{"id":"https://openalex.org/W2558781461","doi":"https://doi.org/10.1080/00207179.2016.1266513","title":"Exact controllability of a class of nonlinear distributed parameter systems using back-and-forth iterations","display_name":"Exact controllability of a class of nonlinear distributed parameter systems using back-and-forth iterations","publication_year":2016,"publication_date":"2016-11-30","ids":{"openalex":"https://openalex.org/W2558781461","doi":"https://doi.org/10.1080/00207179.2016.1266513","mag":"2558781461"},"language":"en","primary_location":{"id":"doi:10.1080/00207179.2016.1266513","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207179.2016.1266513","pdf_url":null,"source":{"id":"https://openalex.org/S88061139","display_name":"International Journal of Control","issn_l":"0020-7179","issn":["0020-7179","1366-5820"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Control","raw_type":"journal-article"},"type":"article","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":true,"raw_author_name":"Vivek Natarajan","raw_affiliation_strings":["Systems and Control Engineering Group, Indian Institute of Technology Bombay , Mumbai, India"],"affiliations":[{"raw_affiliation_string":"Systems and Control Engineering Group, Indian Institute of Technology 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"],"affiliations":[{"raw_affiliation_string":"School of Electrical Engineering, Tel Aviv University , Ramat Aviv, Israel","institution_ids":["https://openalex.org/I16391192"]}]},{"author_position":"middle","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"],"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/A5007830129","display_name":"Emilia Fridman","orcid":"https://orcid.org/0000-0002-8773-9494"},"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":"Emilia Fridman","raw_affiliation_strings":["School of Electrical Engineering, Tel Aviv University , Ramat Aviv, Israel"],"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":4,"corresponding_author_ids":["https://openalex.org/A5083858098"],"corresponding_institution_ids":["https://openalex.org/I162827531"],"apc_list":null,"apc_paid":null,"fwci":0.2707,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.62198336,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"92","issue":"1","first_page":"145","last_page":"162"},"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9965999722480774,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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":0.9894000291824341,"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/lipschitz-continuity","display_name":"Lipschitz continuity","score":0.7694805860519409},{"id":"https://openalex.org/keywords/hilbert-space","display_name":"Hilbert space","score":0.7275060415267944},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6751277446746826},{"id":"https://openalex.org/keywords/controllability","display_name":"Controllability","score":0.6091822385787964},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5829207301139832},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.4760211110115051},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.47523143887519836},{"id":"https://openalex.org/keywords/constructive-proof","display_name":"Constructive proof","score":0.44100168347358704},{"id":"https://openalex.org/keywords/generator","display_name":"Generator (circuit theory)","score":0.4356614053249359},{"id":"https://openalex.org/keywords/state","display_name":"State (computer science)","score":0.4285101294517517},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4094986617565155},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.40812957286834717},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4026850163936615},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.21749508380889893},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1745186448097229},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.09798264503479004}],"concepts":[{"id":"https://openalex.org/C22324862","wikidata":"https://www.wikidata.org/wiki/Q652707","display_name":"Lipschitz continuity","level":2,"score":0.7694805860519409},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.7275060415267944},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6751277446746826},{"id":"https://openalex.org/C48209547","wikidata":"https://www.wikidata.org/wiki/Q1331104","display_name":"Controllability","level":2,"score":0.6091822385787964},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5829207301139832},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.4760211110115051},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.47523143887519836},{"id":"https://openalex.org/C202854965","wikidata":"https://www.wikidata.org/wiki/Q3044470","display_name":"Constructive proof","level":2,"score":0.44100168347358704},{"id":"https://openalex.org/C2780992000","wikidata":"https://www.wikidata.org/wiki/Q17016113","display_name":"Generator (circuit theory)","level":3,"score":0.4356614053249359},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.4285101294517517},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4094986617565155},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.40812957286834717},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4026850163936615},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.21749508380889893},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1745186448097229},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.09798264503479004},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1080/00207179.2016.1266513","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207179.2016.1266513","pdf_url":null,"source":{"id":"https://openalex.org/S88061139","display_name":"International