{"id":"https://openalex.org/W4293243623","doi":"https://doi.org/10.1109/tcad.2022.3197971","title":"Efficient Backward Reachability Using the Minkowski Difference of Constrained Zonotopes","display_name":"Efficient Backward Reachability Using the Minkowski Difference of Constrained Zonotopes","publication_year":2022,"publication_date":"2022-08-10","ids":{"openalex":"https://openalex.org/W4293243623","doi":"https://doi.org/10.1109/tcad.2022.3197971"},"language":"en","primary_location":{"id":"doi:10.1109/tcad.2022.3197971","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcad.2022.3197971","pdf_url":null,"source":{"id":"https://openalex.org/S100835903","display_name":"IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems","issn_l":"0278-0070","issn":["0278-0070","1937-4151"],"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 Computer-Aided Design of Integrated Circuits and Systems","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/A5052314881","display_name":"Liren Yang","orcid":"https://orcid.org/0000-0002-7677-8543"},"institutions":[{"id":"https://openalex.org/I47720641","display_name":"Huazhong University of Science and Technology","ror":"https://ror.org/00p991c53","country_code":"CN","type":"education","lineage":["https://openalex.org/I47720641"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Liren Yang","raw_affiliation_strings":["School of Artificial Intelligence and Automation, Huazhong University of Science and Technology, Wuhan, China"],"raw_orcid":"https://orcid.org/0000-0002-7677-8543","affiliations":[{"raw_affiliation_string":"School of Artificial Intelligence and Automation, Huazhong University of Science and Technology, Wuhan, China","institution_ids":["https://openalex.org/I47720641"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100438486","display_name":"Hang Zhang","orcid":"https://orcid.org/0009-0007-0880-7756"},"institutions":[{"id":"https://openalex.org/I135310074","display_name":"University of Wisconsin\u2013Madison","ror":"https://ror.org/01y2jtd41","country_code":"US","type":"education","lineage":["https://openalex.org/I135310074"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Hang Zhang","raw_affiliation_strings":["Department of Mechanical Engineering, University of Wisconsin&#x2013;Madison, Madison, WI, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mechanical Engineering, University of Wisconsin&#x2013;Madison, Madison, WI, USA","institution_ids":["https://openalex.org/I135310074"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5002069299","display_name":"Jean-Baptiste Jeannin","orcid":"https://orcid.org/0000-0001-6378-1447"},"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":"Jean-Baptiste Jeannin","raw_affiliation_strings":["Department of Aerospace Engineering, University of Michigan, Ann Arbor, MI, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Aerospace Engineering, University of Michigan, Ann Arbor, MI, USA","institution_ids":["https://openalex.org/I27837315"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5054418471","display_name":"Necmiye \u00d6zay","orcid":"https://orcid.org/0000-0002-5552-4392"},"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":"Necmiye Ozay","raw_affiliation_strings":["Department of Electrical Engineering and Computer Science, University of Michigan, Ann Arbor, MI, USA"],"raw_orcid":"https://orcid.org/0000-0002-5552-4392","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":2,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.9127,"has_fulltext":false,"cited_by_count":24,"citation_normalized_percentile":{"value":0.90904389,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":98,"max":99},"biblio":{"volume":"41","issue":"11","first_page":"3969","last_page":"3980"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10791","display_name":"Advanced Control Systems Optimization","score":0.998199999332428,"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":0.998199999332428,"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":0.9973999857902527,"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"}},{"id":"https://openalex.org/T10046","display_name":"Stability and Control of Uncertain Systems","score":0.9943000078201294,"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/minkowski-addition","display_name":"Minkowski addition","score":0.8086355924606323},{"id":"https://openalex.org/keywords/reachability","display_name":"Reachability","score":0.7784315943717957},{"id":"https://openalex.org/keywords/correctness","display_name":"Correctness","score":0.6344185471534729},{"id":"https://openalex.org/keywords/minkowski-space","display_name":"Minkowski space","score":0.6213629841804504},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6194278597831726},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.5801838636398315},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5489736199378967},{"id":"https://openalex.org/keywords/linearization","display_name":"Linearization","score":0.4812700152397156},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.47508445382118225},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.442778617143631},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.40577131509780884},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.3852303624153137},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3382318615913391},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.33348286151885986}],"concepts":[{"id":"https://openalex.org/C10233890","wikidata":"https://www.wikidata.org/wiki/Q1322294","display_name":"Minkowski addition","level":3,"score":0.8086355924606323},{"id":"https://openalex.org/C136643341","wikidata":"https://www.wikidata.org/wiki/Q1361526","display_name":"Reachability","level":2,"score":0.7784315943717957},{"id":"https://openalex.org/C55439883","wikidata":"https://www.wikidata.org/wiki/Q360812","display_name":"Correctness","level":2,"score":0.6344185471534729},{"id":"https://openalex.org/C79464548","wikidata":"https://www.wikidata.org/wiki/Q464794","display_name":"Minkowski