{"id":"https://openalex.org/W4396214277","doi":"https://doi.org/10.1109/tac.2024.3394544","title":"From Relaxed Constraint Satisfaction to <i>p</i>-Invariance of Sets","display_name":"From Relaxed Constraint Satisfaction to <i>p</i>-Invariance of Sets","publication_year":2024,"publication_date":"2024-04-29","ids":{"openalex":"https://openalex.org/W4396214277","doi":"https://doi.org/10.1109/tac.2024.3394544"},"language":"en","primary_location":{"id":"doi:10.1109/tac.2024.3394544","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2024.3394544","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Automatic Control","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://centralesupelec.hal.science/hal-04565096v1/document","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5106497955","display_name":"Sorin Olaru","orcid":"https://orcid.org/0000-0003-3256-9595"},"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/I4210097418","display_name":"Laboratoire des signaux et syst\u00e8mes","ror":"https://ror.org/00skw9v43","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I277688954","https://openalex.org/I277688954","https://openalex.org/I4210097418","https://openalex.org/I4210107720"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Sorin Olaru","raw_affiliation_strings":["Universit&#x00E9; Paris-Saclay, CNRS, CentraleSup&#x00E9;lec, Laboratoire des Signaux et Syst&#x00E8;mes, Gif-sur-Yvette, France"],"raw_orcid":"https://orcid.org/0000-0003-3256-9595","affiliations":[{"raw_affiliation_string":"Universit&#x00E9; Paris-Saclay, CNRS, CentraleSup&#x00E9;lec, Laboratoire des Signaux et Syst&#x00E8;mes, Gif-sur-Yvette, France","institution_ids":["https://openalex.org/I4210097418","https://openalex.org/I1294671590"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5103039016","display_name":"Martin Soyer","orcid":"https://orcid.org/0000-0003-1892-4319"},"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/I4210097418","display_name":"Laboratoire des signaux et syst\u00e8mes","ror":"https://ror.org/00skw9v43","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I277688954","https://openalex.org/I277688954","https://openalex.org/I4210097418","https://openalex.org/I4210107720"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Martin Soyer","raw_affiliation_strings":["Universit&#x00E9; Paris-Saclay, CNRS, CentraleSup&#x00E9;lec, Laboratoire des Signaux et Syst&#x00E8;mes, Gif-sur-Yvette, France"],"raw_orcid":"https://orcid.org/0000-0003-1892-4319","affiliations":[{"raw_affiliation_string":"Universit&#x00E9; Paris-Saclay, CNRS, CentraleSup&#x00E9;lec, Laboratoire des Signaux et Syst&#x00E8;mes, Gif-sur-Yvette, France","institution_ids":["https://openalex.org/I4210097418","https://openalex.org/I1294671590"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5021839290","display_name":"Zhixin Zhao","orcid":"https://orcid.org/0009-0006-0911-564X"},"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/I4210097418","display_name":"Laboratoire des signaux et syst\u00e8mes","ror":"https://ror.org/00skw9v43","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I277688954","https://openalex.org/I277688954","https://openalex.org/I4210097418","https://openalex.org/I4210107720"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Zhixin Zhao","raw_affiliation_strings":["Universit&#x00E9; Paris-Saclay, CNRS, CentraleSup&#x00E9;lec, Laboratoire des Signaux et Syst&#x00E8;mes, Gif-sur-Yvette, France"],"raw_orcid":"https://orcid.org/0009-0006-0911-564X","affiliations":[{"raw_affiliation_string":"Universit&#x00E9; Paris-Saclay, CNRS, CentraleSup&#x00E9;lec, Laboratoire des Signaux et Syst&#x00E8;mes, Gif-sur-Yvette, France","institution_ids":["https://openalex.org/I4210097418","https://openalex.org/I1294671590"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5062837641","display_name":"Carlos E.T. D\u00f3rea","orcid":"https://orcid.org/0000-0002-3999-2874"},"institutions":[{"id":"https://openalex.org/I35046152","display_name":"Universidade Federal do Rio Grande do Norte","ror":"https://ror.org/04wn09761","country_code":"BR","type":"education","lineage":["https://openalex.org/I35046152"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Carlos E. T. D\u00f3rea","raw_affiliation_strings":["Department of Computer Engineering and Automation, UFRN, Natal, Brazil"],"raw_orcid":"https://orcid.org/0000-0002-3999-2874","affiliations":[{"raw_affiliation_string":"Department of Computer Engineering and Automation, UFRN, Natal, Brazil","institution_ids":["https://openalex.org/I35046152"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5005907522","display_name":"Ernesto