{"id":"https://openalex.org/W1995098197","doi":"https://doi.org/10.1109/cdc.2013.6759936","title":"Sensitivity interpretations of the co-state trajectory for opimal control problems with state constraints","display_name":"Sensitivity interpretations of the co-state trajectory for opimal control problems with state constraints","publication_year":2013,"publication_date":"2013-12-01","ids":{"openalex":"https://openalex.org/W1995098197","doi":"https://doi.org/10.1109/cdc.2013.6759936","mag":"1995098197"},"language":"en","primary_location":{"id":"doi:10.1109/cdc.2013.6759936","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2013.6759936","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"52nd IEEE Conference on Decision and Control","raw_type":"proceedings-article"},"type":"preprint","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/A5109351634","display_name":"Piernicola Bettiol","orcid":"https://orcid.org/0000-0003-4969-6144"},"institutions":[{"id":"https://openalex.org/I161929037","display_name":"Universit\u00e9 de Bretagne Occidentale","ror":"https://ror.org/01b8h3982","country_code":"FR","type":"education","lineage":["https://openalex.org/I161929037"]},{"id":"https://openalex.org/I4210155549","display_name":"Laboratoire de Math\u00e9matiques Blaise Pascal","ror":"https://ror.org/05sd5r855","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I198244214","https://openalex.org/I4210141950","https://openalex.org/I4210155549"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Piernicola Bettiol","raw_affiliation_strings":["Laboratoire de Mathematiques, Universit\u00e9 de Bretagne Occidentale, Brest, France","Lab. de Math., Univ. de Bretagne Occidentale, Brest, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Laboratoire de Mathematiques, Universit\u00e9 de Bretagne Occidentale, Brest, France","institution_ids":["https://openalex.org/I161929037","https://openalex.org/I4210155549"]},{"raw_affiliation_string":"Lab. de Math., Univ. de Bretagne Occidentale, Brest, France","institution_ids":["https://openalex.org/I161929037"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5034818712","display_name":"H\u00e9l\u00e8ne Frankowska","orcid":"https://orcid.org/0000-0001-6237-4137"},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I3017942884","display_name":"Institut de Math\u00e9matiques de Jussieu-Paris Rive Gauche","ror":"https://ror.org/03fk87k11","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I204730241","https://openalex.org/I3017942884","https://openalex.org/I39804081","https://openalex.org/I4210141950"]},{"id":"https://openalex.org/I39804081","display_name":"Sorbonne Universit\u00e9","ror":"https://ror.org/02en5vm52","country_code":"FR","type":"education","lineage":["https://openalex.org/I39804081"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Helene Frankowska","raw_affiliation_strings":["CNRS, Universit\u00e9 Pierre et Marie Curie (Paris 6), Paris cedex 05, France","Inst. de Math. de Jussieu, Univ. Pierre et Marie Curie (Paris 6), Paris, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"CNRS, Universit\u00e9 Pierre et Marie Curie (Paris 6), Paris cedex 05, France","institution_ids":["https://openalex.org/I39804081","https://openalex.org/I1294671590"]},{"raw_affiliation_string":"Inst. de Math. de Jussieu, Univ. Pierre et Marie Curie (Paris 6), Paris, France","institution_ids":["https://openalex.org/I39804081","https://openalex.org/I3017942884"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5031053402","display_name":"Richard Vinter","orcid":"https://orcid.org/0000-0002-3585-0473"},"institutions":[{"id":"https://openalex.org/I47508984","display_name":"Imperial College London","ror":"https://ror.org/041kmwe10","country_code":"GB","type":"education","lineage":["https://openalex.org/I47508984"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Richard Vinter","raw_affiliation_strings":["Department of Electrical and Electronic Engineering, Imperial College London, London, UK","Dept. of Electr. & Electron. Eng., Imperial Coll., London, London, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical and Electronic Engineering, Imperial College London, London, UK","institution_ids":["https://openalex.org/I47508984"]},{"raw_affiliation_string":"Dept. of Electr. & Electron. Eng., Imperial