space","level":2,"score":0.6213629841804504},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6194278597831726},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.5801838636398315},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5489736199378967},{"id":"https://openalex.org/C11210021","wikidata":"https://www.wikidata.org/wiki/Q1520713","display_name":"Linearization","level":3,"score":0.4812700152397156},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.47508445382118225},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.442778617143631},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.40577131509780884},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.3852303624153137},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3382318615913391},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.33348286151885986},{"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/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"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/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tcad.2022.3197971","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcad.2022.3197971","pdf_url":null,"source":{"id":"https://openalex.org/S100835903","display_name":"IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems","issn_l":"0278-0070","issn":["0278-0070","1937-4151"],"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 Computer-Aided Design of Integrated Circuits and Systems","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2270730168","display_name":null,"funder_award_id":"CCF-1918123","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G2306875754","display_name":null,"funder_award_id":"N000141812501","funder_id":"https://openalex.org/F4320337345","funder_display_name":"Office of Naval Research"},{"id":"https://openalex.org/G93384148","display_name":null,"funder_award_id":"ECCS-1553873","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"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"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":26,"referenced_works":["https://openalex.org/W1524886571","https://openalex.org/W1574960890","https://openalex.org/W1973264045","https://openalex.org/W2000147742","https://openalex.org/W2006557476","https://openalex.org/W2015863039","https://openalex.org/W2057133391","https://openalex.org/W2095233962","https://openalex.org/W2158451642","https://openalex.org/W2165489953","https://openalex.org/W2300621294","https://openalex.org/W2936781873","https://openalex.org/W2950769107","https://openalex.org/W2964040381","https://openalex.org/W3012067785","https://openalex.org/W3023279500","https://openalex.org/W3086849158","https://openalex.org/W3107034996","https://openalex.org/W3119746089","https://openalex.org/W3176457131","https://openalex.org/W3186629482","https://openalex.org/W3209748707","https://openalex.org/W3210364203","https://openalex.org/W4293050169","https://openalex.org/W6671531010","https://openalex.org/W6696090594"],"related_works":["https://openalex.org/W2286777929","https://openalex.org/W4293050169","https://openalex.org/W2950428426","https://openalex.org/W2053229390","https://openalex.org/W960999769","https://openalex.org/W4211088175","https://openalex.org/W4309277470","https://openalex.org/W2936973291","https://openalex.org/W4288372977","https://openalex.org/W4313413682"],"abstract_inverted_index":{"Backward":[0],"reachability":[1],"analysis":[2],"is":[3,17,58,109,143],"essential":[4],"to":[5,62,93,100,111,163],"synthesizing":[6],"controllers":[7],"that":[8,23,141],"ensure":[9],"the":[10,25,40,64,83,86,133,150,165,176],"correctness":[11],"of":[12,55,78,82,135,178],"closed-loop":[13],"systems.":[14,35],"This":[15,89],"article":[16],"concerned":[18],"with":[19],"developing":[20],"scalable":[21],"algorithms":[22,162],"underapproximate":[24,63],"backward":[26,158],"reachable":[27,159],"sets,":[28],"for":[29,46,116],"discrete-time":[30],"uncertain":[31],"linear":[32],"and":[33,42,49,72,85,139,168],"nonlinear":[34],"Our":[36,121],"algorithm":[37,57,122],"sequentially":[38],"linearizes":[39],"dynamics":[41],"uses":[43],"constrained":[44,69,98],"zonotopes":[45],"set":[47,160],"representation":[48,115],"computation.":[50],"The":[51],"main":[52],"technical":[53],"ingredient":[54],"our":[56,179],"an":[59],"efficient":[60],"way":[61],"Minkowski":[65,90,152],"difference":[66,91,153],"between":[67],"a":[68,73,97,113,124],"zonotopic":[70,74],"minuend":[71],"subtrahend,":[75],"which":[76],"consists":[77],"all":[79],"possible":[80],"values":[81],"uncertainties":[84],"linearization":[87,166],"error.":[88],"needs":[92],"be":[94],"represented":[95],"as":[96,105],"zonotope":[99],"enable":[101],"subsequent":[102],"computation,":[103],"but,":[104],"we":[106,155],"show,":[107],"it":[108,117,142],"impossible":[110],"find":[112],"polynomial-size":[114,125],"in":[118,127],"polynomial":[119,128],"time.":[120,129],"finds":[123],"underapproximation":[126,137],"We":[130],"further":[131],"analyze":[132],"conservatism":[134],"this":[136],"technique":[138],"show":[140],"exact":[144],"under":[145],"some":[146],"conditions.":[147],"Based":[148],"on":[149],"developed":[151],"technique,":[154],"detail":[156],"two":[157],"computation":[161],"control":[164],"error":[167],"incorporate":[169],"nonconvex":[170],"state":[171],"constraints.":[172],"Several":[173],"examples":[174],"illustrate":[175],"effectiveness":[177],"algorithms.":[180]},"counts_by_year":[{"year":2025,"cited_by_count":9},{"year":2024,"cited_by_count":10},{"year":2023,"cited_by_count":5}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
