NUM
cana-259	239	73	-	-	PUNCT
cana-259	239	74	133x	133x	NUM
cana-259	239	75	vol	vol	NOUN
cana-259	239	76	30	30	NUM
cana-259	239	77	no	no	NOUN
cana-259	239	78	.	.	NOUN
cana-259	239	79	2	2	NUM
cana-259	239	80	(	(	PUNCT
cana-259	239	81	2023	2023	NUM
cana-259	239	82	)	)	PUNCT
cana-259	239	83	12	12	NUM
cana-259	239	84	https://internationalpubls.com	https://internationalpubls.com	X
cana-259	239	85	p	p	PROPN
cana-259	239	86	and	and	CCONJ
cana-259	239	87	v˰∗	v˰∗	NUM
cana-259	239	88	have	have	VERB
cana-259	239	89	yet	yet	ADV
cana-259	239	90	to	to	PART
cana-259	239	91	be	be	AUX
cana-259	239	92	ascertained	ascertain	VERB
cana-259	239	93	.	.	PUNCT
cana-259	240	1	it	it	PRON
cana-259	240	2	follows	follow	VERB
cana-259	240	3	from	from	ADP
cana-259	240	4	(	(	PUNCT
cana-259	240	5	22	22	NUM
cana-259	240	6	)	)	PUNCT
cana-259	240	7	that	that	SCONJ
cana-259	240	8	a	a	DET
cana-259	240	9	novel	novel	ADJ
cana-259	240	10	kind	kind	NOUN
cana-259	240	11	of	of	ADP
cana-259	240	12	ghjb	ghjb	NOUN
cana-259	240	13	-	-	PUNCT
cana-259	240	14	like	like	ADJ
cana-259	240	15	formula	formula	NOUN
cana-259	240	16	is	be	AUX
cana-259	240	17	provided	provide	VERB
cana-259	240	18	by	by	ADP
cana-259	240	19	employing	employ	VERB
cana-259	240	20	(	(	PUNCT
cana-259	240	21	26)–(29	26)–(29	NUM
cana-259	240	22	)	)	PUNCT
cana-259	240	23	.	.	PUNCT
cana-259	241	1	[	[	X
cana-259	241	2	from	from	ADP
cana-259	241	3	(	(	PUNCT
cana-259	241	4	24	24	NUM
cana-259	241	5	)	)	PUNCT
cana-259	241	6	]	]	PUNCT
cana-259	242	1	it	it	PRON
cana-259	242	2	is	be	AUX
cana-259	242	3	evident	evident	ADJ
cana-259	242	4	that	that	SCONJ
cana-259	242	5	the	the	DET
cana-259	242	6	synthesized	synthesize	VERB
cana-259	242	7	ideal	ideal	ADJ
cana-259	242	8	system	system	NOUN
cana-259	242	9	for	for	ADP
cana-259	242	10	control	control	NOUN
cana-259	242	11	(	(	PUNCT
cana-259	242	12	30	30	NUM
cana-259	242	13	)	)	PUNCT
cana-259	242	14	[	[	X
cana-259	242	15	which	which	PRON
cana-259	242	16	is	be	AUX
cana-259	242	17	equivalent	equivalent	ADJ
cana-259	242	18	to	to	ADP
cana-259	242	19	(	(	PUNCT
cana-259	242	20	21	21	NUM
cana-259	242	21	)	)	PUNCT
cana-259	242	22	]	]	PUNCT
cana-259	242	23	can	can	AUX
cana-259	242	24	both	both	PRON
cana-259	242	25	maximize	maximize	VERB
cana-259	242	26	velocity	velocity	NOUN
cana-259	242	27	across	across	ADP
cana-259	242	28	the	the	DET
cana-259	242	29	rom	rom	NOUN
cana-259	242	30	and	and	CCONJ
cana-259	242	31	ensure	ensure	VERB
cana-259	242	32	the	the	DET
cana-259	242	33	rom	rom	NOUN
cana-259	242	34	's	's	PART
cana-259	242	35	maximal	maximal	ADJ
cana-259	242	36	closed	close	VERB
cana-259	242	37	-	-	PUNCT
cana-259	242	38	loop	loop	NOUN
cana-259	242	39	applications	application	NOUN
cana-259	242	40	stability	stability	NOUN
cana-259	242	41	(	(	PUNCT
cana-259	242	42	18	18	NUM
cana-259	242	43	)	)	PUNCT
cana-259	242	44	.	.	PUNCT
cana-259	243	1	additionally	additionally	ADV
cana-259	243	2	,	,	PUNCT
cana-259	243	3	(	(	PUNCT
cana-259	243	4	12	12	NUM
cana-259	243	5	)	)	PUNCT
cana-259	243	6	's	's	PART
cana-259	243	7	closed	closed	ADJ
cana-259	243	8	-	-	PUNCT
cana-259	243	9	loop	loop	NOUN
cana-259	243	10	architecture	architecture	NOUN
cana-259	243	11	is	be	AUX
cana-259	243	12	highly	highly	ADV
cana-259	243	13	stable	stable	ADJ
cana-259	243	14	,	,	PUNCT
cana-259	243	15	as	as	SCONJ
cana-259	243	16	demonstrated	demonstrate	VERB
cana-259	243	17	by	by	ADP
cana-259	243	18	theorem	theorem	NOUN
cana-259	243	19	1	1	NUM
cana-259	243	20	.	.	PUNCT
cana-259	244	1	in	in	ADP
cana-259	244	2	the	the	DET
cana-259	244	3	case	case	NOUN
cana-259	244	4	of	of	ADP
cana-259	244	5	the	the	DET
cana-259	244	6	nonlinear	nonlinear	ADJ
cana-259	244	7	parabolic	parabolic	ADJ
cana-259	244	8	pde	pde	NOUN
cana-259	244	9	system	system	NOUN
cana-259	244	10	(	(	PUNCT
cana-259	244	11	5	5	NUM
cana-259	244	12	)	)	PUNCT
cana-259	244	13	,	,	PUNCT
cana-259	244	14	the	the	DET
cana-259	244	15	first	first	ADJ
cana-259	244	16	assumption	assumption	NOUN
cana-259	244	17	is	be	AUX
cana-259	244	18	false	false	ADJ
cana-259	244	19	is	be	AUX
cana-259	244	20	true	true	ADJ
cana-259	244	21	,	,	PUNCT
cana-259	244	22	is	be	AUX
cana-259	244	23	the	the	DET
cana-259	244	24	subject	subject	NOUN
cana-259	244	25	of	of	ADP
cana-259	244	26	theorem	theorem	NOUN
cana-259	244	27	1	1	NUM
cana-259	244	28	.	.	PUNCT
cana-259	245	1	next	next	ADV
cana-259	245	2	,	,	PUNCT
cana-259	245	3	if	if	SCONJ
cana-259	245	4	xs0	xs0	PROPN
cana-259	245	5	\1	\1	PROPN
cana-259	245	6	,	,	PUNCT
cana-259	245	7	xf0	xf0	NUM
cana-259	245	8	\2	\2	PROPN
cana-259	245	9	,	,	PUNCT
cana-259	245	10	and	and	CCONJ
cana-259	245	11	ε	ε	PROPN
cana-259	245	12	(	(	PUNCT
cana-259	245	13	0	0	NUM
cana-259	245	14	,	,	PUNCT
cana-259	245	15	ε∗	ε∗	PROPN
cana-259	245	16	)	)	PUNCT
cana-259	245	17	,	,	PUNCT
cana-259	245	18	thus	thus	ADV
cana-259	245	19	,	,	PUNCT
cana-259	245	20	in	in	ADP
cana-259	245	21	an	an	DET
cana-259	245	22	identical	identical	ADJ
cana-259	245	23	manner	manner	NOUN
cana-259	245	24	,	,	PUNCT
cana-259	245	25	the	the	DET
cana-259	245	26	optimal	optimal	ADJ
cana-259	245	27	operator	operator	NOUN
cana-259	245	28	(	(	PUNCT
cana-259	245	29	30	30	NUM
cana-259	245	30	)	)	PUNCT
cana-259	246	1	[	[	X
cana-259	246	2	or	or	CCONJ
cana-259	246	3	(	(	PUNCT
cana-259	246	4	21	21	NUM
cana-259	246	5	)	)	PUNCT
cana-259	246	6	may	may	AUX
cana-259	246	7	guarantee	guarantee	VERB
cana-259	246	8	that	that	SCONJ
cana-259	246	9	the	the	DET
cana-259	246	10	closed	closed	ADJ
cana-259	246	11	-	-	PUNCT
cana-259	246	12	loop	loop	NOUN
cana-259	246	13	system	system	NOUN
cana-259	246	14	of	of	ADP
cana-259	246	15	(	(	PUNCT
cana-259	246	16	12	12	NUM
cana-259	246	17	)	)	PUNCT
cana-259	246	18	is	be	AUX
cana-259	246	19	asymmetrically	asymmetrically	ADV
cana-259	246	20	stable	stable	ADJ
cana-259	246	21	.	.	PUNCT
cana-259	247	1	this	this	PRON
cana-259	247	2	is	be	AUX
cana-259	247	3	because	because	SCONJ
cana-259	247	4	there	there	PRON
cana-259	247	5	are	be	VERB
cana-259	247	6	positive	positive	ADJ
cana-259	247	7	real	real	ADJ
cana-259	247	8	values	value	NOUN
cana-259	247	9	δ1	δ1	NOUN
cana-259	247	10	,	,	PUNCT
cana-259	247	11	δ2	δ2	ADJ
cana-259	247	12	,	,	PUNCT
cana-259	247	13	and	and	CCONJ
cana-259	247	14	ε∗.	ε∗.	NOUN
cana-259	247	15	note	note	VERB
cana-259	247	16	that	that	SCONJ
cana-259	247	17	the	the	DET
cana-259	247	18	best	good	ADJ
cana-259	247	19	controller	controller	NOUN
cana-259	247	20	can	can	AUX
cana-259	247	21	make	make	VERB
cana-259	247	22	sure	sure	ADJ
cana-259	247	23	the	the	DET
cana-259	247	24	system	system	NOUN
cana-259	247	25	stays	stay	VERB
cana-259	247	26	stable	stable	ADJ
cana-259	247	27	over	over	ADP
cana-259	247	28	time	time	NOUN
cana-259	247	29	.	.	PUNCT
cana-259	248	1	this	this	PRON
cana-259	248	2	is	be	AUX
cana-259	248	3	because	because	SCONJ
cana-259	248	4	the	the	DET
cana-259	248	5	solution	solution	NOUN
cana-259	248	6	obtained	obtain	VERB
cana-259	248	7	through	through	ADP
cana-259	248	8	a	a	DET
cana-259	248	9	specific	specific	ADJ
cana-259	248	10	equation	equation	NOUN
cana-259	248	11	will	will	AUX
cana-259	248	12	keep	keep	VERB
cana-259	248	13	getting	get	VERB
cana-259	248	14	closer	close	ADJ
cana-259	248	15	to	to	ADP
cana-259	248	16	a	a	DET
cana-259	248	17	specific	specific	ADJ
cana-259	248	18	value.additionally	value.additionally	NOUN
cana-259	248	19	,	,	PUNCT
cana-259	248	20	[	[	X
cana-259	248	21	20	20	NUM
cana-259	248	22	,	,	PUNCT
cana-259	248	23	proposition	proposition	NOUN
cana-259	248	24	1	1	NUM
cana-259	248	25	]	]	PUNCT
cana-259	248	26	shows	show	VERB
cana-259	248	27	that	that	SCONJ
cana-259	248	28	the	the	DET
cana-259	248	29	pde	pde	PROPN
cana-259	248	30	scheme	scheme	NOUN
cana-259	248	31	(	(	PUNCT
cana-259	248	32	5	5	NUM
cana-259	248	33	)	)	PUNCT
cana-259	248	34	's	's	PART
cana-259	248	35	resolution	resolution	NOUN
cana-259	248	36	y(z	y(z	PROPN
cana-259	248	37	,	,	PUNCT
cana-259	248	38	t	t	PROPN
cana-259	248	39	)	)	PUNCT
