{"id":"https://openalex.org/W2952138851","doi":"https://doi.org/10.1109/tac.2020.2990665","title":"Forward Invariance of Sets for Hybrid Dynamical Systems (Part II)","display_name":"Forward Invariance of Sets for Hybrid Dynamical Systems (Part II)","publication_year":2020,"publication_date":"2020-04-27","ids":{"openalex":"https://openalex.org/W2952138851","doi":"https://doi.org/10.1109/tac.2020.2990665","mag":"2952138851"},"language":"en","primary_location":{"id":"doi:10.1109/tac.2020.2990665","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2020.2990665","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":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5022625561","display_name":"Jun Chai","orcid":"https://orcid.org/0000-0001-7567-6580"},"institutions":[{"id":"https://openalex.org/I185103710","display_name":"University of California, Santa Cruz","ror":"https://ror.org/03s65by71","country_code":"US","type":"education","lineage":["https://openalex.org/I185103710"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jun Chai","raw_affiliation_strings":["Hybrid System Lab, University of California, Santa Cruz, CA, USA"],"raw_orcid":"https://orcid.org/0000-0001-7567-6580","affiliations":[{"raw_affiliation_string":"Hybrid System Lab, University of California, Santa Cruz, CA, USA","institution_ids":["https://openalex.org/I185103710"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5028224738","display_name":"Ricardo G. Sanfelice","orcid":"https://orcid.org/0000-0002-6671-5362"},"institutions":[{"id":"https://openalex.org/I185103710","display_name":"University of California, Santa Cruz","ror":"https://ror.org/03s65by71","country_code":"US","type":"education","lineage":["https://openalex.org/I185103710"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Ricardo G. Sanfelice","raw_affiliation_strings":["Department of Electrical and Computer Engineering, University of California, Santa Cruz, CA, USA"],"raw_orcid":"https://orcid.org/0000-0002-6671-5362","affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, University of California, Santa Cruz, CA, USA","institution_ids":["https://openalex.org/I185103710"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I185103710"],"apc_list":null,"apc_paid":null,"fwci":1.7492,"has_fulltext":false,"cited_by_count":23,"citation_normalized_percentile":{"value":0.83820762,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"66","issue":"1","first_page":"89","last_page":"104"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10791","display_name":"Advanced Control Systems Optimization","score":0.9998999834060669,"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":0.9998999834060669,"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/T14083","display_name":"Extremum Seeking Control Systems","score":0.9897000193595886,"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/T11236","display_name":"Control Systems and Identification","score":0.9894000291824341,"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/control-theory","display_name":"Control theory (sociology)","score":0.6591759324073792},{"id":"https://openalex.org/keywords/lyapunov-function","display_name":"Lyapunov function","score":0.6064672470092773},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.5442474484443665},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.49964451789855957},{"id":"https://openalex.org/keywords/robust-control","display_name":"Robust control","score":0.4868902266025543},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.46701580286026},{"id":"https://openalex.org/keywords/invariance-principle","display_name":"Invariance principle","score":0.4625638425350189},{"id":"https://openalex.org/keywords/property","display_name":"Property (philosophy)","score":0.4451446235179901},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4407111406326294},{"id":"https://openalex.org/keywords/state","display_name":"State (computer science)","score":0.4369448721408844},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4326745271682739},{"id":"https://openalex.org/keywords/law","display_name":"Law","score":0.3275924623012543},{"id":"https://openalex.org/keywords/control-system","display_name":"Control system","score":0.3159759044647217},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.29755765199661255},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.15144768357276917},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.14341530203819275},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.13142132759094238},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.09014460444450378}],"concepts":[{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.6591759324073792},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.6064672470092773},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.5442474484443665},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.49964451789855957},{"id":"https://openalex.org/C31531917","wikidata":"https://www.wikidata.org/wiki/Q915157","display_name":"Robust control","level":3,"score":0.4868902266025543},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.46701580286026},{"id":"https://openalex.org/C156387681","wikidata":"https://www.wikidata.org/wiki/Q6059484","display_name":"Invariance principle","level":2,"score":0.4625638425350189},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.4451446235179901},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4407111406326294},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.4369448721408844},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4326745271682739},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.3275924623012543},{"id":"https://openalex.org/C17500928","wikidata":"https://www.wikidata.org/wiki/Q959968","display_name":"Control system","level":2,"score":0.3159759044647217},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.29755765199661255},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.15144768357276917},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.14341530203819275},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.13142132759094238},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.09014460444450378},{"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/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C119599485","wikidata":"https://www.wikidata.org/wiki/Q43035","display_name":"Electrical