{"id":"https://openalex.org/W3127322525","doi":"https://doi.org/10.1109/tac.2021.3056611","title":"Backward Reachability for Polynomial Systems on a Finite Horizon","display_name":"Backward Reachability for Polynomial Systems on a Finite Horizon","publication_year":2021,"publication_date":"2021-02-03","ids":{"openalex":"https://openalex.org/W3127322525","doi":"https://doi.org/10.1109/tac.2021.3056611","mag":"3127322525"},"language":"en","primary_location":{"id":"doi:10.1109/tac.2021.3056611","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2021.3056611","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/A5042593365","display_name":"He Yin","orcid":"https://orcid.org/0000-0003-3338-148X"},"institutions":[{"id":"https://openalex.org/I95457486","display_name":"University of California, Berkeley","ror":"https://ror.org/01an7q238","country_code":"US","type":"education","lineage":["https://openalex.org/I95457486"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"He Yin","raw_affiliation_strings":["Mechanical Engineering, University of California, Berkeley, Burlingame, CA, USA"],"raw_orcid":"https://orcid.org/0000-0003-3338-148X","affiliations":[{"raw_affiliation_string":"Mechanical Engineering, University of California, Berkeley, Burlingame, CA, USA","institution_ids":["https://openalex.org/I95457486"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5025743742","display_name":"Murat Arcak","orcid":"https://orcid.org/0000-0001-9060-4032"},"institutions":[{"id":"https://openalex.org/I95457486","display_name":"University of California, Berkeley","ror":"https://ror.org/01an7q238","country_code":"US","type":"education","lineage":["https://openalex.org/I95457486"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Murat Arcak","raw_affiliation_strings":["Mechanical Engineering, University of California, Berkeley, Burlingame, CA, USA"],"raw_orcid":"https://orcid.org/0000-0001-9060-4032","affiliations":[{"raw_affiliation_string":"Mechanical Engineering, University of California, Berkeley, Burlingame, CA, USA","institution_ids":["https://openalex.org/I95457486"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5076844884","display_name":"Andrew Packard","orcid":null},"institutions":[{"id":"https://openalex.org/I95457486","display_name":"University of California, Berkeley","ror":"https://ror.org/01an7q238","country_code":"US","type":"education","lineage":["https://openalex.org/I95457486"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Andrew Packard","raw_affiliation_strings":["Mechanical Engineering, University of California, Berkeley, Burlingame, CA, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mechanical Engineering, University of California, Berkeley, Burlingame, CA, USA","institution_ids":["https://openalex.org/I95457486"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5009028512","display_name":"Peter Seiler","orcid":"https://orcid.org/0000-0003-3423-1109"},"institutions":[{"id":"https://openalex.org/I27837315","display_name":"University of Michigan","ror":"https://ror.org/00jmfr291","country_code":"US","type":"education","lineage":["https://openalex.org/I27837315"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Peter Seiler","raw_affiliation_strings":["Department of Electrical Engineering and Computer Science, University of Michigan, Ann Arbor, MI, USA"],"raw_orcid":"https://orcid.org/0000-0003-3423-1109","affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering and Computer Science, University of Michigan, Ann Arbor, MI, USA","institution_ids":["https://openalex.org/I27837315"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.1654,"has_fulltext":false,"cited_by_count":20,"citation_normalized_percentile":{"value":0.87096659,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"66","issue":"12","first_page":"6025","last_page":"6032"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10046","display_name":"Stability and Control of Uncertain Systems","score":0.9990000128746033,"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/T10046","display_name":"Stability and Control of Uncertain Systems","score":0.9990000128746033,"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/T11081","display_name":"Advanced Control Systems Design","score":0.9968000054359436,"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/T10791","display_name":"Advanced Control Systems Optimization","score":0.9965999722480774,"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/reachability","display_name":"Reachability","score":0.7215784192085266},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6041167974472046},{"id":"https://openalex.org/keywords/parametric-statistics","display_name":"Parametric