cana-259	248	40	will	will	AUX
cana-259	248	41	approach	approach	VERB
cana-259	248	42	the	the	DET
cana-259	248	43	solution	solution	NOUN
cana-259	248	44	yˆ(z	yˆ(z	NOUN
cana-259	248	45	,	,	PUNCT
cana-259	248	46	t	t	PROPN
cana-259	248	47	)	)	PUNCT
cana-259	248	48	as	as	SCONJ
cana-259	248	49	m	m	NOUN
cana-259	248	50	grows	grow	VERB
cana-259	248	51	.	.	PUNCT
cana-259	249	1	actually	actually	ADV
cana-259	249	2	,	,	PUNCT
cana-259	249	3	because	because	SCONJ
cana-259	249	4	of	of	ADP
cana-259	249	5	the	the	DET
cana-259	249	6	curved	curved	ADJ
cana-259	249	7	shape	shape	NOUN
cana-259	249	8	of	of	ADP
cana-259	249	9	the	the	DET
cana-259	249	10	sdo	sdo	NOUN
cana-259	249	11	,	,	PUNCT
cana-259	249	12	we	we	PRON
cana-259	249	13	can	can	AUX
cana-259	249	14	accurately	accurately	ADV
cana-259	249	15	describe	describe	VERB
cana-259	249	16	the	the	DET
cana-259	249	17	main	main	ADJ
cana-259	249	18	way	way	NOUN
cana-259	249	19	parabolic	parabolic	PROPN
cana-259	249	20	pde	pde	NOUN
cana-259	249	21	systems	system	NOUN
cana-259	249	22	behave	behave	AUX
cana-259	249	23	using	use	VERB
cana-259	249	24	just	just	ADV
cana-259	249	25	a	a	DET
cana-259	249	26	few	few	ADJ
cana-259	249	27	patterns	pattern	NOUN
cana-259	249	28	.	.	PUNCT
cana-259	250	1	several	several	ADJ
cana-259	250	2	studies	study	NOUN
cana-259	250	3	have	have	AUX
cana-259	250	4	shown	show	VERB
cana-259	250	5	that	that	SCONJ
cana-259	250	6	a	a	DET
cana-259	250	7	very	very	ADV
cana-259	250	8	small	small	ADJ
cana-259	250	9	m	m	NOUN
cana-259	250	10	can	can	AUX
cana-259	250	11	give	give	VERB
cana-259	250	12	good	good	ADJ
cana-259	250	13	results	result	NOUN
cana-259	250	14	,	,	PUNCT
cana-259	250	15	meaning	mean	VERB
cana-259	250	16	that	that	SCONJ
cana-259	250	17	yˆ(z	yˆ(z	NOUN
cana-259	250	18	,	,	PUNCT
cana-259	250	19	t	t	PROPN
cana-259	250	20	)	)	PUNCT
cana-259	250	21	and	and	CCONJ
cana-259	250	22	y(z	y(z	PROPN
cana-259	250	23	,	,	PUNCT
cana-259	250	24	t	t	PROPN
cana-259	250	25	)	)	PUNCT
cana-259	250	26	behave	behave	VERB
cana-259	250	27	similarly	similarly	ADV
cana-259	250	28	.	.	PUNCT
cana-259	251	1	the	the	DET
cana-259	251	2	top	top	ADJ
cana-259	251	3	control	control	NOUN
cana-259	251	4	system	system	NOUN
cana-259	251	5	for	for	ADP
cana-259	251	6	rom	rom	NOUN
cana-259	251	7	(	(	PUNCT
cana-259	251	8	18	18	NUM
cana-259	251	9	)	)	PUNCT
cana-259	251	10	can	can	AUX
cana-259	251	11	achieve	achieve	VERB
cana-259	251	12	results	result	NOUN
cana-259	251	13	that	that	PRON
cana-259	251	14	are	be	AUX
cana-259	251	15	almost	almost	ADV
cana-259	251	16	as	as	ADV
cana-259	251	17	good	good	ADJ
cana-259	251	18	as	as	ADP
cana-259	251	19	the	the	DET
cana-259	251	20	original	original	ADJ
cana-259	251	21	pde	pde	NOUN
cana-259	251	22	system	system	NOUN
cana-259	251	23	(	(	PUNCT
cana-259	251	24	5	5	NUM
cana-259	251	25	)	)	PUNCT
cana-259	251	26	.	.	PUNCT
cana-259	252	1	v.	v.	ADP
cana-259	252	2	conclusion	conclusion	NOUN
cana-259	252	3	within	within	ADP
cana-259	252	4	the	the	DET
cana-259	252	5	context	context	NOUN
cana-259	252	6	of	of	ADP
cana-259	252	7	hjb	hjb	NOUN
cana-259	252	8	theories	theory	NOUN
cana-259	252	9	,	,	PUNCT
cana-259	252	10	an	an	DET
cana-259	252	11	approximation	approximation	NOUN
cana-259	252	12	optimum	optimum	ADJ
cana-259	252	13	control	control	NOUN
cana-259	252	14	system	system	NOUN
cana-259	252	15	has	have	AUX
cana-259	252	16	been	be	AUX
cana-259	252	17	synthesized	synthesize	VERB
cana-259	252	18	in	in	ADP
cana-259	252	19	this	this	DET
cana-259	252	20	research	research	NOUN
cana-259	252	21	for	for	ADP
cana-259	252	22	a	a	DET
cana-259	252	23	group	group	NOUN
cana-259	252	24	of	of	ADP
cana-259	252	25	parabolic	parabolic	ADJ
cana-259	252	26	pde	pde	NOUN
cana-259	252	27	solutions	solution	NOUN
cana-259	252	28	that	that	PRON
cana-259	252	29	are	be	AUX
cana-259	252	30	nonlinear	nonlinear	ADJ
cana-259	252	31	.	.	PUNCT
cana-259	253	1	the	the	DET
cana-259	253	2	prevailing	prevail	VERB
cana-259	253	3	dynamics	dynamic	NOUN
cana-259	253	4	of	of	ADP
cana-259	253	5	the	the	DET
cana-259	253	6	pde	pde	NOUN
cana-259	253	7	system	system	NOUN
cana-259	253	8	may	may	AUX
cana-259	253	9	be	be	AUX
cana-259	253	10	accurately	accurately	ADV
cana-259	253	11	characterised	characterise	VERB
cana-259	253	12	by	by	ADP
cana-259	253	13	the	the	DET
cana-259	253	14	rom	rom	NOUN
cana-259	253	15	that	that	PRON
cana-259	253	16	is	be	AUX
cana-259	253	17	created	create	VERB
cana-259	253	18	using	use	VERB
cana-259	253	19	the	the	DET
cana-259	253	20	data	data	NOUN
cana-259	253	21	-	-	PUNCT
cana-259	253	22	based	base	VERB
cana-259	253	23	kld	kld	PROPN
cana-259	253	24	method	method	NOUN
cana-259	253	25	and	and	CCONJ
cana-259	253	26	sp	sp	ADP
cana-259	253	27	technique	technique	NOUN
cana-259	253	28	,	,	PUNCT
cana-259	253	29	because	because	SCONJ
cana-259	253	30	the	the	DET
cana-259	253	31	sdo	sdo	NOUN
cana-259	253	32	of	of	ADP
cana-259	253	33	the	the	DET
cana-259	253	34	pde	pde	NOUN
cana-259	253	35	component	component	NOUN
cana-259	253	36	is	be	AUX
cana-259	253	37	nonlinear	nonlinear	ADJ
cana-259	253	38	.	.	PUNCT
cana-259	254	1	the	the	DET
cana-259	254	2	high	high	ADJ
cana-259	254	3	-	-	PUNCT
cana-259	254	4	order	order	NOUN
cana-259	254	5	ode	ode	ADJ
cana-259	254	6	system	system	NOUN
cana-259	254	7	's	's	PART
cana-259	254	8	closed	closed	ADJ
cana-259	254	9	-	-	PUNCT
cana-259	254	10	loop	loop	NOUN
cana-259	254	11	systems	system	NOUN
cana-259	254	12	terminal	terminal	PROPN
cana-259	254	13	stability	stability	NOUN
cana-259	254	14	is	be	AUX
cana-259	254	15	ensured	ensure	VERB
cana-259	254	16	,	,	PUNCT
cana-259	254	17	and	and	CCONJ
cana-259	254	18	an	an	DET
cana-259	254	19	estimated	estimate	VERB
cana-259	254	20	optimum	optimum	ADJ
cana-259	254	21	controller	controller	NOUN
cana-259	254	22	is	be	AUX
cana-259	254	23	offered	offer	VERB
cana-259	254	24	by	by	ADP
cana-259	254	25	two	two	NUM
cana-259	254	26	sections	section	NOUN
cana-259	254	27	to	to	PART
cana-259	254	28	fully	fully	ADV
cana-259	254	29	use	use	VERB
cana-259	254	30	the	the	DET
cana-259	254	31	linear	linear	ADJ
cana-259	254	32	portion	portion	NOUN
cana-259	254	33	of	of	ADP
cana-259	254	34	the	the	DET
cana-259	254	35	rom	rom	NOUN
cana-259	254	36	.	.	PUNCT
cana-259	255	1	the	the	DET
cana-259	255	2	linear	linear	ADJ
cana-259	255	3	portion	portion	NOUN
cana-259	255	4	of	of	ADP
cana-259	255	5	the	the	DET
cana-259	255	6	rom	rom	NOUN
cana-259	255	7	,	,	PUNCT
cana-259	255	8	which	which	PRON
cana-259	255	9	is	be	AUX
cana-259	255	10	acquired	acquire	VERB
cana-259	255	11	by	by	ADP
cana-259	255	12	solving	solve	VERB
cana-259	255	13	and	and	CCONJ
cana-259	255	14	are	be	AUX
cana-259	255	15	,	,	PUNCT
cana-259	255	16	is	be	AUX
cana-259	255	17	the	the	DET
cana-259	255	18	target	target	NOUN
cana-259	255	19	of	of	ADP
cana-259	255	20	the	the	DET
cana-259	255	21	first	first	ADJ
cana-259	255	22	section	section	NOUN
cana-259	255	23	of	of	ADP
cana-259	255	24	the	the	DET
cana-259	255	25	synthesized	synthesize	VERB
cana-259	255	26	controller	controller	NOUN
cana-259	255	27	.	.	PUNCT
cana-259	256	1	conversely	conversely	ADV
cana-259	256	2	,	,	PUNCT
cana-259	256	3	the	the	DET
cana-259	256	4	latter	latter	ADJ
cana-259	256	5	portion	portion	NOUN
cana-259	256	6	is	be	AUX
cana-259	256	7	which	which	PRON
cana-259	256	8	nn	nn	PROPN
cana-259	256	9	is	be	AUX
cana-259	256	10	used	use	VERB
cana-259	256	11	in	in	ADP
cana-259	256	12	the	the	DET
cana-259	256	13	cost	cost	NOUN
cana-259	256	14	function	function	NOUN
cana-259	256	15	estimation	estimation	NOUN
cana-259	256	16	process	process	NOUN
cana-259	256	17	.	.	PUNCT
cana-259	257	1	ultimately	ultimately	ADV
cana-259	257	2	,	,	PUNCT
cana-259	257	3	the	the	DET
cana-259	257	4	case	case	NOUN
cana-259	257	5	the	the	DET
cana-259	257	6	investigation	investigation	NOUN
cana-259	257	7	's	's	PART
cana-259	257	8	stochastic	stochastic	ADJ
cana-259	257	9	diffusion	diffusion	NOUN
cana-259	257	10	–	–	PUNCT