engineering","level":1,"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","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/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"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:10.1109/tac.2020.2990665","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2020.2990665","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"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.5299999713897705,"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10"},{"score":0.4699999988079071,"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16"}],"awards":[{"id":"https://openalex.org/G2464323602","display_name":null,"funder_award_id":"FA9550-16-1-0015","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G5079805135","display_name":null,"funder_award_id":"CNS-1544396","funder_id":"https://openalex.org/F4320335353","funder_display_name":"National Science Foundation of Sri Lanka"},{"id":"https://openalex.org/G5479611822","display_name":null,"funder_award_id":"FA9550-19-1-0053","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G6191118875","display_name":null,"funder_award_id":"FA9550-19-1-0169","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G6697474879","display_name":null,"funder_award_id":"ECS-1450484","funder_id":"https://openalex.org/F4320335353","funder_display_name":"National Science Foundation of Sri Lanka"}],"funders":[{"id":"https://openalex.org/F4320308590","display_name":"University of California","ror":"https://ror.org/00pjdza24"},{"id":"https://openalex.org/F4320310688","display_name":"Center for Information Technology Research in the Interest of Society","ror":"https://ror.org/00zv0wd17"},{"id":"https://openalex.org/F4320335353","display_name":"National Science Foundation of Sri Lanka","ror":"https://ror.org/010xaa060"},{"id":"https://openalex.org/F4320338279","display_name":"Air Force Office of Scientific Research","ror":"https://ror.org/011e9bt93"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":66,"referenced_works":["https://openalex.org/W1506290449","https://openalex.org/W1537653646","https://openalex.org/W1539252391","https://openalex.org/W1551360398","https://openalex.org/W1569239057","https://openalex.org/W1594563152","https://openalex.org/W1607353007","https://openalex.org/W1749724378","https://openalex.org/W1792923791","https://openalex.org/W1968718177","https://openalex.org/W1972149633","https://openalex.org/W1978929829","https://openalex.org/W1984576694","https://openalex.org/W1988538197","https://openalex.org/W1994712640","https://openalex.org/W1999935017","https://openalex.org/W2001617075","https://openalex.org/W2014574550","https://openalex.org/W2015676613","https://openalex.org/W2023384404","https://openalex.org/W2031728730","https://openalex.org/W2033118636","https://openalex.org/W2049514064","https://openalex.org/W2055737857","https://openalex.org/W2057553555","https://openalex.org/W2061440050","https://openalex.org/W2067459192","https://openalex.org/W2077367989","https://openalex.org/W2093472053","https://openalex.org/W2106575022","https://openalex.org/W2114472256","https://openalex.org/W2117973005","https://openalex.org/W2118699821","https://openalex.org/W2119202112","https://openalex.org/W2127067432","https://openalex.org/W2128047640","https://openalex.org/W2129729773","https://openalex.org/W2138151497","https://openalex.org/W2142283990","https://openalex.org/W2147439098","https://openalex.org/W2152511979","https://openalex.org/W2162791642","https://openalex.org/W2165399435","https://openalex.org/W2165489953","https://openalex.org/W2165690864","https://openalex.org/W2166943987","https://openalex.org/W2171505650","https://openalex.org/W2263152509","https://openalex.org/W2290806986","https://openalex.org/W2297307567","https://openalex.org/W2340142654","https://openalex.org/W2340680995","https://openalex.org/W2468433498","https://openalex.org/W2560504659","https://openalex.org/W2565514923","https://openalex.org/W2571255159","https://openalex.org/W2612952478","https://openalex.org/W2885835093","https://openalex.org/W2912352293","https://openalex.org/W2952138851","https://openalex.org/W3098925401","https://openalex.org/W3104453365","https://openalex.org/W4240329752","https://openalex.org/W4251507077","https://openalex.org/W6677613344","https://openalex.org/W6959016377"],"related_works":["https://openalex.org/W2080247273","https://openalex.org/W2143156927","https://openalex.org/W2009266145","https://openalex.org/W3150847492","https://openalex.org/W2490383829","https://openalex.org/W2764621242","https://openalex.org/W2097501889","https://openalex.org/W2019725099","https://openalex.org/W2924160392","https://openalex.org/W2566394519"],"abstract_inverted_index":{"This":[0],"article":[1,166],"presents":[2],"tools":[3],"for":[4,18,55,83,106,147],"the":[5,29,43,49,53,61,64,68,99,130,136,148],"design":[6,149],"of":[7,15,60,63,71,101,132,138,150],"control":[8,37,103,123],"laws":[9,141,153],"inducing":[10,96],"robust":[11,30,102],"controlled":[12,31],"forward":[13,32,107],"invariance":[14,33,95,108],"a":[16,36,89,168,174],"set":[17,27,50,54,131],"hybrid":[19,24],"dynamical":[20],"systems":[21],"modeled":[22],"as":[23],"inclusions.":[25],"A":[26],"has":[28],"property":[34,90],"via":[35],"law":[38],"if":[39],"every":[40],"solution":[41],"to":[42,86],"closed-loop":[44,127],"system":[45,172],"that":[46,119,125],"starts":[47],"from":[48],"stays":[51],"within":[52,129],"all":[56,121],"future":[57],"time,":[58],"regardless":[59],"value":[62],"disturbances.":[65],"Building":[66],"on":[67,76,116],"first":[69],"part":[70],"this":[72,79,165],"article,":[73,80],"which":[74],"focuses":[75],"analysis,":[77],"in":[78,167],"sufficient":[81],"conditions":[82,146],"generic":[84],"sets":[85],"enjoy":[87],"such":[88,139],"are":[91,142,158,162],"proposed.":[92],"To":[93],"construct":[94],"state-feedback":[97,140,152],"laws,":[98],"notion":[100],"Lyapunov":[104],"function":[105],"is":[109],"defined.":[110],"The":[111],"proposed":[112],"synthesis":[113],"results":[114,161],"rely":[115],"set-valued":[117],"maps":[118],"include":[120],"admissible":[122],"inputs":[124],"keep":[126],"solutions":[128],"interest.":[133],"Results":[134],"guaranteeing":[135],"existence":[137],"also":[143],"presented.":[144],"Moreover,":[145],"continuous":[151],"with":[154],"minimum":[155],"point-wise":[156],"norm":[157],"provided.":[159],"Major":[160],"illustrated":[163],"throughout":[164],"constrained":[169],"bouncing":[170],"ball":[171],"and":[173],"robotic":[175],"manipulator":[176],"application.":[177]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":7},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