statistics","score":0.5525673031806946},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5520598292350769},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5418738722801208},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4463983178138733},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.38623046875},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.37090229988098145},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3504880666732788},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3283340334892273},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.24577966332435608},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.13854458928108215}],"concepts":[{"id":"https://openalex.org/C136643341","wikidata":"https://www.wikidata.org/wiki/Q1361526","display_name":"Reachability","level":2,"score":0.7215784192085266},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6041167974472046},{"id":"https://openalex.org/C117251300","wikidata":"https://www.wikidata.org/wiki/Q1849855","display_name":"Parametric statistics","level":2,"score":0.5525673031806946},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5520598292350769},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5418738722801208},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4463983178138733},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.38623046875},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.37090229988098145},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3504880666732788},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3283340334892273},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.24577966332435608},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.13854458928108215},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tac.2021.3056611","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2021.3056611","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/G144984909","display_name":null,"funder_award_id":"FA9550- 18-1-0253","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G199887932","display_name":null,"funder_award_id":"ECCS-1906164","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6320102633","display_name":null,"funder_award_id":"N00014-18-1-2209","funder_id":"https://openalex.org/F4320337345","funder_display_name":"Office of Naval Research"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320337345","display_name":"Office of Naval Research","ror":"https://ror.org/00rk2pe57"},{"id":"https://openalex.org/F4320338279","display_name":"Air Force Office of Scientific Research","ror":"https://ror.org/011e9bt93"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":30,"referenced_works":["https://openalex.org/W1574960890","https://openalex.org/W1675131299","https://openalex.org/W1879112630","https://openalex.org/W1960771713","https://openalex.org/W1999497797","https://openalex.org/W2037539475","https://openalex.org/W2045814149","https://openalex.org/W2057789475","https://openalex.org/W2060602079","https://openalex.org/W2071593980","https://openalex.org/W2089024379","https://openalex.org/W2095477585","https://openalex.org/W2096156227","https://openalex.org/W2106985815","https://openalex.org/W2116364955","https://openalex.org/W2120865142","https://openalex.org/W2133404041","https://openalex.org/W2141281488","https://openalex.org/W2141662368","https://openalex.org/W2148247550","https://openalex.org/W2491336180","https://openalex.org/W2939501205","https://openalex.org/W2962822210","https://openalex.org/W2970690852","https://openalex.org/W2972887175","https://openalex.org/W3037216378","https://openalex.org/W4250589301","https://openalex.org/W6637424042","https://openalex.org/W6668196169","https://openalex.org/W6679392325"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2127267268","https://openalex.org/W2136512912","https://openalex.org/W2067910792","https://openalex.org/W2156446763","https://openalex.org/W3082487952","https://openalex.org/W2998030147","https://openalex.org/W3040348990","https://openalex.org/W4288357225","https://openalex.org/W2379877967"],"abstract_inverted_index":{"A":[0],"method":[1,87],"is":[2,60,88],"presented":[3],"to":[4,63],"obtain":[5],"an":[6,20,48],"inner-approximation":[7],"of":[8,13,85],"the":[9,52,86],"backward":[10],"reachable":[11],"set":[12],"a":[14],"given":[15],"target":[16],"tube,":[17],"along":[18],"with":[19,67,97],"admissible":[21],"controller":[22],"that":[23],"maintains":[24],"trajectories":[25],"inside":[26],"this":[27],"tube.":[28],"The":[29,83],"proposed":[30],"optimization":[31,37],"algorithms":[32],"are":[33,40],"formulated":[34],"as":[35],"nonlinear":[36,65,92],"problems,":[38],"which":[39],"decoupled":[41],"into":[42],"tractable":[43],"subproblems":[44],"and":[45,55,74,94],"solved":[46],"by":[47],"iterative":[49],"algorithm":[50],"using":[51],"polynomial":[53],"S-procedure":[54],"sum-of-squares":[56],"techniques.":[57],"This":[58],"framework":[59],"also":[61],"extended":[62],"uncertain":[64],"systems":[66,96],"<inline-formula":[68,75],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[69,76],"xmlns:xlink=\"http://www.w3.org/1999/xlink\"><tex-math":[70,77],"notation=\"LaTeX\">$\\mathcal":[71,78],"{L}_2$</tex-math></inline-formula>":[72],"disturbances":[73],"{L}_{\\infty":[79],"}$</tex-math></inline-formula>":[80],"parametric":[81],"uncertainties.":[82],"effectiveness":[84],"demonstrated":[89],"on":[90],"several":[91],"robotics":[93],"aircraft":[95],"control":[98],"saturation.":[99]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":6},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1}],"updated_date":"2026-03-27T05:58:40.876381","created_date":"2025-10-10T00:00:00"}