cana-259	257	11	reaction	reaction	NOUN
cana-259	257	12	processes	process	NOUN
cana-259	257	13	is	be	AUX
cana-259	257	14	used	use	VERB
cana-259	257	15	to	to	PART
cana-259	257	16	demonstrate	demonstrate	VERB
cana-259	257	17	the	the	DET
cana-259	257	18	effectiveness	effectiveness	NOUN
cana-259	257	19	of	of	ADP
cana-259	257	20	the	the	DET
cana-259	257	21	mechanism	mechanism	NOUN
cana-259	257	22	of	of	ADP
cana-259	257	23	control	control	NOUN
cana-259	257	24	that	that	PRON
cana-259	257	25	was	be	AUX
cana-259	257	26	developed	develop	VERB
cana-259	257	27	,	,	PUNCT
cana-259	257	28	according	accord	VERB
cana-259	257	29	to	to	ADP
cana-259	257	30	the	the	DET
cana-259	257	31	simulation	simulation	NOUN
cana-259	257	32	findings	finding	NOUN
cana-259	257	33	.	.	PUNCT
cana-259	258	1	communications	communication	NOUN
cana-259	258	2	on	on	ADP
cana-259	258	3	applied	apply	VERB
cana-259	258	4	nonlinear	nonlinear	ADJ
cana-259	258	5	analysis	analysis	NOUN
cana-259	258	6	issn	issn	NOUN
cana-259	258	7	:	:	PUNCT
cana-259	258	8	1074	1074	NUM
cana-259	258	9	-	-	PUNCT
cana-259	258	10	133x	133x	NUM
cana-259	258	11	vol	vol	NOUN
cana-259	258	12	30	30	NUM
cana-259	258	13	no	no	NOUN
cana-259	258	14	.	.	NOUN
cana-259	258	15	2	2	NUM
cana-259	258	16	(	(	PUNCT
cana-259	258	17	2023	2023	NUM
cana-259	258	18	)	)	PUNCT
cana-259	258	19	13	13	NUM
cana-259	258	20	https://internationalpubls.com	https://internationalpubls.com	X
cana-259	258	21	refrences	refrence	VERB
cana-259	259	1	[	[	X
cana-259	259	2	1	1	X
cana-259	259	3	]	]	PUNCT
cana-259	259	4	f.	f.	PROPN
cana-259	259	5	l.	l.	PROPN
cana-259	259	6	lewis	lewis	PROPN
cana-259	259	7	and	and	CCONJ
cana-259	259	8	v.	v.	PROPN
cana-259	259	9	l.	l.	PROPN
cana-259	259	10	syrmos	syrmos	PROPN
cana-259	259	11	,	,	PUNCT
cana-259	259	12	optimal	optimal	ADJ
cana-259	259	13	control	control	NOUN
cana-259	259	14	.	.	PUNCT
cana-259	260	1	new	new	PROPN
cana-259	260	2	york	york	PROPN
cana-259	260	3	:	:	PUNCT
cana-259	260	4	wiley	wiley	PROPN
cana-259	260	5	,	,	PUNCT
cana-259	260	6	1995	1995	NUM
cana-259	260	7	.	.	PUNCT
cana-259	261	1	[	[	X
cana-259	261	2	2	2	X
cana-259	261	3	]	]	PUNCT
cana-259	261	4	d.	d.	PROPN
cana-259	261	5	p.	p.	PROPN
cana-259	261	6	bertsekas	bertsekas	PROPN
cana-259	261	7	,	,	PUNCT
cana-259	261	8	dynamic	dynamic	ADJ
cana-259	261	9	programming	programming	NOUN
cana-259	261	10	and	and	CCONJ
cana-259	261	11	optimal	optimal	ADJ
cana-259	261	12	control	control	NOUN
cana-259	261	13	,	,	PUNCT
cana-259	261	14	3rd	3rd	ADJ
cana-259	261	15	ed	ed	NOUN
cana-259	261	16	.	.	PUNCT
cana-259	261	17	nashua	nashua	PROPN
cana-259	261	18	,	,	PUNCT
cana-259	261	19	nh	nh	PROPN
cana-259	261	20	:	:	PUNCT
cana-259	261	21	athena	athena	PROPN
cana-259	261	22	scientific	scientific	PROPN
cana-259	261	23	,	,	PUNCT
cana-259	261	24	2005	2005	NUM
cana-259	261	25	.	.	PUNCT
cana-259	262	1	[	[	X
cana-259	262	2	3	3	NUM
cana-259	262	3	]	]	PUNCT
cana-259	262	4	a.	a.	NOUN
cana-259	262	5	g.	g.	NOUN
cana-259	262	6	butkovskiy	butkovskiy	NOUN
cana-259	262	7	,	,	PUNCT
cana-259	262	8	distributed	distribute	VERB
cana-259	262	9	control	control	NOUN
cana-259	262	10	systems	system	NOUN
cana-259	262	11	.	.	PUNCT
cana-259	263	1	new	new	PROPN
cana-259	263	2	york	york	PROPN
cana-259	263	3	:	:	PUNCT
cana-259	263	4	american	american	PROPN
cana-259	263	5	elsevier	elsevier	PROPN
cana-259	263	6	,	,	PUNCT
cana-259	263	7	1969	1969	NUM
cana-259	263	8	.	.	PUNCT
cana-259	264	1	[	[	X
cana-259	264	2	4	4	X
cana-259	264	3	]	]	PUNCT
cana-259	264	4	p.	p.	NOUN
cana-259	264	5	k.	k.	PROPN
cana-259	265	1	c.	c.	PROPN
cana-259	265	2	wang	wang	PROPN
cana-259	265	3	and	and	CCONJ
cana-259	265	4	f.	f.	PROPN
cana-259	265	5	tung	tung	PROPN
cana-259	265	6	,	,	PUNCT
cana-259	265	7	“	"	PUNCT
cana-259	265	8	optimum	optimum	ADJ
cana-259	265	9	control	control	NOUN
cana-259	265	10	of	of	ADP
cana-259	265	11	distributed	distribute	VERB
cana-259	265	12	parameter	parameter	NOUN
cana-259	265	13	systems	system	NOUN
cana-259	265	14	,	,	PUNCT
cana-259	265	15	”	"	PUNCT
cana-259	265	16	j.	j.	PROPN
cana-259	265	17	basic	basic	PROPN
cana-259	265	18	eng	eng	PROPN
cana-259	265	19	.	.	PROPN
cana-259	265	20	,	,	PUNCT
cana-259	265	21	vol	vol	NOUN
cana-259	265	22	.	.	PROPN
cana-259	265	23	86	86	NUM
cana-259	265	24	,	,	PUNCT
cana-259	265	25	no	no	INTJ
cana-259	265	26	.	.	NOUN
cana-259	265	27	1	1	NUM
cana-259	265	28	,	,	PUNCT
cana-259	265	29	pp	pp	ADJ
cana-259	265	30	.	.	PUNCT
cana-259	266	1	67–79	67–79	NUM
cana-259	266	2	,	,	PUNCT
cana-259	266	3	mar	mar	PROPN
cana-259	266	4	.	.	PROPN
cana-259	266	5	1964	1964	NUM
cana-259	266	6	.	.	PUNCT
cana-259	267	1	[	[	X
cana-259	267	2	5	5	X
cana-259	267	3	]	]	PUNCT
cana-259	267	4	j.	j.	PROPN
cana-259	267	5	l.	l.	PROPN
cana-259	267	6	lions	lions	PROPN
cana-259	267	7	,	,	PUNCT
cana-259	267	8	optimal	optimal	ADJ
cana-259	267	9	control	control	NOUN
cana-259	267	10	of	of	ADP
cana-259	267	11	systems	system	NOUN
cana-259	267	12	governed	govern	VERB
cana-259	267	13	by	by	ADP
cana-259	267	14	partial	partial	ADJ
cana-259	267	15	differential	differential	ADJ
cana-259	267	16	equations	equation	NOUN
cana-259	267	17	.	.	PUNCT
cana-259	268	1	new	new	PROPN
cana-259	268	2	york	york	PROPN
cana-259	268	3	:	:	PUNCT
cana-259	268	4	springer	springer	NOUN
cana-259	268	5	-	-	PUNCT
cana-259	268	6	verlag	verlag	PROPN
cana-259	268	7	,	,	PUNCT
cana-259	268	8	1971	1971	NUM
cana-259	268	9	.	.	PUNCT
cana-259	269	1	[	[	X
cana-259	269	2	6	6	NUM
cana-259	269	3	]	]	PUNCT
cana-259	269	4	h.	h.	PROPN
cana-259	269	5	o.	o.	PROPN
cana-259	269	6	fattorini	fattorini	PROPN
cana-259	269	7	,	,	PUNCT
cana-259	269	8	infinite	infinite	ADJ
cana-259	269	9	dimensional	dimensional	ADJ
cana-259	269	10	optimization	optimization	NOUN
cana-259	269	11	theory	theory	NOUN
cana-259	269	12	and	and	CCONJ
cana-259	269	13	optimal	optimal	ADJ
cana-259	269	14	control	control	NOUN
cana-259	269	15	.	.	PUNCT
cana-259	270	1	cambridge	cambridge	PROPN
cana-259	270	2	,	,	PUNCT
cana-259	270	3	u.k	u.k	PROPN
cana-259	270	4	.	.	PROPN
cana-259	270	5	:	:	PUNCT
cana-259	271	1	cambridge	cambridge	PROPN
cana-259	271	2	univ	univ	PROPN
cana-259	271	3	.	.	PUNCT
cana-259	272	1	press	press	PROPN
cana-259	272	2	,	,	PUNCT
cana-259	272	3	1999	1999	NUM
cana-259	272	4	.	.	PUNCT
cana-259	273	1	[	[	X
cana-259	273	2	7	7	X
cana-259	273	3	]	]	PUNCT
cana-259	273	4	x.	x.	NOUN
cana-259	273	5	li	li	PROPN
cana-259	273	6	and	and	CCONJ
cana-259	273	7	j.	j.	PROPN
cana-259	273	8	yong	yong	PROPN
cana-259	273	9	,	,	PUNCT
cana-259	273	10	optimal	optimal	ADJ
cana-259	273	11	control	control	NOUN
cana-259	273	12	theory	theory	NOUN
cana-259	273	13	for	for	ADP
cana-259	273	14	infinite	infinite	ADJ
cana-259	273	15	dimensional	dimensional	ADJ
cana-259	273	16	systems	system	NOUN
cana-259	273	17	.	.	PUNCT
cana-259	274	1	boston	boston	PROPN
cana-259	274	2	,	,	PUNCT
cana-259	274	3	ma	ma	PROPN
cana-259	274	4	:	:	PUNCT
cana-259	274	5	birkhäuser	birkhäuser	ADJ
cana-259	274	6	,	,	PUNCT
cana-259	274	7	1995	1995	NUM
cana-259	274	8	.	.	PUNCT
cana-259	275	1	[	[	X
cana-259	275	2	8	8	NUM
cana-259	275	3	]	]	X
cana-259	275	4	r.	r.	PROPN
cana-259	275	5	f.	f.	PROPN
cana-259	275	6	curtain	curtain	PROPN
cana-259	275	7	and	and	CCONJ
cana-259	275	8	h.	h.	PROPN
cana-259	275	9	j.	j.	PROPN
cana-259	275	10	zwart	zwart	PROPN
cana-259	275	11	,	,	PUNCT
cana-259	275	12	an	an	DET
cana-259	275	13	introduction	introduction	NOUN
cana-259	275	14	to	to	ADP
cana-259	275	15	infinite	infinite	VERB
cana-259	275	16	-	-	PUNCT
cana-259	275	17	dimensional	dimensional	ADJ
cana-259	275	18	linear	linear	NOUN
cana-259	275	19	systems	system	NOUN
cana-259	275	20	theory	theory	NOUN
cana-259	275	21	.	.	PUNCT
cana-259	276	1	new	new	PROPN
cana-259	276	2	york	york	PROPN
cana-259	276	3	:	:	PUNCT
cana-259	276	4	springer	springer	NOUN
cana-259	276	5	-	-	PUNCT
cana-259	276	6	verlag	verlag	PROPN
cana-259	276	7	,	,	PUNCT
cana-259	276	8	1995	1995	NUM
cana-259	276	9	.	.	PUNCT
cana-259	277	1	[	[	X
