{"id":"https://openalex.org/W2734837047","doi":"https://doi.org/10.23919/acc.2017.7963326","title":"How to establish the exact controllability of nonlinear DPS using iterations back and forth in time","display_name":"How to establish the exact controllability of nonlinear DPS using iterations back and forth in time","publication_year":2017,"publication_date":"2017-05-01","ids":{"openalex":"https://openalex.org/W2734837047","doi":"https://doi.org/10.23919/acc.2017.7963326","mag":"2734837047"},"language":"en","primary_location":{"id":"doi:10.23919/acc.2017.7963326","is_oa":false,"landing_page_url":"https://doi.org/10.23919/acc.2017.7963326","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2017 American Control Conference (ACC)","raw_type":"proceedings-article"},"type":"conference-paper","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5083858098","display_name":"Vivek Natarajan","orcid":"https://orcid.org/0000-0001-6757-6176"},"institutions":[{"id":"https://openalex.org/I162827531","display_name":"Indian Institute of Technology Bombay","ror":"https://ror.org/02qyf5152","country_code":"IN","type":"education","lineage":["https://openalex.org/I162827531"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Vivek Natarajan","raw_affiliation_strings":["Systems and Control Engineering Group, Indian Institute of Technology (IIT) Bombay, Mumbai, India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Systems and Control Engineering Group, Indian Institute of Technology (IIT) Bombay, Mumbai, India","institution_ids":["https://openalex.org/I162827531"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5027244392","display_name":"Hua\u2010Cheng Zhou","orcid":"https://orcid.org/0000-0001-6856-2358"},"institutions":[{"id":"https://openalex.org/I16391192","display_name":"Tel Aviv University","ror":"https://ror.org/04mhzgx49","country_code":"IL","type":"education","lineage":["https://openalex.org/I16391192"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Hua-Cheng Zhou","raw_affiliation_strings":["School of Electrical Engineering, Tel Aviv University, Ramat Aviv, Israel"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Electrical Engineering, Tel Aviv University, Ramat Aviv, Israel","institution_ids":["https://openalex.org/I16391192"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5003773351","display_name":"George H. Weiss","orcid":"https://orcid.org/0000-0002-9524-2795"},"institutions":[{"id":"https://openalex.org/I16391192","display_name":"Tel Aviv University","ror":"https://ror.org/04mhzgx49","country_code":"IL","type":"education","lineage":["https://openalex.org/I16391192"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"George Weiss","raw_affiliation_strings":["School of Electrical Engineering, Tel Aviv University, Ramat Aviv, Israel"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Electrical Engineering, Tel Aviv University, Ramat Aviv, Israel","institution_ids":["https://openalex.org/I16391192"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.07883623,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"2485","last_page":"2490"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11110","display_name":"Stability and Controllability of Differential Equations","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11110","display_name":"Stability and Controllability of Differential Equations","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9975000023841858,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9970999956130981,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3586256802082062},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3328860402107239},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.29171156883239746},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.25511327385902405}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3586256802082062},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3328860402107239},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.29171156883239746},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.25511327385902405}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.23919/acc.2017.7963326","is_oa":false,"landing_page_url":"https://doi.org/10.23919/acc.2017.7963326","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2017 