{"id":"https://openalex.org/W2003440751","doi":"https://doi.org/10.1080/00207170601113907","title":"Continuous representation and control of hybrid systems","display_name":"Continuous representation and control of hybrid systems","publication_year":2007,"publication_date":"2007-11-16","ids":{"openalex":"https://openalex.org/W2003440751","doi":"https://doi.org/10.1080/00207170601113907","mag":"2003440751"},"language":"en","primary_location":{"id":"doi:10.1080/00207170601113907","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207170601113907","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/A5076472193","display_name":"M. Gapaillard","orcid":null},"institutions":[{"id":"https://openalex.org/I4210135273","display_name":"Laboratoire Interuniversitaire des Syst\u00e8mes Atmosph\u00e9riques","ror":"https://ror.org/046cjf283","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I197681013","https://openalex.org/I204730241","https://openalex.org/I4210135273","https://openalex.org/I4210148025"]},{"id":"https://openalex.org/I4210116740","display_name":"Laboratoire d'Informatique et d'Automatique pour les Syst\u00e8mes","ror":"https://ror.org/02b5vq778","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I4210113334","https://openalex.org/I4210116740","https://openalex.org/I4210139971"]},{"id":"https://openalex.org/I4392021213","display_name":"Laboratoire d'Ing\u00e9nierie des Syst\u00e8mes","ror":"https://ror.org/005ba5y61","country_code":null,"type":"facility","lineage":["https://openalex.org/I194210350","https://openalex.org/I4210105918","https://openalex.org/I4210105918","https://openalex.org/I4392021213","https://openalex.org/I98702875"]},{"id":"https://openalex.org/I4210159180","display_name":"Laboratoire Techniques, Territoires et Soci\u00e9t\u00e9s","ror":"https://ror.org/05fc1hn07","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I142631665","https://openalex.org/I4210145102","https://openalex.org/I4210150854","https://openalex.org/I4210154111","https://openalex.org/I4210159180"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"M. Gapaillard","raw_affiliation_strings":["\n Laboratoire d\u2019Ing\u00e9nierie des Syst\u00e8mes Automatis\u00e9s, LISA 62, Avenue Notre-Dame du Lac, 49000, Angers, France","Laboratoire d\u2019Ing\u00e9nierie des Syst\u00e8mes Automatis\u00e9s , LISA 62, Avenue Notre-Dame du Lac, 49000, Angers, France"],"affiliations":[{"raw_affiliation_string":"\n Laboratoire d\u2019Ing\u00e9nierie des Syst\u00e8mes Automatis\u00e9s, LISA 62, Avenue Notre-Dame du Lac, 49000, Angers, France","institution_ids":["https://openalex.org/I4210116740","https://openalex.org/I4210135273","https://openalex.org/I4210159180"]},{"raw_affiliation_string":"Laboratoire d\u2019Ing\u00e9nierie des Syst\u00e8mes Automatis\u00e9s , LISA 62, Avenue Notre-Dame du Lac, 49000, Angers, France","institution_ids":["https://openalex.org/I4210116740","https://openalex.org/I4210135273","https://openalex.org/I4210159180","https://openalex.org/I4392021213"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5076472193"],"corresponding_institution_ids":["https://openalex.org/I4210116740","https://openalex.org/I4210135273","https://openalex.org/I4210159180","https://openalex.org/I4392021213"],"apc_list":null,"apc_paid":null,"fwci":1.7976,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.85951107,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"81","issue":"1","first_page":"1","last_page":"20"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12158","display_name":"Guidance and Control Systems","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2202","display_name":"Aerospace 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/T12158","display_name":"Guidance and Control Systems","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2202","display_name":"Aerospace 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/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.9836999773979187,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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/T14083","display_name":"Extremum Seeking Control Systems","score":0.9779000282287598,"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/hybrid-system","display_name":"Hybrid system","score":0.7792527675628662},{"id":"https://openalex.org/keywords/classification-of-discontinuities","display_name":"Classification of discontinuities","score":0.7556584477424622},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.6410353183746338},{"id":"https://openalex.org/keywords/jump","display_name":"Jump","score":0.5930371880531311},{"id":"https://openalex.org/keywords/formalism","display_name":"Formalism (music)","score":0.5396599173545837},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4555181562900543},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4541267454624176},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.44552695751190186},{"id":"https://openalex.org/keywords/state","display_name":"State (computer science)","score":0.44433778524398804},{"id":"https://openalex.org/keywords/trajectory","display_name":"Trajectory","score":0.4247826933860779},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.41922298073768616},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.3609620928764343},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.3033531606197357},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2616502642631531},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.15350428223609924},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.08886328339576721}],"concepts":[{"id":"https://openalex.org/C50897621","wikidata":"https://www.wikidata.org/wiki/Q2665508","display_name":"Hybrid system","level":2,"score":0.7792527675628662},{"id":"https://openalex.org/C15627037","wikidata":"https://www.wikidata.org/wiki/Q541961","display_name":"Classification of