Kofman","orcid":"https://orcid.org/0000-0001-7657-3612"},"institutions":[{"id":"https://openalex.org/I4141589","display_name":"National University of Rosario","ror":"https://ror.org/02tphfq59","country_code":"AR","type":"education","lineage":["https://openalex.org/I4141589"]}],"countries":["AR"],"is_corresponding":false,"raw_author_name":"Ernesto Kofman","raw_affiliation_strings":["Departamento de Control, UNR, FCEIA, Rosario, Argentina"],"raw_orcid":"https://orcid.org/0000-0001-7657-3612","affiliations":[{"raw_affiliation_string":"Departamento de Control, UNR, FCEIA, Rosario, Argentina","institution_ids":["https://openalex.org/I4141589"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5081751699","display_name":"Antoine Girard","orcid":"https://orcid.org/0000-0002-4075-9041"},"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/I4210097418","display_name":"Laboratoire des signaux et syst\u00e8mes","ror":"https://ror.org/00skw9v43","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I277688954","https://openalex.org/I277688954","https://openalex.org/I4210097418","https://openalex.org/I4210107720"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Antoine Girard","raw_affiliation_strings":["Universit&#x00E9; Paris-Saclay, CNRS, CentraleSup&#x00E9;lec, Laboratoire des Signaux et Syst&#x00E8;mes, Gif-sur-Yvette, France"],"raw_orcid":"https://orcid.org/0000-0002-4075-9041","affiliations":[{"raw_affiliation_string":"Universit&#x00E9; Paris-Saclay, CNRS, CentraleSup&#x00E9;lec, Laboratoire des Signaux et Syst&#x00E8;mes, Gif-sur-Yvette, France","institution_ids":["https://openalex.org/I4210097418","https://openalex.org/I1294671590"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":6,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.8739,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.7230547,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"69","issue":"10","first_page":"7036","last_page":"7042"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10791","display_name":"Advanced Control Systems Optimization","score":0.9995999932289124,"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/T10791","display_name":"Advanced Control Systems Optimization","score":0.9995999932289124,"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/T10551","display_name":"Scheduling and Optimization Algorithms","score":0.9933000206947327,"subfield":{"id":"https://openalex.org/subfields/2209","display_name":"Industrial and Manufacturing 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/T11801","display_name":"Reservoir Engineering and Simulation Methods","score":0.9869999885559082,"subfield":{"id":"https://openalex.org/subfields/2212","display_name":"Ocean 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/constraint-satisfaction-problem","display_name":"Constraint satisfaction problem","score":0.6280964612960815},{"id":"https://openalex.org/keywords/constraint-satisfaction","display_name":"Constraint satisfaction","score":0.603748619556427},{"id":"https://openalex.org/keywords/constraint","display_name":"Constraint (computer-aided design)","score":0.5474435091018677},{"id":"https://openalex.org/keywords/local-consistency","display_name":"Local consistency","score":0.45502761006355286},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.45071941614151},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3895258903503418},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3817245364189148},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.34757259488105774},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.1837179958820343},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.06729596853256226}],"concepts":[{"id":"https://openalex.org/C199622910","wikidata":"https://www.wikidata.org/wiki/Q1128326","display_name":"Constraint satisfaction problem","level":3,"score":0.6280964612960815},{"id":"https://openalex.org/C44616089","wikidata":"https://www.wikidata.org/wiki/Q30158686","display_name":"Constraint satisfaction","level":3,"score":0.603748619556427},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.5474435091018677},{"id":"https://openalex.org/C137105694","wikidata":"https://www.wikidata.org/wiki/Q3407510","display_name":"Local