American Control Conference (ACC)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":20,"referenced_works":["https://openalex.org/W203646022","https://openalex.org/W1481364825","https://openalex.org/W1514844366","https://openalex.org/W1833425995","https://openalex.org/W1967822522","https://openalex.org/W1975362409","https://openalex.org/W1985945078","https://openalex.org/W1999475633","https://openalex.org/W2026905679","https://openalex.org/W2066096538","https://openalex.org/W2080312705","https://openalex.org/W2129820524","https://openalex.org/W2165368325","https://openalex.org/W2168279726","https://openalex.org/W2476721866","https://openalex.org/W4230203276","https://openalex.org/W4301712264","https://openalex.org/W6629052479","https://openalex.org/W6720740778","https://openalex.org/W6845259194"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2051487156","https://openalex.org/W2073681303","https://openalex.org/W2053286651","https://openalex.org/W2181743346","https://openalex.org/W2187401768","https://openalex.org/W2181413294","https://openalex.org/W2989452537","https://openalex.org/W2052122378","https://openalex.org/W2544423928"],"abstract_inverted_index":{"Consider":[0],"a":[1,26,34,104,241,255],"nonlinear":[2,93,224],"distributed":[3],"parameter":[4],"system":[5],"(DPS)":[6],"described":[7],"by":[8,158],"\u1e8b":[9],"(t)":[10],"=":[11],"Ax(t)+Bu(t)+BNN(x(t),":[12],"t)":[13,96],"for":[14,53,135,244],"all":[15],"t":[16,65],"\u2265":[17],"0.":[18,234],"Here":[19],"A":[20,192],"is":[21,100,117,125,226,237],"the":[22,92,98,111,145,150,223,246],"infinitesimal":[23],"generator":[24],"of":[25,30,74,149,199],"strongly":[27,200],"continuous":[28,63,201],"group":[29],"operators":[31,52,83,174],"T":[32,54],"on":[33,42],"Hilbert":[35,43],"space":[36,113],"X,":[37,88,141],"B":[38,77],"and":[39,46,55,66,78,86,176,183,191,239],"BN,":[40],"defined":[41],"spaces":[44],"U":[45,85],"UN,":[47],"respectively,":[48],"are":[49,188],"admissible":[50],"control":[51,248],"N":[56],":":[57],"X":[58,108,157,205],"\u00d7":[59],"[0,\u221e)":[60],"\u2192":[61],"UNis":[62],"in":[64,68,89,97,101,128,156,229],"Lipschitz":[67,71,105],"x,":[69],"with":[70],"constant":[72],"LNindependent":[73],"t.":[75],"Thus":[76],"BNcan":[79],"be":[80],"unbounded":[81],"as":[82],"from":[84,107],"UNto":[87],"which":[90,122,132],"case":[91],"term":[94],"BNN(x(t),":[95],"DPS":[99,124,151,225],"general":[102],"not":[103],"map":[106],"\u00d7[0,\u221e)":[109],"to":[110,118,152,212],"state":[112,138,147],"X.":[114],"Our":[115,235],"goal":[116],"find":[119],"conditions":[120],"under":[121],"this":[123],"exactly":[126,227],"controllable":[127,228],"some":[129,230],"time":[130,231],"\u03c4,":[131],"means":[133],"that":[134,170,178,207,217],"any":[136,153],"initial":[137],"x(0)":[139],"\u2208":[140,165],"we":[142],"can":[143],"steer":[144],"final":[146],"x(\u03c4)":[148],"chosen":[154],"point":[155],"using":[159,254],"an":[160],"appropriate":[161],"input":[162],"function":[163],"u":[164],"L2([0,":[166],"\u03c4];U).":[167],"We":[168,215,250],"suppose":[169],"there":[171],"exist":[172],"linear":[173],"F":[175],"Fbsuch":[177],"(A,":[179],"[B":[180,185],"BN],":[181,186],"F)":[182],"(-A;":[184],"Fb)":[187],"regular":[189],"triples":[190],"+":[193,196],"BF\u039band":[194],"-A":[195],"BFb,\u039bare":[197],"generators":[198],"semigroups":[202],"Tfand":[203],"Tbon":[204],"such":[206],"\u2225Ttf\u2225":[208],"\u00b7":[209],"\u2225Ttb\u2225":[210],"decays":[211],"zero":[213],"exponentially.":[214],"prove":[216],"if":[218],"LNis":[219],"sufficiently":[220],"small,":[221],"then":[222],"\u03c4":[232],">":[233],"proof":[236],"constructive":[238],"provides":[240],"numerical":[242],"algorithm":[243],"approximating":[245],"required":[247],"signal.":[249],"illustrate":[251],"our":[252],"approach":[253],"simple":[256],"example.":[257]},"counts_by_year":[],"updated_date":"2026-07-29T14:22:42.915294","created_date":"2025-10-10T00:00:00"}