discontinuities","level":2,"score":0.7556584477424622},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.6410353183746338},{"id":"https://openalex.org/C2780695682","wikidata":"https://www.wikidata.org/wiki/Q4005959","display_name":"Jump","level":2,"score":0.5930371880531311},{"id":"https://openalex.org/C73301696","wikidata":"https://www.wikidata.org/wiki/Q5469984","display_name":"Formalism (music)","level":3,"score":0.5396599173545837},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4555181562900543},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4541267454624176},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.44552695751190186},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.44433778524398804},{"id":"https://openalex.org/C13662910","wikidata":"https://www.wikidata.org/wiki/Q193139","display_name":"Trajectory","level":2,"score":0.4247826933860779},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.41922298073768616},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.3609620928764343},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.3033531606197357},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2616502642631531},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.15350428223609924},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.08886328339576721},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","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/C142362112","wikidata":"https://www.wikidata.org/wiki/Q735","display_name":"Art","level":0,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C153349607","wikidata":"https://www.wikidata.org/wiki/Q36649","display_name":"Visual arts","level":1,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C558565934","wikidata":"https://www.wikidata.org/wiki/Q2743","display_name":"Musical","level":2,"score":0.0},{"id":"https://openalex.org/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/00207170601113907","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207170601113907","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":39,"referenced_works":["https://openalex.org/W283036238","https://openalex.org/W628962280","https://openalex.org/W1499154045","https://openalex.org/W1507372516","https://openalex.org/W1515852644","https://openalex.org/W1525403950","https://openalex.org/W1530117215","https://openalex.org/W1547397412","https://openalex.org/W1547403762","https://openalex.org/W1594130515","https://openalex.org/W1594563152","https://openalex.org/W1604980813","https://openalex.org/W1897974356","https://openalex.org/W1987795693","https://openalex.org/W1993516198","https://openalex.org/W2050240106","https://openalex.org/W2067480733","https://openalex.org/W2078554646","https://openalex.org/W2117271243","https://openalex.org/W2126726109","https://openalex.org/W2130519480","https://openalex.org/W2135230043","https://openalex.org/W2135667955","https://openalex.org/W2146447376","https://openalex.org/W2152185829","https://openalex.org/W2163439084","https://openalex.org/W2167916919","https://openalex.org/W2170485821","https://openalex.org/W2499792849","https://openalex.org/W2593901252","https://openalex.org/W2738306895","https://openalex.org/W2798500587","https://openalex.org/W2798534591","https://openalex.org/W2798574506","https://openalex.org/W4213195758","https://openalex.org/W4236400251","https://openalex.org/W4247645076","https://openalex.org/W4254594825","https://openalex.org/W6639853348"],"related_works":["https://openalex.org/W2062507148","https://openalex.org/W4390110666","https://openalex.org/W2476229636","https://openalex.org/W2349295756","https://openalex.org/W3217615048","https://openalex.org/W1968813561","https://openalex.org/W1201114281","https://openalex.org/W2154236742","https://openalex.org/W4229002777","https://openalex.org/W2104769107"],"abstract_inverted_index":{"Abstract":[0],"This":[1],"article":[2],"introduces":[3],"a":[4,16,121,162,191],"continuous":[5,42,58,69,80,103,109,169],"representation":[6,17,81,126],"for":[7,207],"controlled":[8],"model":[9],"and":[10,62,91,110,168,172,204,211],"state":[11],"jump":[12],"hybrid":[13,49,74,94,111,139,167],"systems.":[14,59],"Such":[15],"is":[18,45,82,148],"valuable":[19,209],"in":[20,166],"that":[21,40,117],"it":[22],"manages":[23],"to":[24,30,71,129,150,199],"cope":[25],"with":[26,55,161],"the":[27,34,66,79,85,118,125,134,137,142,152,155,177],"difficulties":[28],"related":[29],"discontinuities,":[31],"by":[32,39,176,188],"replacing":[33],"study":[35],"of":[36,41,65,68,73,106,120,133,136,144,146,154,157,190],"these":[37],"systems":[38,50,70,75],"ones,":[43],"which":[44,115],"simple.":[46],"The":[47,195],"studied":[48],"are":[51,76,96,113,179],"first":[52],"introduced,":[53],"together":[54],"their":[56,101,208],"associated":[57,160],"Some":[60],"localized":[61],"global":[63],"convergences":[64],"states":[67],"those":[72],"proved.":[77],"Then,":[78],"used":[83,149],"within":[84],"optimal":[86],"control":[87],"framework.":[88],"Free":[89],"end-time":[90],"trajectory":[92,163],"pursuit":[93,164],"problems":[95,112],"studied,":[97],"as":[98,100,181,183],"well":[99,182],"respective":[102],"versions.":[104],"Convergences":[105],"solutions":[107],"between":[108],"established,":[114],"shows":[116],"resolution":[119],"problem":[122,165],"ensuing":[123],"from":[124],"enables":[127],"one":[128],"obtain":[130,151],"an":[131],"approximation":[132],"solution":[135],"initial":[138],"problem.":[140],"Finally,":[141],"formalism":[143],"calculus":[145],"variations":[147],"expressions":[153],"gradients":[156],"cost":[158],"functions":[159],"cases.":[170],"Theoretical":[171],"technical":[173],"simplifications,":[174],"brought":[175],"representation,":[178],"highlighted,":[180],"its":[184],"practical":[185],"interest":[186],"shown":[187],"means":[189],"numerical":[192],"application.":[193],"Acknowledgments":[194],"author":[196],"would":[197],"like":[198],"thank":[200],"Professors":[201],"J.":[202],"Burger":[203],"M.":[205],"Pogu":[206],"advice":[210],"assistance.":[212]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}