Coll., London, London, UK","institution_ids":["https://openalex.org/I47508984"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":6,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.7291,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.71904389,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"317","issue":null,"first_page":"532","last_page":"537"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9975000023841858,"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"}},"topics":[{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9975000023841858,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9955000281333923,"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"}},{"id":"https://openalex.org/T10791","display_name":"Advanced Control Systems Optimization","score":0.982200026512146,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/sensitivity","display_name":"Sensitivity (control systems)","score":0.7126778364181519},{"id":"https://openalex.org/keywords/differential-inclusion","display_name":"Differential inclusion","score":0.6425078511238098},{"id":"https://openalex.org/keywords/trajectory","display_name":"Trajectory","score":0.5834606289863586},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5818626284599304},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.5409951210021973},{"id":"https://openalex.org/keywords/subgradient-method","display_name":"Subgradient method","score":0.5201390385627747},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4845956563949585},{"id":"https://openalex.org/keywords/partial-derivative","display_name":"Partial derivative","score":0.47099965810775757},{"id":"https://openalex.org/keywords/state-variable","display_name":"State variable","score":0.4627978503704071},{"id":"https://openalex.org/keywords/state","display_name":"State (computer science)","score":0.4545357823371887},{"id":"https://openalex.org/keywords/hamiltonian","display_name":"Hamiltonian (control theory)","score":0.4458085000514984},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.44311606884002686},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.41676560044288635},{"id":"https://openalex.org/keywords/relation","display_name":"Relation (database)","score":0.4156695306301117},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.34140002727508545},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2962508797645569},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1883602738380432},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.16857728362083435},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.08234071731567383}],"concepts":[{"id":"https://openalex.org/C21200559","wikidata":"https://www.wikidata.org/wiki/Q7451068","display_name":"Sensitivity (control systems)","level":2,"score":0.7126778364181519},{"id":"https://openalex.org/C70834904","wikidata":"https://www.wikidata.org/wiki/Q1054638","display_name":"Differential inclusion","level":2,"score":0.6425078511238098},{"id":"https://openalex.org/C13662910","wikidata":"https://www.wikidata.org/wiki/Q193139","display_name":"Trajectory","level":2,"score":0.5834606289863586},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5818626284599304},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.5409951210021973},{"id":"https://openalex.org/C158968445","wikidata":"https://www.wikidata.org/wiki/Q7631150","display_name":"Subgradient method","level":2,"score":0.5201390385627747},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4845956563949585},{"id":"https://openalex.org/C53846429","wikidata":"https://www.wikidata.org/wiki/Q186475","display_name":"Partial derivative","level":2,"score":0.47099965810775757},{"id":"https://openalex.org/C129537906","wikidata":"https://www.wikidata.org/wiki/Q7603913","display_name":"State variable","level":2,"score":0.4627978503704071},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.4545357823371887},{"id":"https://openalex.org/C130787639","wikidata":"https://www.wikidata.org/wiki/Q5645293","display_name":"Hamiltonian (control theory)","level":2,"score":0.4458085000514984},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.44311606884002686},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.41676560044288635},{"id":"https://openalex.org/C25343380","wikidata":"https://www.wikidata.org/wiki/Q277521","display_name":"Relation (database)","level":2,"score":0.4156695306301117},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.34140002727508545},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2962508797645569},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1883602738380432},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.16857728362083435},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08234071731567383},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","level":1,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C1276947","wikidata":"https://www.wikidata.org/wiki/Q333","display_name":"Astronomy","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","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/C24326235","wikidata":"https://www.wikidata.org/wiki/Q126095","display_name":"Electronic engineering","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/cdc.2013.6759936","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2013.6759936","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"52nd IEEE Conference on Decision and Control","raw_type":"proceedings-article"},{"id":"pmh:oai:HAL:hal-00917558v1","is_oa":false,"landing_page_url":"https://inria.hal.science/hal-00917558","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"52nd IEEE Conference on Decision and Control, IEEE, Dec 2013, Florence, Italy. pp.532-537","raw_type":"info:eu-repo/semantics/conferenceObject"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.8299999833106995,"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities"}],"awards":[{"id":"https://openalex.org/G1823500649","display_name":null,"funder_award_id":"EP/G066477/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"}],"funders":[{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":12,"referenced_works":["https://openalex.org/W1976098248","https://openalex.org/W1983536992","https://openalex.org/W1994996557","https://openalex.org/W2013692585","https://openalex.org/W2015660194","https://openalex.org/W2051552175","https://openalex.org/W2061402583","https://openalex.org/W2092078242","https://openalex.org/W2136361262","https://openalex.org/W2165851458","https://openalex.org/W2175104911","https://openalex.org/W4249513058"],"related_works":["https://openalex.org/W2037613239","https://openalex.org/W2359120930","https://openalex.org/W2781777036","https://openalex.org/W2390469630","https://openalex.org/W2059050877","https://openalex.org/W1971290991","https://openalex.org/W1944783162","https://openalex.org/W4378770495","https://openalex.org/W4361865857","https://openalex.org/W2113133070"],"abstract_inverted_index":{"Sensitivity":[0,23],"relations":[1,24,77,89,193],"in":[2,35],"optimal":[3,26],"control":[4,27],"identify":[5],"the":[6,10,20,51,58,64,68,75,103,110,116,119,124,127,133,178,183,191,208],"costate":[7,104,125,184,200,217],"trajectory":[8,201],"and":[9,33,86,118,126,140,161,211],"Hamiltonian,":[11],"evaluated":[12],"along":[13],"a":[14,71,106,130,163,199],"minimizing":[15],"trajectory,":[16],"as":[17,169],"gradients":[18],"of":[19,37,53,70,109,132,166],"value":[21,111,134],"function.":[22],"for":[25,90,148,162,177],"problems":[28,93],"not":[29],"involving":[30],"state":[31,55,96,149],"constraints":[32],"formulated":[34],"terms":[36],"controlled":[38],"differential":[39,72,91],"equation":[40],"with":[41,94,105,113,129,136,171],"smooth":[42],"data":[43,59],"follow":[44],"easily":[45],"from":[46,80],"standard":[47],"transversality":[48],"conditions.":[49],"In":[50],"presence":[52],"pathwise":[54,95],"constraints,":[56],"if":[57],"is":[60,78,146,156,175,213],"nonsmooth":[61],"or":[62],"when":[63],"dynamic":[65],"constraint":[66,150],"takes":[67],"form":[69,165],"inclusion,":[73],"deriving":[74],"sensitivity":[76,88,100,121,144,154,209],"far":[79],"straightforward.":[81],"We":[82],"announce":[83],"both":[84],"`full'":[85],"`partial'":[87],"inclusion":[92],"constraints.":[97],"The":[98,142,152],"partial":[99,107,143],"relation":[101,122,145,155],"identifies":[102,123],"subgradient":[108,131],"function":[112,135],"respect":[114,137],"to":[115,138,189,206,220],"state,":[117],"full":[120,153],"Hamiltonian":[128],"time":[139,180],"state.":[141],"new":[147],"problems.":[151],"valid":[157],"under":[158],"reduced":[159],"hypotheses":[160],"stronger":[164],"necessary":[167],"conditions,":[168],"compared":[170],"earlier":[172],"literature.":[173],"It":[174],"shown":[176],"first":[179],"also":[181],"that":[182,198,215],"arc":[185],"can":[186],"be":[187,203],"chosen":[188,205],"satisfy":[190,207],"two":[192],"simultaneously.":[194],"An":[195],"example":[196],"illustrates":[197],"may":[202],"specially":[204],"relations,":[210],"it":[212],"possible":[214],"some":[216],"trajectories":[218],"fail":[219],"do":[221],"so.":[222]},"counts_by_year":[{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2026-07-02T09:51:11.867554","created_date":"2025-10-10T00:00:00"}
