{"id":"https://openalex.org/W2964102294","doi":"https://doi.org/10.1109/tac.2019.2923049","title":"Inner-Approximating Reachable Sets for Polynomial Systems With Time-Varying Uncertainties","display_name":"Inner-Approximating Reachable Sets for Polynomial Systems With Time-Varying Uncertainties","publication_year":2019,"publication_date":"2019-06-14","ids":{"openalex":"https://openalex.org/W2964102294","doi":"https://doi.org/10.1109/tac.2019.2923049","mag":"2964102294"},"language":"en","primary_location":{"id":"doi:10.1109/tac.2019.2923049","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2019.2923049","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/A5100781916","display_name":"Xue Bai","orcid":"https://orcid.org/0000-0001-9717-846X"},"institutions":[{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"government","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I4210128818","display_name":"Institute of Software","ror":"https://ror.org/033dfsn42","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210128818"]},{"id":"https://openalex.org/I4210165038","display_name":"University of Chinese Academy of Sciences","ror":"https://ror.org/05qbk4x57","country_code":"CN","type":"education","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210165038"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Bai Xue","raw_affiliation_strings":["State Key Laboratory of Computer Science, Institute of Software Chinese Academy of Sciences, Beijing, China","University of Chinese Academy of Sciences, Beijing, China"],"affiliations":[{"raw_affiliation_string":"State Key Laboratory of Computer Science, Institute of Software Chinese Academy of Sciences, Beijing, China","institution_ids":["https://openalex.org/I4210128818","https://openalex.org/I19820366"]},{"raw_affiliation_string":"University of Chinese Academy of Sciences, Beijing, China","institution_ids":["https://openalex.org/I4210165038"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5089746112","display_name":"Martin Fr\u00e4nzle","orcid":"https://orcid.org/0000-0002-9138-8340"},"institutions":[{"id":"https://openalex.org/I129877168","display_name":"Carl von Ossietzky Universit\u00e4t Oldenburg","ror":"https://ror.org/033n9gh91","country_code":"DE","type":"education","lineage":["https://openalex.org/I129877168"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Martin Franzle","raw_affiliation_strings":["Carl von Ossietzky Universit\u00e4t Oldenburg, Oldenburg, Germany"],"affiliations":[{"raw_affiliation_string":"Carl von Ossietzky Universit\u00e4t Oldenburg, Oldenburg, Germany","institution_ids":["https://openalex.org/I129877168"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5026435847","display_name":"Naijun Zhan","orcid":"https://orcid.org/0000-0003-3298-3817"},"institutions":[{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"government","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I4210128818","display_name":"Institute of Software","ror":"https://ror.org/033dfsn42","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210128818"]},{"id":"https://openalex.org/I4210165038","display_name":"University of Chinese Academy of Sciences","ror":"https://ror.org/05qbk4x57","country_code":"CN","type":"education","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210165038"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Naijun Zhan","raw_affiliation_strings":["State Key Laboratory of Computer Science, Institute of Software Chinese Academy of Sciences, Beijing, China","University of Chinese Academy of Sciences, Beijing, China"],"affiliations":[{"raw_affiliation_string":"State Key Laboratory of Computer Science, Institute of Software Chinese Academy of Sciences, Beijing, China","institution_ids":["https://openalex.org/I4210128818","https://openalex.org/I19820366"]},{"raw_affiliation_string":"University of Chinese Academy of Sciences, Beijing, China","institution_ids":["https://openalex.org/I4210165038"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5100781916"],"corresponding_institution_ids":["https://openalex.org/I19820366","https://openalex.org/I4210128818","https://openalex.org/I4210165038"],"apc_list":null,"apc_paid":null,"fwci":9.0854,"has_fulltext":false,"cited_by_count":50,"citation_normalized_percentile":{"value":0.98666053,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":99},"biblio":{"volume":"65","issue":"4","first_page":"1468","last_page":"1483"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9983999729156494,"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"}},"topics":[{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9983999729156494,"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":0.9890999794006348,"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/T10142","display_name":"Formal Methods in Verification","score":0.9624999761581421,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7055392265319824},{"id":"https://openalex.org/keywords/semidefinite-programming","display_name":"Semidefinite programming","score":0.700600802898407},{"id":"https://openalex.org/keywords/lipschitz-continuity","display_name":"Lipschitz continuity","score":0.6492744088172913},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5921028852462769},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.5212745666503906},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.499035120010376},{"id":"https://openalex.org/keywords/state","display_name":"State (computer science)","score":0.4803984463214874},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4287341237068176},{"id":"https://openalex.org/keywords/viscosity-solution","display_name":"Viscosity solution","score":0.4271276593208313},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3772052526473999},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2309480607509613},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.186566561460495},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.14149001240730286}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7055392265319824},{"id":"https://openalex.org/C101901036","wikidata":"https://www.wikidata.org/wiki/Q2269096","display_name":"Semidefinite