cana-259	277	2	9	9	NUM
cana-259	277	3	]	]	SYM
cana-259	277	4	i.	i.	NOUN
cana-259	277	5	aksikas	aksikas	PROPN
cana-259	277	6	,	,	PUNCT
cana-259	277	7	a.	a.	PROPN
cana-259	277	8	fuxman	fuxman	PROPN
cana-259	277	9	,	,	PUNCT
cana-259	277	10	j.	j.	PROPN
cana-259	277	11	f.	f.	PROPN
cana-259	277	12	forbes	forbes	PROPN
cana-259	277	13	,	,	PUNCT
cana-259	277	14	and	and	CCONJ
cana-259	277	15	j.	j.	PROPN
cana-259	277	16	j.	j.	PROPN
cana-259	277	17	winkin	winkin	PROPN
cana-259	277	18	,	,	PUNCT
cana-259	277	19	“	"	PUNCT
cana-259	277	20	lq	lq	X
cana-259	277	21	control	control	NOUN
cana-259	277	22	design	design	NOUN
cana-259	277	23	of	of	ADP
cana-259	277	24	a	a	DET
cana-259	277	25	class	class	NOUN
cana-259	277	26	of	of	ADP
cana-259	277	27	hyperbolic	hyperbolic	ADJ
cana-259	277	28	pde	pde	NOUN
cana-259	277	29	systems	system	NOUN
cana-259	277	30	:	:	PUNCT
cana-259	277	31	application	application	NOUN
cana-259	277	32	to	to	ADP
cana-259	277	33	fixed	fix	VERB
cana-259	277	34	-	-	PUNCT
cana-259	277	35	bed	bed	NOUN
cana-259	277	36	reactor	reactor	NOUN
cana-259	277	37	,	,	PUNCT
cana-259	277	38	”	"	PUNCT
cana-259	277	39	automatica	automatica	PROPN
cana-259	277	40	,	,	PUNCT
cana-259	277	41	vol	vol	NOUN
cana-259	277	42	.	.	PROPN
cana-259	277	43	45	45	NUM
cana-259	277	44	,	,	PUNCT
cana-259	277	45	no	no	INTJ
cana-259	277	46	.	.	NOUN
cana-259	277	47	6	6	NUM
cana-259	277	48	,	,	PUNCT
cana-259	277	49	pp	pp	ADJ
cana-259	277	50	.	.	PUNCT
cana-259	277	51	1542–1548	1542–1548	NUM
cana-259	277	52	,	,	PUNCT
cana-259	277	53	jun	jun	PROPN
cana-259	277	54	.	.	PROPN
cana-259	277	55	2009	2009	NUM
cana-259	277	56	.	.	PUNCT
cana-259	278	1	[	[	X
cana-259	278	2	10	10	NUM
cana-259	278	3	]	]	X
cana-259	278	4	i.	i.	NOUN
cana-259	278	5	aksikas	aksikas	PROPN
cana-259	278	6	,	,	PUNCT
cana-259	278	7	j.	j.	PROPN
cana-259	278	8	j.	j.	PROPN
cana-259	278	9	winkin	winkin	PROPN
cana-259	278	10	,	,	PUNCT
cana-259	278	11	and	and	CCONJ
cana-259	278	12	d.	d.	PROPN
cana-259	278	13	dochain	dochain	PROPN
cana-259	278	14	,	,	PUNCT
cana-259	278	15	“	"	PUNCT
cana-259	278	16	optimal	optimal	ADJ
cana-259	278	17	lq	lq	ADJ
cana-259	278	18	-	-	PUNCT
cana-259	278	19	feedback	feedback	NOUN
cana-259	278	20	regulation	regulation	NOUN
cana-259	278	21	of	of	ADP
cana-259	278	22	a	a	DET
cana-259	278	23	nonisothermal	nonisothermal	NOUN
cana-259	278	24	plug	plug	NOUN
cana-259	278	25	flow	flow	NOUN
cana-259	278	26	reactor	reactor	NOUN
cana-259	278	27	model	model	NOUN
cana-259	278	28	by	by	ADP
cana-259	278	29	spectral	spectral	ADJ
cana-259	278	30	factorization	factorization	NOUN
cana-259	278	31	,	,	PUNCT
cana-259	278	32	”	"	PUNCT
cana-259	278	33	ieee	ieee	NOUN
cana-259	278	34	trans	trans	PROPN
cana-259	278	35	.	.	PUNCT
cana-259	279	1	autom	autom	PROPN
cana-259	279	2	.	.	PUNCT
cana-259	280	1	control	control	PROPN
cana-259	280	2	,	,	PUNCT
cana-259	280	3	vol	vol	NOUN
cana-259	280	4	.	.	PROPN
cana-259	280	5	52	52	NUM
cana-259	280	6	,	,	PUNCT
cana-259	280	7	no	no	INTJ
cana-259	280	8	.	.	NOUN
cana-259	280	9	7	7	NUM
cana-259	280	10	,	,	PUNCT
cana-259	280	11	pp	pp	ADJ
cana-259	280	12	.	.	PUNCT
cana-259	281	1	1179–1193	1179–1193	NUM
cana-259	281	2	,	,	PUNCT
cana-259	281	3	jul	jul	PROPN
cana-259	281	4	.	.	PROPN
cana-259	281	5	2007	2007	NUM
cana-259	281	6	.	.	PUNCT
cana-259	282	1	[	[	X
cana-259	282	2	11	11	NUM
cana-259	282	3	]	]	PUNCT
cana-259	282	4	w.	w.	PROPN
cana-259	282	5	h.	h.	PROPN
cana-259	282	6	ray	ray	PROPN
cana-259	282	7	,	,	PUNCT
cana-259	282	8	advanced	advanced	ADJ
cana-259	282	9	process	process	NOUN
cana-259	282	10	control	control	NOUN
cana-259	282	11	.	.	PUNCT
cana-259	283	1	new	new	PROPN
cana-259	283	2	york	york	PROPN
cana-259	283	3	:	:	PUNCT
cana-259	283	4	mcgraw	mcgraw	PROPN
cana-259	283	5	-	-	PUNCT
cana-259	283	6	hill	hill	NOUN
cana-259	283	7	,	,	PUNCT
cana-259	283	8	1981	1981	NUM
cana-259	283	9	.	.	PUNCT
cana-259	284	1	[	[	X
cana-259	284	2	12	12	NUM
cana-259	284	3	]	]	PUNCT
cana-259	284	4	m.	m.	NOUN
cana-259	284	5	li	li	PROPN
cana-259	284	6	and	and	CCONJ
cana-259	284	7	p.	p.	PROPN
cana-259	284	8	d.	d.	PROPN
cana-259	284	9	christofides	christofides	PROPN
cana-259	284	10	,	,	PUNCT
cana-259	284	11	“	"	PUNCT
cana-259	284	12	an	an	DET
cana-259	284	13	input	input	NOUN
cana-259	284	14	/	/	SYM
cana-259	284	15	output	output	NOUN
cana-259	284	16	approach	approach	NOUN
cana-259	284	17	to	to	ADP
cana-259	284	18	the	the	DET
cana-259	284	19	optimal	optimal	ADJ
cana-259	284	20	transition	transition	NOUN
cana-259	284	21	control	control	NOUN
cana-259	284	22	of	of	ADP
cana-259	284	23	a	a	DET
cana-259	284	24	class	class	NOUN
cana-259	284	25	of	of	ADP
cana-259	284	26	distributed	distribute	VERB
cana-259	284	27	chemical	chemical	NOUN
cana-259	284	28	reactors	reactor	NOUN
cana-259	284	29	,	,	PUNCT
cana-259	284	30	”	"	PUNCT
cana-259	284	31	chem	chem	NOUN
cana-259	284	32	.	.	PUNCT
cana-259	285	1	eng	eng	PROPN
cana-259	285	2	.	.	PUNCT
cana-259	286	1	sci	sci	PROPN
cana-259	286	2	.	.	PROPN
cana-259	286	3	,	,	PUNCT
cana-259	286	4	vol	vol	NOUN
cana-259	286	5	.	.	PROPN
cana-259	287	1	62	62	NUM
cana-259	287	2	,	,	PUNCT
cana-259	287	3	no	no	INTJ
cana-259	287	4	.	.	NOUN
cana-259	287	5	11	11	NUM
cana-259	287	6	,	,	PUNCT
cana-259	287	7	pp	pp	ADJ
cana-259	287	8	.	.	PUNCT
cana-259	288	1	2979–2988	2979–2988	NUM
cana-259	288	2	,	,	PUNCT
cana-259	288	3	2007	2007	NUM
cana-259	288	4	.	.	PUNCT
cana-259	289	1	[	[	X
cana-259	289	2	13	13	NUM
cana-259	289	3	]	]	PUNCT
cana-259	289	4	m.	m.	NOUN
cana-259	289	5	li	li	PROPN
cana-259	289	6	and	and	CCONJ
cana-259	289	7	p.	p.	PROPN
cana-259	289	8	d.	d.	PROPN
cana-259	289	9	christofides	christofide	NOUN
cana-259	289	10	,	,	PUNCT
cana-259	289	11	“	"	PUNCT
cana-259	289	12	optimal	optimal	ADJ
cana-259	289	13	control	control	NOUN
cana-259	289	14	of	of	ADP
cana-259	289	15	diffusion	diffusion	NOUN
cana-259	289	16	–	–	PUNCT
cana-259	289	17	convection	convection	NOUN
cana-259	289	18	–	–	PUNCT
cana-259	289	19	reaction	reaction	NOUN
cana-259	289	20	processes	process	NOUN
cana-259	289	21	using	use	VERB
cana-259	289	22	reduced	reduce	VERB
cana-259	289	23	-	-	PUNCT
cana-259	289	24	order	order	NOUN
cana-259	289	25	models	model	NOUN
cana-259	289	26	,	,	PUNCT
cana-259	289	27	”	"	PUNCT
cana-259	289	28	comput	comput	NOUN
cana-259	289	29	.	.	PUNCT
cana-259	290	1	chem	chem	NOUN
cana-259	290	2	.	.	PUNCT
cana-259	291	1	eng	eng	PROPN
cana-259	291	2	.	.	PROPN
cana-259	291	3	,	,	PUNCT
cana-259	291	4	vol	vol	NOUN
cana-259	291	5	.	.	PROPN
cana-259	292	1	32	32	NUM
cana-259	292	2	,	,	PUNCT
cana-259	292	3	no	no	INTJ
cana-259	292	4	.	.	NOUN
cana-259	292	5	9	9	NUM
cana-259	292	6	,	,	PUNCT
cana-259	292	7	pp	pp	ADJ
cana-259	292	8	.	.	PUNCT
cana-259	293	1	2123–2135	2123–2135	NUM
cana-259	293	2	,	,	PUNCT
cana-259	293	3	sep	sep	PROPN
cana-259	293	4	.	.	PROPN
cana-259	293	5	2008	2008	NUM
cana-259	293	6	.	.	PUNCT
cana-259	294	1	[	[	X
cana-259	294	2	14	14	NUM
cana-259	294	3	]	]	X
cana-259	294	4	c.	c.	PROPN
cana-259	294	5	xu	xu	PROPN
cana-259	294	6	,	,	PUNCT
cana-259	294	7	y.	y.	PROPN
cana-259	294	8	ou	ou	PROPN
cana-259	294	9	,	,	PUNCT
cana-259	294	10	and	and	CCONJ
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cana-259	294	13	,	,	PUNCT
cana-259	294	14	“	"	PUNCT
cana-259	294	15	sequential	sequential	ADJ
cana-259	294	16	linear	linear	ADJ
cana-259	294	17	quadratic	quadratic	ADJ
cana-259	294	18	control	control	NOUN
cana-259	294	19	of	of	ADP
cana-259	294	20	bilinear	bilinear	PROPN
cana-259	294	21	parabolic	parabolic	PROPN
cana-259	294	22	pdes	pde	NOUN
cana-259	294	23	based	base	VERB
cana-259	294	24	on	on	ADP
cana-259	294	25	pod	pod	NOUN
cana-259	294	26	model	model	NOUN
cana-259	294	27	reduction	reduction	NOUN
cana-259	294	28	,	,	PUNCT
cana-259	294	29	”	"	PUNCT
cana-259	294	30	automatica	automatica	PROPN
cana-259	294	31	,	,	PUNCT
cana-259	294	32	vol	vol	NOUN
cana-259	294	33	.	.	PROPN
cana-259	295	1	47	47	NUM
cana-259	295	2	,	,	PUNCT
cana-259	295	3	no	no	INTJ
cana-259	295	4	.	.	NOUN