Journal of Control","issn_l":"0020-7179","issn":["0020-7179","1366-5820"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Control","raw_type":"journal-article"},{"id":"pmh:oai:dsapce.library.iitb.ac.in:100/26211","is_oa":false,"landing_page_url":"http://dspace.library.iitb.ac.in/xmlui/handle/100/26211","pdf_url":null,"source":{"id":"https://openalex.org/S4306400899","display_name":"DSpace (IIT Bombay)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I162827531","host_organization_name":"Indian Institute of Technology Bombay","host_organization_lineage":["https://openalex.org/I162827531"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2480933529","display_name":null,"funder_award_id":"800/14","funder_id":"https://openalex.org/F4320322252","funder_display_name":"Israel Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320322252","display_name":"Israel Science Foundation","ror":"https://ror.org/04sazxf24"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":28,"referenced_works":["https://openalex.org/W203646022","https://openalex.org/W240029891","https://openalex.org/W1481364825","https://openalex.org/W1514844366","https://openalex.org/W1527296550","https://openalex.org/W1833425995","https://openalex.org/W1967822522","https://openalex.org/W1975362409","https://openalex.org/W1985945078","https://openalex.org/W1999475633","https://openalex.org/W2002475330","https://openalex.org/W2026905679","https://openalex.org/W2029710005","https://openalex.org/W2042080864","https://openalex.org/W2049094266","https://openalex.org/W2066096538","https://openalex.org/W2067265108","https://openalex.org/W2074719561","https://openalex.org/W2080312705","https://openalex.org/W2129820524","https://openalex.org/W2133627030","https://openalex.org/W2150467770","https://openalex.org/W2165368325","https://openalex.org/W2168279726","https://openalex.org/W2476721866","https://openalex.org/W4230203276","https://openalex.org/W4248589278","https://openalex.org/W4366819356"],"related_works":["https://openalex.org/W2036697162","https://openalex.org/W2332386680","https://openalex.org/W2248621902","https://openalex.org/W2003779889","https://openalex.org/W2561315646","https://openalex.org/W4205698120","https://openalex.org/W4239246781","https://openalex.org/W2542825942","https://openalex.org/W3201620972","https://openalex.org/W1496421768"],"abstract_inverted_index":{"We":[0,103,151,224],"investigate":[1],"the":[2,11,21,53,89,94,116,160,208],"exact":[3,252],"controllability":[4,253],"of":[5,24,69,136,203,248,257],"a":[6,25,31,186,199,231,235,255],"nonlinear":[7,90,161,209,236,258],"plant":[8,95,162,210],"described":[9],"by":[10],"equation":[12,233],"x\u02d9(t)=Ax(t)+Bu(t)+BNN(x(t),t),":[13],"where":[14],"t":[15,59],"\u2265":[16],"0.":[17,171],"Here":[18],"A":[19,124],"is":[20,56,96,156,163,174],"infinitesimal":[22],"generator":[23],"strongly":[26],"continuous":[27,57],"group":[28],"T":[29,51],"on":[30,39,142,251],"Hilbert":[32,40],"space":[33],"X,":[34,85,192],"B":[35,72],"and":[36,43,52,60,73,82,111,119,123,128,140,185,234],"BN,":[37],"defined":[38],"spaces":[41],"U":[42,81],"UN,":[44],"respectively,":[45],"are":[46,121,134],"admissible":[47],"control":[48,200],"operators":[49,79,109],"for":[50,197,207],"function":[54],"N:X\u00d7[0,\u221e)\u21a6UN":[55],"in":[58,62,86,93,97,101,166],"Lipschitz":[61,65,100],"x,":[63],"with":[64],"constant":[66],"LN":[67,155],"independent":[68],"t.":[70],"Thus,":[71],"BN":[74],"can":[75,242],"be":[76,243],"unbounded":[77],"as":[78,245],"from":[80],"UN":[83],"to":[84,148,254],"which":[87,211],"case":[88],"term":[91],"BNN(x(t),t)":[92],"general":[98],"not":[99],"x.":[102],"assume":[104],"that":[105,115,145,153,213],"there":[106],"exist":[107],"linear":[108],"F":[110,112],"b":[113],"such":[114,144],"triples":[117],"(A,[BBN],F)":[118],"(-A,[BBN],Fb)":[120],"regular":[122],"+":[125,130],"BF":[126,131],"\u039b":[127,133],"\u2212A":[129],"b,":[132],"generators":[135],"operator":[137],"semigroups":[138],"Tf":[139],"Tb":[141],"X":[143,184],"\u2225Ttf\u2225\u00b7\u2225Ttb\u2225":[146],"decays":[147],"zero":[149],"exponentially.":[150],"prove":[152],"if":[154,214],"sufficiently":[157],"small,":[158],"then":[159,219],"exactly":[164],"controllable":[165],"some":[167],"time":[168],"\u03c4":[169,190],">":[170],"Our":[172,239],"proof":[173],"constructive,":[175],"i.e.":[176],"given":[177],"an":[178,195,246],"initial":[179],"state":[180,188],"x":[181,189,217,222],"0":[182],"\u2208":[183,191],"final":[187],"we":[193],"propose":[194],"approach":[196,227],"constructing":[198],"signal":[201],"u":[202],"class":[204,256],"L":[205],"2":[206],"ensures":[212],"x(0)":[215],"=":[216,221],"0,":[218],"x(\u03c4)":[220],"\u03c4.":[223],"illustrate":[225],"our":[226],"using":[228],"two":[229],"examples:":[230],"sine-Gordon":[232],"wave":[237],"equation.":[238],"main":[240],"result":[241],"regarded":[244],"extension":[247],"Russell's":[249],"principle":[250],"plants.":[259]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":1}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}