programming","level":2,"score":0.700600802898407},{"id":"https://openalex.org/C22324862","wikidata":"https://www.wikidata.org/wiki/Q652707","display_name":"Lipschitz continuity","level":2,"score":0.6492744088172913},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5921028852462769},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.5212745666503906},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.499035120010376},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.4803984463214874},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4287341237068176},{"id":"https://openalex.org/C88731125","wikidata":"https://www.wikidata.org/wiki/Q7935676","display_name":"Viscosity solution","level":2,"score":0.4271276593208313},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3772052526473999},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2309480607509613},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.186566561460495},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.14149001240730286},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tac.2019.2923049","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2019.2923049","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":[],"awards":[{"id":"https://openalex.org/G130015549","display_name":null,"funder_award_id":"61872341","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3291759789","display_name":null,"funder_award_id":"61732001","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5543570208","display_name":null,"funder_award_id":"61625206","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7074371790","display_name":null,"funder_award_id":"DFG GRK 1765","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G8384231897","display_name":null,"funder_award_id":"FR 2715/4-1","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"}],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":46,"referenced_works":["https://openalex.org/W1487586009","https://openalex.org/W1726255445","https://openalex.org/W1918406761","https://openalex.org/W1964345118","https://openalex.org/W1969710845","https://openalex.org/W1975236902","https://openalex.org/W1992402930","https://openalex.org/W2004902288","https://openalex.org/W2012592827","https://openalex.org/W2025669802","https://openalex.org/W2029518379","https://openalex.org/W2045814149","https://openalex.org/W2046491103","https://openalex.org/W2070323046","https://openalex.org/W2071555678","https://openalex.org/W2084859862","https://openalex.org/W2085426894","https://openalex.org/W2096326343","https://openalex.org/W2106816694","https://openalex.org/W2111216640","https://openalex.org/W2116364955","https://openalex.org/W2131332110","https://openalex.org/W2147936671","https://openalex.org/W2151136609","https://openalex.org/W2158451642","https://openalex.org/W2167019375","https://openalex.org/W2167710281","https://openalex.org/W2265178974","https://openalex.org/W2349709726","https://openalex.org/W2483544051","https://openalex.org/W2536620281","https://openalex.org/W2555697178","https://openalex.org/W2606692557","https://openalex.org/W2606891832","https://openalex.org/W2741978752","https://openalex.org/W2796287609","https://openalex.org/W2938029150","https://openalex.org/W2946136565","https://openalex.org/W2962904907","https://openalex.org/W3005835038","https://openalex.org/W3125479578","https://openalex.org/W4245376853","https://openalex.org/W4247052790","https://openalex.org/W4249492311","https://openalex.org/W4255442211","https://openalex.org/W6671531010"],"related_works":["https://openalex.org/W3185235544","https://openalex.org/W2911623553","https://openalex.org/W4297791327","https://openalex.org/W2897842840","https://openalex.org/W2397777611","https://openalex.org/W1502031429","https://openalex.org/W2417585376","https://openalex.org/W2043536252","https://openalex.org/W3036139884","https://openalex.org/W4306167235"],"abstract_inverted_index":{"In":[0],"this":[1,127,184],"paper,":[2],"we":[3,113],"propose":[4],"a":[5,12,33,45,52,58,85,119,130,140,159],"convex":[6],"programming":[7],"based":[8],"method":[9,135],"to":[10,25,73,84,118,126,150,165],"address":[11],"long-standing":[13],"problem":[14,117,120],"of":[15,20,35,51,60,65,68,78,96,108,121,162,168,183,192],"inner-approximating":[16],"backward":[17,29,98,170],"reachable":[18,30,99,171],"sets":[19,107],"state-constrained":[21],"polynomial":[22,123,131,148],"systems":[23],"subject":[24],"time-varying":[26],"uncertainties.":[27,69],"The":[28],"set":[31,34,59,77,100,172],"is":[32,71,136,179],"states,":[36],"from":[37],"which":[38],"all":[39],"trajectories":[40],"starting":[41],"will":[42],"surely":[43],"enter":[44],"target":[46],"region":[47],"at":[48],"the":[49,66,74,79,97,115,151,166,169,180,190],"end":[50],"given":[53],"time":[54],"horizon":[55],"without":[56],"violating":[57],"state":[61],"constraints":[62],"in":[63,133,173],"spite":[64],"actions":[67],"It":[70],"equal":[72],"zero":[75,105],"sublevel":[76,106],"unique":[80],"Lipschitz":[81],"viscosity":[82,110,124],"solution":[83,132],"Hamilton-Jacobi":[86],"partial":[87],"differential":[88],"equation":[89],"(HJE).":[90],"We":[91,144],"show":[92],"that":[93,147],"inner":[94,163],"approximations":[95,164],"can":[101,157],"be":[102],"formed":[103],"by":[104,138],"its":[109],"supersolutions.":[111],"Consequently,":[112],"reduce":[114],"inner-approximation":[116],"synthesizing":[122],"supersolutions":[125],"HJE.":[128],"Such":[129],"our":[134,193],"synthesized":[137],"solving":[139],"single":[141],"semidefinite":[142,153],"program.":[143],"also":[145],"prove":[146],"solutions":[149],"formulated":[152],"program":[154],"exist":[155],"and":[156],"produce":[158],"convergent":[160],"sequence":[161],"interior":[167],"measure":[174],"under":[175],"appropriate":[176],"assumptions.":[177],"This":[178],"main":[181],"contribution":[182],"paper.":[185],"Several":[186],"illustrative":[187],"examples":[188],"demonstrate":[189],"merits":[191],"approach.":[194]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":8},{"year":2023,"cited_by_count":6},{"year":2022,"cited_by_count":6},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":13},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":3}],"updated_date":"2026-04-09T08:11:56.329763","created_date":"2025-10-10T00:00:00"}