cana-259	295	5	2	2	NUM
cana-259	295	6	,	,	PUNCT
cana-259	295	7	pp	pp	ADJ
cana-259	295	8	.	.	PUNCT
cana-259	296	1	418–426	418–426	NUM
cana-259	296	2	,	,	PUNCT
cana-259	296	3	feb	feb	PROPN
cana-259	296	4	.	.	PROPN
cana-259	296	5	2011	2011	NUM
cana-259	296	6	.	.	PUNCT
cana-259	297	1	[	[	X
cana-259	297	2	15	15	NUM
cana-259	297	3	]	]	X
cana-259	297	4	i.	i.	PROPN
cana-259	297	5	s.	s.	PROPN
cana-259	297	6	sadek	sadek	PROPN
cana-259	297	7	and	and	CCONJ
cana-259	297	8	m.	m.	NOUN
cana-259	297	9	a.	a.	NOUN
cana-259	297	10	bokhari	bokhari	PROPN
cana-259	297	11	,	,	PUNCT
cana-259	297	12	“	"	PUNCT
cana-259	297	13	optimal	optimal	ADJ
cana-259	297	14	control	control	NOUN
cana-259	297	15	of	of	ADP
cana-259	297	16	a	a	DET
cana-259	297	17	parabolic	parabolic	NOUN
cana-259	297	18	distributed	distribute	VERB
cana-259	297	19	parameter	parameter	NOUN
cana-259	297	20	system	system	NOUN
cana-259	297	21	via	via	ADP
cana-259	297	22	orthogonal	orthogonal	ADJ
cana-259	297	23	polynomials	polynomial	NOUN
cana-259	297	24	,	,	PUNCT
cana-259	297	25	”	"	PUNCT
cana-259	297	26	optim	optim	ADJ
cana-259	297	27	.	.	PUNCT
cana-259	298	1	control	control	PROPN
cana-259	298	2	appl	appl	PROPN
cana-259	298	3	.	.	PUNCT
cana-259	299	1	methods	method	NOUN
cana-259	299	2	,	,	PUNCT
cana-259	299	3	vol	vol	NOUN
cana-259	299	4	.	.	PROPN
cana-259	299	5	19	19	NUM
cana-259	299	6	,	,	PUNCT
cana-259	299	7	no	no	INTJ
cana-259	299	8	.	.	NOUN
cana-259	299	9	3	3	NUM
cana-259	299	10	,	,	PUNCT
cana-259	299	11	pp	pp	ADJ
cana-259	299	12	.	.	PUNCT
cana-259	300	1	205–213	205–213	NUM
cana-259	300	2	,	,	PUNCT
cana-259	300	3	may	may	AUX
cana-259	300	4	/	/	SYM
cana-259	300	5	jun	jun	PROPN
cana-259	300	6	.	.	PROPN
cana-259	300	7	1998	1998	NUM
cana-259	300	8	.	.	PUNCT
cana-259	301	1	[	[	X
cana-259	301	2	16	16	NUM
cana-259	301	3	]	]	PUNCT
cana-259	301	4	s.	s.	PROPN
cana-259	301	5	s.	s.	PROPN
cana-259	301	6	ravindran	ravindran	PROPN
cana-259	301	7	,	,	PUNCT
cana-259	301	8	“	"	PUNCT
cana-259	301	9	a	a	DET
cana-259	301	10	reduced	reduce	VERB
cana-259	301	11	-	-	PUNCT
cana-259	301	12	order	order	NOUN
cana-259	301	13	approach	approach	NOUN
cana-259	301	14	for	for	ADP
cana-259	301	15	optimal	optimal	ADJ
cana-259	301	16	control	control	NOUN
cana-259	301	17	of	of	ADP
cana-259	301	18	fluids	fluid	NOUN
cana-259	301	19	using	use	VERB
cana-259	301	20	proper	proper	ADJ
cana-259	301	21	orthogonal	orthogonal	ADJ
cana-259	301	22	decomposition	decomposition	NOUN
cana-259	301	23	,	,	PUNCT
cana-259	301	24	”	"	PUNCT
cana-259	301	25	int	int	NOUN
cana-259	301	26	.	.	PUNCT
cana-259	302	1	j.	j.	PROPN
cana-259	302	2	numer	numer	PROPN
cana-259	302	3	.	.	PROPN
cana-259	302	4	method	method	PROPN
cana-259	302	5	fluid	fluid	NOUN
cana-259	302	6	,	,	PUNCT
cana-259	302	7	vol	vol	NOUN
cana-259	302	8	.	.	PROPN
cana-259	303	1	34	34	NUM
cana-259	303	2	,	,	PUNCT
cana-259	303	3	no	no	INTJ
cana-259	303	4	.	.	NOUN
cana-259	303	5	5	5	NUM
cana-259	303	6	,	,	PUNCT
cana-259	303	7	pp	pp	ADJ
cana-259	303	8	.	.	PUNCT
cana-259	304	1	425–448	425–448	NUM
cana-259	304	2	,	,	PUNCT
cana-259	304	3	nov	nov	PROPN
cana-259	304	4	.	.	PROPN
cana-259	304	5	2000	2000	NUM
cana-259	304	6	.	.	PUNCT
cana-259	305	1	[	[	X
cana-259	305	2	17	17	NUM
cana-259	305	3	]	]	X
cana-259	305	4	v.	v.	CCONJ
cana-259	305	5	yadav	yadav	PROPN
cana-259	305	6	,	,	PUNCT
cana-259	305	7	r.	r.	PROPN
cana-259	305	8	padhi	padhi	PROPN
cana-259	305	9	,	,	PUNCT
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cana-259	305	11	s.	s.	PROPN
cana-259	305	12	n.	n.	PROPN
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cana-259	305	14	,	,	PUNCT
cana-259	305	15	“	"	PUNCT
cana-259	305	16	robust	robust	ADJ
cana-259	305	17	/	/	SYM
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cana-259	305	19	temperature	temperature	NOUN
cana-259	305	20	profile	profile	NOUN
cana-259	305	21	control	control	NOUN
cana-259	305	22	of	of	ADP
cana-259	305	23	a	a	DET
cana-259	305	24	high	high	ADJ
cana-259	305	25	-	-	PUNCT
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cana-259	305	27	aerospace	aerospace	NOUN
cana-259	305	28	vehicle	vehicle	NOUN
cana-259	305	29	using	use	VERB
cana-259	305	30	neural	neural	ADJ
cana-259	305	31	networks	network	NOUN
cana-259	305	32	,	,	PUNCT
cana-259	305	33	”	"	PUNCT
cana-259	305	34	ieee	ieee	NOUN
cana-259	305	35	trans	trans	PROPN
cana-259	305	36	.	.	PUNCT
cana-259	306	1	neural	neural	ADJ
cana-259	306	2	netw	netw	NOUN
cana-259	306	3	.	.	PUNCT
cana-259	307	1	,	,	PUNCT
cana-259	307	2	vol	vol	NOUN
cana-259	307	3	.	.	PROPN
cana-259	307	4	18	18	NUM
cana-259	307	5	,	,	PUNCT
cana-259	307	6	no	no	INTJ
cana-259	307	7	.	.	NOUN
cana-259	307	8	4	4	NUM
cana-259	307	9	,	,	PUNCT
cana-259	307	10	pp	pp	ADJ
cana-259	307	11	.	.	PUNCT
cana-259	308	1	1115–1128	1115–1128	NUM
cana-259	308	2	,	,	PUNCT
cana-259	308	3	jul	jul	PROPN
cana-259	308	4	.	.	PROPN
cana-259	308	5	2007	2007	NUM
cana-259	308	6	.	.	PUNCT
cana-259	309	1	[	[	X
cana-259	309	2	18	18	NUM
cana-259	309	3	]	]	X
cana-259	309	4	r.	r.	PROPN
cana-259	309	5	padhi	padhi	PROPN
cana-259	309	6	,	,	PUNCT
cana-259	309	7	s.	s.	PROPN
cana-259	309	8	n.	n.	PROPN
cana-259	309	9	balakrishnan	balakrishnan	PROPN
cana-259	309	10	,	,	PUNCT
cana-259	309	11	and	and	CCONJ
cana-259	309	12	t.	t.	PROPN
cana-259	309	13	randolph	randolph	PROPN
cana-259	309	14	,	,	PUNCT
cana-259	309	15	“	"	PUNCT
cana-259	309	16	adaptive	adaptive	ADJ
cana-259	309	17	-	-	PUNCT
cana-259	309	18	critic	critic	NOUN
cana-259	309	19	based	base	VERB
cana-259	309	20	optimal	optimal	ADJ
cana-259	309	21	neuro	neuro	PROPN
cana-259	309	22	control	control	NOUN
cana-259	309	23	synthesis	synthesis	NOUN
cana-259	309	24	for	for	ADP
cana-259	309	25	distributed	distribute	VERB
cana-259	309	26	parameter	parameter	NOUN
cana-259	309	27	systems	system	NOUN
cana-259	309	28	,	,	PUNCT
cana-259	309	29	”	"	PUNCT
cana-259	309	30	automatica	automatica	PROPN
cana-259	309	31	,	,	PUNCT
cana-259	309	32	vol	vol	NOUN
cana-259	309	33	.	.	PROPN
cana-259	310	1	37	37	NUM
cana-259	310	2	,	,	PUNCT
cana-259	310	3	no	no	INTJ
cana-259	310	4	.	.	NOUN
cana-259	310	5	8	8	NUM
cana-259	310	6	,	,	PUNCT
cana-259	310	7	pp	pp	ADJ
cana-259	310	8	.	.	PUNCT
cana-259	311	1	1223–1234	1223–1234	NUM
cana-259	311	2	,	,	PUNCT
cana-259	311	3	2001	2001	NUM
cana-259	311	4	.	.	PUNCT
cana-259	312	1	[	[	X
cana-259	312	2	19	19	NUM
cana-259	312	3	]	]	X
cana-259	312	4	r.	r.	PROPN
cana-259	312	5	padhi	padhi	PROPN
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cana-259	312	7	s.	s.	PROPN
cana-259	312	8	n.	n.	PROPN
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cana-259	312	11	“	"	PUNCT
cana-259	312	12	proper	proper	ADJ
cana-259	312	13	orthogonal	orthogonal	ADJ
cana-259	312	14	decomposition	decomposition	NOUN
cana-259	312	15	based	base	VERB
cana-259	312	16	optimal	optimal	ADJ
cana-259	312	17	neurocontrol	neurocontrol	ADJ
cana-259	312	18	synthesis	synthesis	NOUN
cana-259	312	19	of	of	ADP
cana-259	312	20	a	a	DET
cana-259	312	21	chemical	chemical	NOUN
cana-259	312	22	reactor	reactor	NOUN
cana-259	312	23	process	process	NOUN
cana-259	312	24	using	use	VERB
cana-259	312	25	approximate	approximate	ADJ
cana-259	312	26	dynamic	dynamic	ADJ
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cana-259	312	28	,	,	PUNCT
cana-259	312	29	”	"	PUNCT
cana-259	312	30	j.	j.	PROPN
cana-259	312	31	neural	neural	PROPN
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cana-259	313	1	,	,	PUNCT
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cana-259	314	1	16	16	NUM
cana-259	314	2	,	,	PUNCT
cana-259	315	1	no	no	INTJ
cana-259	315	2	.	.	NOUN
cana-259	316	1	5/6	5/6	NUM
cana-259	316	2	,	,	PUNCT
cana-259	316	3	pp	pp	ADJ
cana-259	316	4	.	.	PUNCT
cana-259	317	1	719–728	719–728	NUM
cana-259	317	2	,	,	PUNCT
cana-259	317	3	jun	jun	PROPN
cana-259	317	4	.	.	PROPN
cana-259	317	5	2003	2003	NUM
cana-259	317	6	.	.	PUNCT
cana-259	318	1	communications	communication	NOUN
cana-259	318	2	on	on	ADP