consistency","level":4,"score":0.45502761006355286},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.45071941614151},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3895258903503418},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3817245364189148},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.34757259488105774},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.1837179958820343},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.06729596853256226},{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tac.2024.3394544","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2024.3394544","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Automatic Control","raw_type":"journal-article"},{"id":"pmh:oai:HAL:hal-04565096v1","is_oa":true,"landing_page_url":"https://centralesupelec.hal.science/hal-04565096","pdf_url":"https://centralesupelec.hal.science/hal-04565096v1/document","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":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IEEE Transactions on Automatic Control, 2024, 69 (10), pp.7036 - 7042. &#x27E8;10.1109/TAC.2024.3394544&#x27E9;","raw_type":"Journal articles"}],"best_oa_location":{"id":"pmh:oai:HAL:hal-04565096v1","is_oa":true,"landing_page_url":"https://centralesupelec.hal.science/hal-04565096","pdf_url":"https://centralesupelec.hal.science/hal-04565096v1/document","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":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IEEE Transactions on Automatic Control, 2024, 69 (10), pp.7036 - 7042. &#x27E8;10.1109/TAC.2024.3394544&#x27E9;","raw_type":"Journal articles"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4396214277.pdf","grobid_xml":"https://content.openalex.org/works/W4396214277.grobid-xml"},"referenced_works_count":23,"referenced_works":["https://openalex.org/W165896801","https://openalex.org/W1838714828","https://openalex.org/W1985326327","https://openalex.org/W1992187244","https://openalex.org/W1993489396","https://openalex.org/W1994546875","https://openalex.org/W2041387588","https://openalex.org/W2048375164","https://openalex.org/W2096948320","https://openalex.org/W2138452863","https://openalex.org/W2138700249","https://openalex.org/W2165136011","https://openalex.org/W2171505650","https://openalex.org/W2396495043","https://openalex.org/W2413875992","https://openalex.org/W2487779201","https://openalex.org/W2589273562","https://openalex.org/W2964117770","https://openalex.org/W3084125797","https://openalex.org/W3090249696","https://openalex.org/W3104168345","https://openalex.org/W4200468227","https://openalex.org/W4388065110"],"related_works":["https://openalex.org/W2569549435","https://openalex.org/W2091348864","https://openalex.org/W2784687883","https://openalex.org/W4303044088","https://openalex.org/W96881443","https://openalex.org/W1486916474","https://openalex.org/W2012694101","https://openalex.org/W1550482496","https://openalex.org/W2737098235","https://openalex.org/W2140769824"],"abstract_inverted_index":{"The":[0,22,38,100],"present":[1],"article":[2],"proposes":[3],"a":[4,19,27,63,81,92,98,106,114,144,154],"general":[5],"framework":[6,29,146],"for":[7,147],"the":[8,16,33,45,48,52,57,60,76,86,89,136,148,165],"analysis":[9,149],"of":[10,18,35,47,59,62,78,95,116,122,150,164],"constraints":[11,79,117],"satisfaction":[12,55,102],"with":[13,103,162],"respect":[14,104],"to":[15,32,42,105,113,120,135],"trajectories":[17,61],"dynamical":[20,64,151],"system.":[21,65],"results":[23],"are":[24,69],"presented":[25],"in":[26,71,153],"discrete-time":[28],"and":[30,85,118,170],"pertain":[31],"class":[34],"set-theoretic":[36,155],"methods.":[37],"main":[39],"objective":[40],"is":[41,125,160],"go":[43],"beyond":[44],"state":[46],"art":[49],"by":[50],"characterizing":[51,75],"intermittent":[53],"constraint":[54,101],"along":[56],"evolution":[58],"Two":[66],"relaxed":[67],"notions":[68,130],"introduced":[70],"this":[72],"sense,":[73],"one":[74],"validation":[77,90],"within":[80],"given":[82],"finite":[83],"window":[84],"other":[87],"imposing":[88],"after":[91],"fixed":[93],"number":[94],"time-steps":[96],"following":[97],"violation.":[99],"controlled":[107,138],"trajectory":[108],"will":[109],"then":[110,119],"be":[111,132],"extended":[112],"set":[115,140],"tubes":[121],"trajectories.":[123],"It":[124],"shown":[126],"that":[127],"all":[128],"these":[129],"can":[131],"accordingly":[133],"anchored":[134],"well-known":[137],"positive":[139],"invariance,":[141],"thus":[142],"offering":[143],"generalized":[145],"systems":[152],"framework.":[156],"This":[157],"technical":[158],"note":[159],"completed":[161],"illustrations":[163],"constructions":[166],"on":[167],"both":[168],"linear":[169],"nonlinear":[171],"case.":[172]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2024-04-30T00:00:00"}