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cana-259	318	4	nonlinear	nonlinear	ADJ
cana-259	318	5	analysis	analysis	NOUN
cana-259	318	6	issn	issn	NOUN
cana-259	318	7	:	:	PUNCT
cana-259	318	8	1074	1074	NUM
cana-259	318	9	-	-	PUNCT
cana-259	318	10	133x	133x	NUM
cana-259	318	11	vol	vol	NOUN
cana-259	318	12	30	30	NUM
cana-259	318	13	no	no	NOUN
cana-259	318	14	.	.	NOUN
cana-259	318	15	2	2	NUM
cana-259	318	16	(	(	PUNCT
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cana-259	318	18	)	)	PUNCT
cana-259	318	19	14	14	NUM
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cana-259	319	1	[	[	X
cana-259	319	2	20	20	NUM
cana-259	319	3	]	]	PUNCT
cana-259	319	4	j.	j.	PROPN
cana-259	319	5	baker	baker	PROPN
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cana-259	319	8	d.	d.	PROPN
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cana-259	319	11	“	"	PUNCT
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cana-259	319	13	-	-	ADJ
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cana-259	319	18	of	of	ADP
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cana-259	319	22	systems	system	NOUN
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cana-259	319	24	”	"	PUNCT
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cana-259	320	1	j.	j.	PROPN
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cana-259	320	3	,	,	PUNCT
cana-259	320	4	vol	vol	NOUN
cana-259	320	5	.	.	PROPN
cana-259	320	6	73	73	NUM
cana-259	320	7	,	,	PUNCT
cana-259	320	8	no	no	INTJ
cana-259	320	9	.	.	NOUN
cana-259	320	10	5	5	NUM
cana-259	320	11	,	,	PUNCT
cana-259	320	12	pp	pp	ADJ
cana-259	320	13	.	.	PUNCT
cana-259	321	1	439–456	439–456	NUM
cana-259	321	2	,	,	PUNCT
cana-259	321	3	2000	2000	NUM
cana-259	321	4	.	.	PUNCT
cana-259	322	1	[	[	X
cana-259	322	2	21	21	NUM
cana-259	322	3	]	]	X
cana-259	322	4	j.	j.	PROPN
cana-259	322	5	baker	baker	PROPN
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cana-259	322	7	p.	p.	PROPN
cana-259	322	8	d.	d.	PROPN
cana-259	322	9	christofides	christofides	PROPN
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cana-259	322	11	“	"	PUNCT
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cana-259	322	14	control	control	NOUN
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cana-259	322	17	pde	pde	NOUN
cana-259	322	18	systems	system	NOUN
cana-259	322	19	with	with	ADP
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cana-259	322	21	spatial	spatial	ADJ
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cana-259	322	25	”	"	PUNCT
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cana-259	323	2	.	.	PROPN
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cana-259	324	1	res	re	NOUN
cana-259	324	2	.	.	PROPN
cana-259	324	3	,	,	PUNCT
cana-259	324	4	vol	vol	NOUN
cana-259	324	5	.	.	PROPN
cana-259	325	1	38	38	NUM
cana-259	325	2	,	,	PUNCT
cana-259	325	3	no	no	INTJ
cana-259	325	4	.	.	NOUN
cana-259	325	5	11	11	NUM
cana-259	325	6	,	,	PUNCT
cana-259	325	7	pp	pp	ADJ
cana-259	325	8	.	.	PUNCT
cana-259	326	1	4372–4380	4372–4380	NUM
cana-259	326	2	,	,	PUNCT
cana-259	326	3	nov	nov	PROPN
cana-259	326	4	.	.	PROPN
cana-259	326	5	1999	1999	NUM
cana-259	326	6	.	.	PUNCT
cana-259	327	1	[	[	X
cana-259	327	2	22	22	NUM
cana-259	327	3	]	]	PUNCT
cana-259	327	4	a.	a.	NOUN
cana-259	327	5	armaou	armaou	PROPN
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cana-259	327	7	p.	p.	PROPN
cana-259	327	8	d.	d.	PROPN
cana-259	327	9	christofides	christofide	NOUN
cana-259	327	10	,	,	PUNCT
cana-259	327	11	“	"	PUNCT
cana-259	327	12	dynamic	dynamic	ADJ
cana-259	327	13	optimization	optimization	NOUN
cana-259	327	14	of	of	ADP
cana-259	327	15	dissipative	dissipative	ADJ
cana-259	327	16	pde	pde	NOUN
cana-259	327	17	systems	system	NOUN
cana-259	327	18	using	use	VERB
cana-259	327	19	nonlinear	nonlinear	ADJ
cana-259	327	20	order	order	NOUN
cana-259	327	21	reduction	reduction	NOUN
cana-259	327	22	,	,	PUNCT
cana-259	327	23	”	"	PUNCT
cana-259	327	24	chem	chem	NOUN
cana-259	327	25	.	.	PUNCT
cana-259	328	1	eng	eng	PROPN
cana-259	328	2	.	.	PUNCT
cana-259	329	1	sci	sci	PROPN
cana-259	329	2	.	.	PROPN
cana-259	329	3	,	,	PUNCT
cana-259	329	4	vol	vol	NOUN
cana-259	329	5	.	.	PROPN
cana-259	330	1	57	57	NUM
cana-259	330	2	,	,	PUNCT
cana-259	330	3	no	no	INTJ
cana-259	330	4	.	.	NOUN
cana-259	330	5	24	24	NUM
cana-259	330	6	,	,	PUNCT
cana-259	330	7	pp	pp	ADJ
cana-259	330	8	.	.	PUNCT
cana-259	331	1	5083–5114	5083–5114	NUM
cana-259	331	2	,	,	PUNCT
cana-259	331	3	dec	dec	PROPN
cana-259	331	4	.	.	PROPN
cana-259	331	5	2002	2002	NUM
cana-259	331	6	.	.	PUNCT
cana-259	332	1	[	[	X
cana-259	332	2	23	23	NUM
cana-259	332	3	]	]	X
cana-259	332	4	h.-x	h.-x	NOUN
cana-259	332	5	.	.	PUNCT
cana-259	333	1	li	li	PROPN
cana-259	333	2	and	and	CCONJ
cana-259	333	3	c.	c.	PROPN
cana-259	333	4	k.	k.	PROPN
cana-259	333	5	qi	qi	PROPN
cana-259	333	6	,	,	PUNCT
cana-259	333	7	spatio	spatio	NOUN
cana-259	333	8	-	-	PUNCT
cana-259	333	9	temporal	temporal	ADJ
cana-259	333	10	modeling	modeling	NOUN
cana-259	333	11	of	of	ADP
cana-259	333	12	nonlinear	nonlinear	ADJ
cana-259	333	13	distributed	distribute	VERB
cana-259	333	14	parameter	parameter	NOUN
cana-259	333	15	systems	system	NOUN
cana-259	333	16	:	:	PUNCT
cana-259	333	17	a	a	DET
cana-259	333	18	time	time	NOUN
cana-259	333	19	/	/	SYM
cana-259	333	20	space	space	NOUN
cana-259	333	21	separation	separation	NOUN
cana-259	333	22	based	base	VERB
cana-259	333	23	approach	approach	NOUN
cana-259	333	24	.	.	PUNCT
cana-259	334	1	new	new	PROPN
cana-259	334	2	york	york	PROPN
cana-259	334	3	:	:	PUNCT
cana-259	334	4	springer	springer	NOUN
cana-259	334	5	-	-	PUNCT
cana-259	334	6	verlag	verlag	PROPN
cana-259	334	7	,	,	PUNCT
cana-259	334	8	2011	2011	NUM
cana-259	334	9	.	.	PUNCT
cana-259	335	1	[	[	X
cana-259	335	2	24	24	NUM
cana-259	335	3	]	]	X
cana-259	335	4	p.	p.	NOUN
cana-259	335	5	holmes	holmes	PROPN
cana-259	335	6	,	,	PUNCT
cana-259	335	7	j.	j.	PROPN
cana-259	335	8	l.	l.	PROPN
cana-259	335	9	lumley	lumley	PROPN
cana-259	335	10	,	,	PUNCT
cana-259	335	11	and	and	CCONJ
cana-259	335	12	g.	g.	PROPN
cana-259	335	13	berkooz	berkooz	PROPN
cana-259	335	14	,	,	PUNCT
cana-259	335	15	turbulence	turbulence	NOUN
cana-259	335	16	,	,	PUNCT
cana-259	335	17	coherent	coherent	ADJ
cana-259	335	18	structures	structure	NOUN
cana-259	335	19	,	,	PUNCT
cana-259	335	20	dynamical	dynamical	ADJ
cana-259	335	21	systems	system	NOUN
cana-259	335	22	and	and	CCONJ
cana-259	335	23	symmetry	symmetry	NOUN
cana-259	335	24	.	.	PUNCT
cana-259	336	1	cambridge	cambridge	PROPN
cana-259	336	2	,	,	PUNCT
cana-259	336	3	u.k	u.k	PROPN
cana-259	336	4	.	.	PROPN
cana-259	336	5	:	:	PUNCT
cana-259	337	1	cambridge	cambridge	PROPN
cana-259	337	2	univ	univ	PROPN
cana-259	337	3	.	.	PUNCT
cana-259	338	1	press	press	PROPN
cana-259	338	2	,	,	PUNCT
cana-259	338	3	1996	1996	NUM
cana-259	338	4	.	.	PUNCT
cana-259	339	1	[	[	X
cana-259	339	2	25	25	NUM
cana-259	339	3	]	]	PUNCT
cana-259	339	4	l.	l.	PROPN
cana-259	339	5	g.	g.	PROPN
cana-259	339	6	bleris	bleris	PROPN
cana-259	339	7	and	and	CCONJ
cana-259	339	8	m.	m.	NOUN
cana-259	339	9	v.	v.	ADP
cana-259	339	10	kothare	kothare	PROPN
cana-259	339	11	,	,	PUNCT
cana-259	339	12	“	"	PUNCT
cana-259	339	13	low	low	ADJ
cana-259	339	14	-	-	PUNCT
cana-259	339	15	order	order	NOUN
cana-259	339	16	empirical	empirical	ADJ
cana-259	339	17	modeling	modeling	NOUN
cana-259	339	18	of	of	ADP
cana-259	339	19	distributed	distribute	VERB
cana-259	339	20	parameter	parameter	NOUN
cana-259	339	21	systems	system	NOUN
cana-259	339	22	using	use	VERB
cana-259	339	23	temporal	temporal	ADJ
cana-259	339	24	and	and	CCONJ
cana-259	339	25	spatial	spatial	ADJ
cana-259	339	26	eigenfunctions	eigenfunction	NOUN
cana-259	339	27	,	,	PUNCT
cana-259	339	28	”	"	PUNCT
cana-259	339	29	comput	comput	NOUN
cana-259	339	30	.	.	PUNCT
cana-259	340	1	chem	chem	NOUN
cana-259	340	2	.	.	PUNCT
cana-259	341	1	eng	eng	PROPN
cana-259	341	2	.	.	PROPN
cana-259	341	3	,	,	PUNCT
cana-259	341	4	vol	vol	NOUN
cana-259	341	5	.	.	PROPN
cana-259	341	6	29	29	NUM
cana-259	341	7	,	,	PUNCT
cana-259	341	8	no	no	INTJ
cana-259	341	9	.	.	NOUN
cana-259	341	10	4	4	NUM
cana-259	341	11	,	,	PUNCT
cana-259	341	12	pp	pp	ADJ
cana-259	341	13	.	.	PUNCT
cana-259	342	1	817–827	817–827	NUM
cana-259	342	2	,	,	PUNCT
cana-259	342	3	mar	mar	PROPN
cana-259	342	4	.	.	PROPN
cana-259	342	5	2005	2005	NUM
cana-259	342	6	.	.	PUNCT
cana-259	343	1	[	[	X
cana-259	343	2	26	26	NUM
cana-259	343	3	]	]	X
cana-259	343	4	d.	d.	PROPN
cana-259	343	5	h.	h.	PROPN
cana-259	343	6	gay	gay	PROPN
cana-259	343	7	and	and	CCONJ
cana-259	343	8	w.	w.	PROPN
cana-259	343	9	h.	h.	PROPN
cana-259	343	10	ray	ray	PROPN
cana-259	343	11	,	,	PUNCT
cana-259	343	12	“	"	PUNCT
cana-259	343	13	identification	identification	NOUN
cana-259	343	14	and	and	CCONJ
cana-259	343	15	control	control	NOUN
cana-259	343	16	of	of	ADP
cana-259	343	17	distributed	distribute	VERB
cana-259	343	18	parameter	parameter	NOUN
cana-259	343	19	systems	system	NOUN
cana-259	343	20	by	by	ADP
cana-259	343	21	means	mean	NOUN
cana-259	343	22	of	of	ADP
cana-259	343	23	the	the	DET
cana-259	343	24	singular	singular	ADJ
cana-259	343	25	value	value	NOUN
cana-259	343	26	decomposition	decomposition	NOUN
cana-259	343	27	,	,	PUNCT
cana-259	343	28	”	"	PUNCT
cana-259	343	29	chem	chem	NOUN
cana-259	343	30	.	.	PUNCT
cana-259	344	1	eng	eng	PROPN
cana-259	344	2	.	.	PUNCT
cana-259	345	1	sci	sci	PROPN
cana-259	345	2	.	.	PROPN
cana-259	345	3	,	,	PUNCT
cana-259	345	4	vol	vol	NOUN
cana-259	345	5	.	.	PROPN
cana-259	346	1	50	50	NUM
cana-259	346	2	,	,	PUNCT
cana-259	346	3	no	no	INTJ
cana-259	346	4	.	.	NOUN
cana-259	346	5	10	10	NUM
cana-259	346	6	,	,	PUNCT
cana-259	346	7	pp	pp	ADJ
cana-259	346	8	.	.	PUNCT
cana-259	347	1	1519–1539	1519–1539	NOUN
cana-259	347	2	,	,	PUNCT
cana-259	347	3	may	may	PROPN
cana-259	347	4	1995	1995	NUM
cana-259	347	5	.	.	PUNCT
cana-259	348	1	[	[	X
cana-259	348	2	27	27	NUM
cana-259	348	3	]	]	X
cana-259	348	4	d.	d.	PROPN
cana-259	348	5	g.	g.	PROPN
cana-259	348	6	zheng	zheng	PROPN
cana-259	348	7	,	,	PUNCT
cana-259	348	8	“	"	PUNCT
cana-259	348	9	system	system	NOUN
cana-259	348	10	identification	identification	NOUN
cana-259	348	11	and	and	CCONJ
cana-259	348	12	model	model	NOUN
cana-259	348	13	-	-	PUNCT
cana-259	348	14	based	base	VERB
cana-259	348	15	control	control	NOUN
cana-259	348	16	for	for	ADP
cana-259	348	17	a	a	DET
cana-259	348	18	class	class	NOUN
cana-259	348	19	of	of	ADP
cana-259	348	20	distributed	distribute	VERB
cana-259	348	21	parameter	parameter	NOUN
cana-259	348	22	systems	system	NOUN
cana-259	348	23	,	,	PUNCT
cana-259	348	24	”	"	PUNCT
cana-259	348	25	ph.d	ph.d	PROPN
cana-259	348	26	.	.	PUNCT
cana-259	348	27	dissertation	dissertation	NOUN
cana-259	348	28	,	,	PUNCT
cana-259	348	29	texas	texas	PROPN
cana-259	348	30	tech	tech	PROPN
cana-259	348	31	univ	univ	PROPN
cana-259	348	32	.	.	PROPN
cana-259	348	33	,	,	PUNCT
cana-259	348	34	lubbock	lubbock	PROPN
cana-259	348	35	,	,	PUNCT
cana-259	348	36	tx	tx	PROPN
cana-259	348	37	,	,	PUNCT
cana-259	348	38	2003	2003	NUM
cana-259	348	39	.	.	PUNCT
cana-259	349	1	[	[	X
cana-259	349	2	28	28	NUM
cana-259	349	3	]	]	X
cana-259	349	4	b.	b.	PROPN
cana-259	349	5	widrow	widrow	PROPN
cana-259	349	6	,	,	PUNCT
cana-259	349	7	n.	n.	PROPN
cana-259	349	8	k.	k.	PROPN
cana-259	349	9	gupta	gupta	PROPN
cana-259	349	10	,	,	PUNCT
cana-259	349	11	and	and	CCONJ
cana-259	349	12	s.	s.	PROPN
cana-259	349	13	maitra	maitra	PROPN
cana-259	349	14	,	,	PUNCT
cana-259	349	15	“	"	PUNCT
cana-259	349	16	punish	punish	VERB
cana-259	349	17	/	/	SYM
cana-259	349	18	reward	reward	NOUN
cana-259	349	19	:	:	PUNCT
cana-259	349	20	learning	learn	VERB
cana-259	349	21	with	with	ADP
cana-259	349	22	a	a	DET
cana-259	349	23	critic	critic	NOUN
cana-259	349	24	in	in	ADP
cana-259	349	25	adaptive	adaptive	ADJ
cana-259	349	26	threshold	threshold	NOUN
cana-259	349	27	systems	system	NOUN
cana-259	349	28	,	,	PUNCT
cana-259	349	29	”	"	PUNCT
cana-259	349	30	ieee	ieee	NOUN
cana-259	349	31	trans	trans	PROPN
cana-259	349	32	.	.	PUNCT
cana-259	350	1	syst	syst	PROPN
cana-259	350	2	.	.	PUNCT
cana-259	350	3	,	,	PUNCT
cana-259	350	4	man	man	NOUN
cana-259	350	5	,	,	PUNCT
cana-259	350	6	cybern	cybern	PROPN
cana-259	350	7	.	.	PUNCT
cana-259	350	8	,	,	PUNCT
cana-259	350	9	vol	vol	NOUN
cana-259	350	10	.	.	PUNCT
cana-259	350	11	smc-3	smc-3	PROPN
cana-259	350	12	,	,	PUNCT
cana-259	350	13	no	no	INTJ
cana-259	350	14	.	.	NOUN
cana-259	350	15	5	5	NUM
cana-259	350	16	,	,	PUNCT
cana-259	350	17	pp	pp	ADJ
cana-259	350	18	.	.	PUNCT
cana-259	351	1	455–465	455–465	NUM
cana-259	351	2	,	,	PUNCT
cana-259	351	3	sep	sep	PROPN
cana-259	351	4	.	.	PROPN
cana-259	351	5	1973	1973	NUM
cana-259	351	6	.	.	PUNCT
cana-259	352	1	[	[	X
cana-259	352	2	29	29	NUM
cana-259	352	3	]	]	X
cana-259	352	4	j.	j.	PROPN
cana-259	352	5	seiffertt	seiffertt	PROPN
cana-259	352	6	,	,	PUNCT
cana-259	352	7	s.	s.	PROPN
cana-259	352	8	sanyal	sanyal	PROPN
cana-259	352	9	,	,	PUNCT
cana-259	352	10	and	and	CCONJ
cana-259	352	11	d.	d.	PROPN
cana-259	352	12	c.	c.	PROPN
cana-259	352	13	wunsch	wunsch	PROPN
cana-259	352	14	,	,	PUNCT
cana-259	352	15	“	"	PUNCT
cana-259	352	16	hamilton	hamilton	PROPN
cana-259	352	17	–	–	PUNCT
cana-259	352	18	jacobi	jacobi	PROPN
cana-259	352	19	–	–	PUNCT
cana-259	352	20	bellman	bellman	NOUN
cana-259	352	21	equations	equation	NOUN
cana-259	352	22	and	and	CCONJ
cana-259	352	23	approximate	approximate	ADJ
cana-259	352	24	dynamic	dynamic	ADJ
cana-259	352	25	programming	programming	NOUN
cana-259	352	26	on	on	ADP
cana-259	352	27	time	time	NOUN
cana-259	352	28	scales	scale	NOUN
cana-259	352	29	,	,	PUNCT
cana-259	352	30	”	"	PUNCT
cana-259	352	31	ieee	ieee	NOUN
cana-259	352	32	trans	trans	PROPN
cana-259	352	33	.	.	PUNCT
cana-259	353	1	syst	syst	PROPN
cana-259	353	2	.	.	PUNCT
cana-259	353	3	,	,	PUNCT
cana-259	353	4	man	man	NOUN
cana-259	353	5	,	,	PUNCT
cana-259	353	6	cybern	cybern	PROPN
cana-259	353	7	.	.	PUNCT
cana-259	354	1	b	b	X
cana-259	354	2	,	,	PUNCT
cana-259	354	3	cybern	cybern	NOUN
cana-259	354	4	.	.	PUNCT
cana-259	355	1	,	,	PUNCT
cana-259	355	2	vol	vol	NOUN
cana-259	355	3	.	.	PROPN
cana-259	356	1	38	38	NUM
cana-259	356	2	,	,	PUNCT
cana-259	356	3	no	no	INTJ
cana-259	356	4	.	.	NOUN
cana-259	356	5	4	4	NUM
cana-259	356	6	,	,	PUNCT
cana-259	356	7	pp	pp	ADJ
cana-259	356	8	.	.	PUNCT
cana-259	357	1	918–923	918–923	NUM
cana-259	357	2	,	,	PUNCT
cana-259	357	3	aug	aug	PROPN
cana-259	357	4	.	.	PROPN
cana-259	357	5	2008	2008	NUM
cana-259	357	6	.	.	PUNCT
cana-259	358	1	[	[	X
cana-259	358	2	30	30	NUM
cana-259	358	3	]	]	X
cana-259	358	4	h.	h.	PROPN
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cana-259	358	11	y.	y.	PROPN
cana-259	358	12	luo	luo	PROPN
cana-259	358	13	,	,	PUNCT
cana-259	358	14	“	"	PUNCT
cana-259	358	15	a	a	DET
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cana-259	358	17	infinite	infinite	NOUN
cana-259	358	18	-	-	PUNCT
cana-259	358	19	time	time	NOUN
cana-259	358	20	optimal	optimal	ADJ
cana-259	358	21	tracking	tracking	NOUN
cana-259	358	22	control	control	NOUN
cana-259	358	23	scheme	scheme	NOUN
cana-259	358	24	for	for	ADP
cana-259	358	25	a	a	DET
cana-259	358	26	class	class	NOUN
cana-259	358	27	of	of	ADP
cana-259	358	28	discrete	discrete	ADJ
cana-259	358	29	-	-	PUNCT
cana-259	358	30	time	time	NOUN
cana-259	358	31	nonlinear	nonlinear	NOUN
cana-259	358	32	systems	system	NOUN
cana-259	358	33	via	via	ADP
cana-259	358	34	the	the	DET
cana-259	358	35	greedy	greedy	ADJ
cana-259	358	36	hdp	hdp	NOUN
cana-259	358	37	iteration	iteration	NOUN
cana-259	358	38	algorithm	algorithm	NOUN
cana-259	358	39	,	,	PUNCT
cana-259	358	40	”	"	PUNCT
cana-259	358	41	ieee	ieee	NOUN
cana-259	358	42	trans	trans	PROPN
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cana-259	359	1	syst	syst	PROPN
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cana-259	359	5	,	,	PUNCT
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cana-259	359	7	.	.	PUNCT
cana-259	360	1	b	b	X
cana-259	360	2	,	,	PUNCT
cana-259	360	3	cybern	cybern	NOUN
cana-259	360	4	.	.	PUNCT
cana-259	361	1	,	,	PUNCT
cana-259	361	2	vol	vol	NOUN
cana-259	361	3	.	.	PROPN
cana-259	362	1	38	38	NUM
cana-259	362	2	,	,	PUNCT
cana-259	362	3	no	no	INTJ
cana-259	362	4	.	.	NOUN
cana-259	362	5	4	4	NUM
cana-259	362	6	,	,	PUNCT
cana-259	362	7	pp	pp	ADJ
cana-259	362	8	.	.	PUNCT
cana-259	363	1	937–942	937–942	NUM
cana-259	363	2	,	,	PUNCT
cana-259	363	3	aug	aug	PROPN
cana-259	363	4	.	.	PROPN
cana-259	363	5	2008	2008	NUM
cana-259	363	6	.	.	PUNCT
cana-259	364	1	[	[	X
cana-259	364	2	31	31	NUM
cana-259	364	3	]	]	PUNCT
cana-259	364	4	a.	a.	PROPN
cana-259	364	5	al	al	PROPN
cana-259	364	6	-	-	PUNCT
cana-259	364	7	tamimi	tamimi	PROPN
cana-259	364	8	,	,	PUNCT
cana-259	364	9	m.	m.	NOUN
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cana-259	364	11	-	-	PUNCT
cana-259	364	12	khalaf	khalaf	PROPN
cana-259	364	13	,	,	PUNCT
cana-259	364	14	and	and	CCONJ
cana-259	364	15	f.	f.	PROPN
cana-259	364	16	l.	l.	PROPN
cana-259	364	17	lewis	lewis	PROPN
cana-259	364	18	,	,	PUNCT
cana-259	364	19	“	"	PUNCT
cana-259	364	20	adaptive	adaptive	ADJ
cana-259	364	21	critic	critic	NOUN
cana-259	364	22	designs	design	NOUN
cana-259	364	23	for	for	ADP
cana-259	364	24	discrete	discrete	ADJ
cana-259	364	25	-	-	PUNCT
cana-259	364	26	time	time	NOUN
cana-259	364	27	zero	zero	NUM
cana-259	364	28	-	-	PUNCT
cana-259	364	29	sum	sum	NOUN
cana-259	364	30	games	game	NOUN
cana-259	364	31	with	with	ADP
cana-259	364	32	application	application	NOUN
cana-259	364	33	to	to	ADP
cana-259	364	34	h	h	PROPN
cana-259	364	35	control	control	NOUN
cana-259	364	36	,	,	PUNCT
cana-259	364	37	”	"	PUNCT
cana-259	364	38	ieee	ieee	NOUN
cana-259	364	39	trans	trans	PROPN
cana-259	364	40	.	.	PUNCT
cana-259	365	1	syst	syst	PROPN
cana-259	365	2	.	.	PUNCT
cana-259	365	3	,	,	PUNCT
cana-259	365	4	man	man	NOUN
cana-259	365	5	,	,	PUNCT
cana-259	365	6	cybern	cybern	PROPN
cana-259	365	7	.	.	PUNCT
cana-259	366	1	b	b	X
cana-259	366	2	,	,	PUNCT
cana-259	366	3	cybern	cybern	NOUN
cana-259	366	4	.	.	PUNCT
cana-259	366	5	,	,	PUNCT
cana-259	366	6	vol	vol	NOUN
cana-259	366	7	.	.	PROPN
cana-259	367	1	37	37	NUM
cana-259	367	2	,	,	PUNCT
cana-259	367	3	no	no	INTJ
cana-259	367	4	.	.	NOUN
cana-259	367	5	1	1	NUM
cana-259	367	6	,	,	PUNCT
cana-259	367	7	pp	pp	ADJ
cana-259	367	8	.	.	PUNCT
cana-259	368	1	240–247	240–247	NUM
cana-259	368	2	,	,	PUNCT
cana-259	368	3	feb	feb	PROPN
cana-259	368	4	.	.	PROPN
cana-259	368	5	2007	2007	NUM
cana-259	368	6	.	.	PUNCT
cana-259	369	1	[	[	X
cana-259	369	2	32	32	NUM
cana-259	369	3	]	]	PUNCT
cana-259	369	4	a.	a.	PROPN
cana-259	369	5	al	al	PROPN
cana-259	369	6	-	-	PUNCT
cana-259	369	7	tamimi	tamimi	PROPN
cana-259	369	8	,	,	PUNCT
cana-259	369	9	f.	f.	PROPN
cana-259	369	10	l.	l.	PROPN
cana-259	369	11	lewis	lewis	PROPN
cana-259	369	12	,	,	PUNCT
cana-259	369	13	and	and	CCONJ
cana-259	369	14	m.	m.	PROPN
cana-259	369	15	abu	abu	PROPN
cana-259	369	16	-	-	PUNCT
cana-259	369	17	khalaf	khalaf	PROPN
cana-259	369	18	,	,	PUNCT
cana-259	369	19	“	"	PUNCT
cana-259	369	20	discrete	discrete	ADJ
cana-259	369	21	-	-	PUNCT
cana-259	369	22	time	time	NOUN
cana-259	369	23	nonlinear	nonlinear	ADJ
cana-259	369	24	hjb	hjb	NOUN
cana-259	369	25	solution	solution	NOUN
cana-259	369	26	using	use	VERB
cana-259	369	27	approximate	approximate	ADJ
cana-259	369	28	dynamic	dynamic	ADJ
cana-259	369	29	programming	programming	NOUN
cana-259	369	30	convergence	convergence	NOUN
cana-259	369	31	proof	proof	NOUN
cana-259	369	32	,	,	PUNCT
cana-259	369	33	”	"	PUNCT
cana-259	369	34	ieee	ieee	NOUN
cana-259	369	35	trans	trans	PROPN
cana-259	369	36	.	.	PUNCT
cana-259	370	1	syst	syst	PROPN
cana-259	370	2	.	.	PUNCT
cana-259	370	3	,	,	PUNCT
cana-259	370	4	man	man	NOUN
cana-259	370	5	,	,	PUNCT
cana-259	370	6	cybern	cybern	PROPN
cana-259	370	7	.	.	PUNCT
cana-259	371	1	b	b	X
cana-259	371	2	,	,	PUNCT
cana-259	371	3	cybern	cybern	NOUN
cana-259	371	4	.	.	PUNCT
cana-259	372	1	,	,	PUNCT
cana-259	372	2	vol	vol	NOUN
cana-259	372	3	.	.	PROPN
cana-259	373	1	38	38	NUM
cana-259	373	2	,	,	PUNCT
cana-259	373	3	no	no	INTJ
cana-259	373	4	.	.	NOUN
cana-259	373	5	4	4	NUM
cana-259	373	6	,	,	PUNCT
cana-259	373	7	pp	pp	ADJ
cana-259	373	8	.	.	PUNCT
cana-259	374	1	943–949	943–949	NUM
cana-259	374	2	,	,	PUNCT
cana-259	374	3	aug	aug	PROPN
cana-259	374	4	.	.	PROPN
cana-259	374	5	2008	2008	NUM
cana-259	374	6	.	.	PUNCT
cana-259	375	1	[	[	X
cana-259	375	2	33	33	NUM
cana-259	375	3	]	]	PUNCT
cana-259	375	4	f.	f.	PROPN
cana-259	375	5	l.	l.	PROPN
cana-259	375	6	lewis	lewis	PROPN
cana-259	375	7	and	and	CCONJ
cana-259	375	8	k.	k.	PROPN
cana-259	375	9	g.	g.	PROPN
cana-259	375	10	vamvoudakis	vamvoudakis	PROPN
cana-259	375	11	,	,	PUNCT
cana-259	375	12	“	"	PUNCT
cana-259	375	13	reinforcement	reinforcement	NOUN
cana-259	375	14	learning	learning	NOUN
cana-259	375	15	for	for	ADP
cana-259	375	16	partially	partially	ADV
cana-259	375	17	observable	observable	ADJ
cana-259	375	18	dynamic	dynamic	ADJ
cana-259	375	19	processes	process	NOUN
cana-259	375	20	:	:	PUNCT
cana-259	375	21	adaptive	adaptive	ADJ
cana-259	375	22	dynamic	dynamic	ADJ
cana-259	375	23	programming	programming	NOUN
cana-259	375	24	using	use	VERB
cana-259	375	25	measured	measure	VERB
cana-259	375	26	output	output	NOUN
cana-259	375	27	data	datum	NOUN
cana-259	375	28	,	,	PUNCT
cana-259	375	29	”	"	PUNCT
cana-259	375	30	ieee	ieee	NOUN
cana-259	375	31	trans	trans	PROPN
cana-259	375	32	.	.	PUNCT
cana-259	376	1	syst	syst	PROPN
cana-259	376	2	.	.	PUNCT
cana-259	376	3	,	,	PUNCT
cana-259	376	4	man	man	NOUN
cana-259	376	5	,	,	PUNCT
cana-259	376	6	cybern	cybern	PROPN
cana-259	376	7	.	.	PUNCT
cana-259	377	1	b	b	X
cana-259	377	2	,	,	PUNCT
cana-259	377	3	cybern	cybern	NOUN
cana-259	377	4	.	.	PUNCT
cana-259	378	1	,	,	PUNCT
cana-259	378	2	vol	vol	NOUN
cana-259	378	3	.	.	PROPN
cana-259	379	1	41	41	NUM
cana-259	379	2	,	,	PUNCT
cana-259	379	3	no	no	INTJ
cana-259	379	4	.	.	NOUN
cana-259	379	5	1	1	NUM
cana-259	379	6	,	,	PUNCT
cana-259	379	7	pp	pp	ADJ
cana-259	379	8	.	.	PUNCT
cana-259	380	1	14–25	14–25	NUM
cana-259	380	2	,	,	PUNCT
cana-259	380	3	feb	feb	PROPN
cana-259	380	4	.	.	PROPN
cana-259	380	5	2011	2011	NUM
cana-259	380	6	.	.	PUNCT
cana-259	381	1	[	[	X
cana-259	381	2	34	34	NUM
cana-259	381	3	]	]	X
cana-259	381	4	h.	h.	PROPN
cana-259	381	5	zhang	zhang	PROPN
cana-259	381	6	and	and	CCONJ
cana-259	381	7	y.	y.	PROPN
cana-259	381	8	luo	luo	PROPN
cana-259	381	9	,	,	PUNCT
cana-259	381	10	“	"	PUNCT
cana-259	381	11	neural	neural	ADJ
cana-259	381	12	-	-	PUNCT
cana-259	381	13	network	network	NOUN
cana-259	381	14	-	-	PUNCT
cana-259	381	15	based	base	VERB
cana-259	381	16	near	near	ADP
cana-259	381	17	-	-	PUNCT
cana-259	381	18	optimal	optimal	ADJ
cana-259	381	19	control	control	NOUN
cana-259	381	20	for	for	ADP
cana-259	381	21	a	a	DET
cana-259	381	22	class	class	NOUN
cana-259	381	23	of	of	ADP
cana-259	381	24	discrete	discrete	ADJ
cana-259	381	25	-	-	PUNCT
cana-259	381	26	time	time	NOUN
cana-259	381	27	affine	affine	NOUN
cana-259	381	28	nonlinear	nonlinear	PROPN
cana-259	381	29	systems	system	NOUN
cana-259	381	30	with	with	ADP
cana-259	381	31	control	control	NOUN
cana-259	381	32	constraints	constraint	NOUN
cana-259	381	33	,	,	PUNCT
cana-259	381	34	”	"	PUNCT
cana-259	381	35	ieee	ieee	NOUN
cana-259	381	36	trans	trans	PROPN
cana-259	381	37	.	.	PUNCT
cana-259	382	1	neural	neural	ADJ
cana-259	382	2	netw	netw	NOUN
cana-259	382	3	.	.	PUNCT
cana-259	383	1	,	,	PUNCT
cana-259	383	2	vol	vol	NOUN
cana-259	383	3	.	.	PROPN
cana-259	383	4	20	20	NUM
cana-259	383	5	,	,	PUNCT
cana-259	383	6	no	no	INTJ
cana-259	383	7	.	.	NOUN
cana-259	383	8	9	9	NUM
cana-259	383	9	,	,	PUNCT
cana-259	383	10	pp	pp	ADJ
cana-259	383	11	.	.	PUNCT
cana-259	384	1	1490–1503	1490–1503	NUM
cana-259	384	2	,	,	PUNCT
cana-259	384	3	sep	sep	PROPN
cana-259	384	4	.	.	PROPN
cana-259	385	1	2009	2009	NUM
cana-259	385	2	.	.	PUNCT