{"id":"https://openalex.org/W4315471930","doi":"https://doi.org/10.1109/cdc51059.2022.9993391","title":"Outer-approximating Controlled Reach-avoid Sets for Polynomial Systems","display_name":"Outer-approximating Controlled Reach-avoid Sets for Polynomial Systems","publication_year":2022,"publication_date":"2022-12-06","ids":{"openalex":"https://openalex.org/W4315471930","doi":"https://doi.org/10.1109/cdc51059.2022.9993391"},"language":"en","primary_location":{"id":"doi:10.1109/cdc51059.2022.9993391","is_oa":false,"landing_page_url":"http://dx.doi.org/10.1109/cdc51059.2022.9993391","pdf_url":null,"source":{"id":"https://openalex.org/S4363607710","display_name":"2022 IEEE 61st Conference on Decision and Control (CDC)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"conference"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2022 IEEE 61st Conference on Decision and Control (CDC)","raw_type":"proceedings-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/A5005541177","display_name":"Changyuan Zhao","orcid":"https://orcid.org/0000-0001-9187-9572"},"institutions":[{"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"]},{"id":"https://openalex.org/I4391767820","display_name":"State Key Laboratory of Computer Science","ror":"https://ror.org/01hsx4r68","country_code":null,"type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210128818","https://openalex.org/I4391767820"]},{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"funder","lineage":["https://openalex.org/I19820366"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Changyuan Zhao","raw_affiliation_strings":["Institute of Software, Chinese Academy of Sciences,State Key Lab. of Computer Science,Beijing,China","University of Chinese Academy of Sciences, Beijing, China","State Key Lab. of Computer Science, Institute of Software, Chinese Academy of Sciences, Beijing, China"],"affiliations":[{"raw_affiliation_string":"Institute of Software, Chinese Academy of Sciences,State Key Lab. of Computer Science,Beijing,China","institution_ids":["https://openalex.org/I4210128818","https://openalex.org/I19820366","https://openalex.org/I4391767820"]},{"raw_affiliation_string":"University of Chinese Academy of Sciences, Beijing, China","institution_ids":["https://openalex.org/I4210165038"]},{"raw_affiliation_string":"State Key Lab. of Computer Science, Institute of Software, Chinese Academy of Sciences, Beijing, China","institution_ids":["https://openalex.org/I4210128818","https://openalex.org/I19820366"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5019603699","display_name":"Chuchu Fan","orcid":"https://orcid.org/0000-0003-4671-233X"},"institutions":[{"id":"https://openalex.org/I46020346","display_name":"American Institute of Aeronautics and Astronautics","ror":"https://ror.org/00a1rzv11","country_code":"US","type":"other","lineage":["https://openalex.org/I46020346"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Chuchu Fan","raw_affiliation_strings":["MIT,Department of Aeronautics and Astronautics,U.S.,MA 02139"],"affiliations":[{"raw_affiliation_string":"MIT,Department of Aeronautics and Astronautics,U.S.,MA 02139","institution_ids":["https://openalex.org/I46020346"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100781916","display_name":"Xue Bai","orcid":"https://orcid.org/0000-0001-9717-846X"},"institutions":[{"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"]},{"id":"https://openalex.org/I4391767820","display_name":"State Key Laboratory of Computer Science","ror":"https://ror.org/01hsx4r68","country_code":null,"type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210128818","https://openalex.org/I4391767820"]},{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"funder","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"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Bai Xue","raw_affiliation_strings":["Institute of Software, Chinese Academy of Sciences,State Key Lab. of Computer Science,Beijing,China","University of Chinese Academy of Sciences, Beijing, China","State Key Lab. of Computer Science, Institute of Software, Chinese Academy of Sciences, Beijing, China"],"affiliations":[{"raw_affiliation_string":"Institute of Software, Chinese Academy of Sciences,State Key Lab. of Computer Science,Beijing,China","institution_ids":["https://openalex.org/I4210128818","https://openalex.org/I19820366","https://openalex.org/I4391767820"]},{"raw_affiliation_string":"University of Chinese Academy of Sciences, Beijing, China","institution_ids":["https://openalex.org/I4210165038"]},{"raw_affiliation_string":"State Key Lab. of Computer Science, Institute of Software, Chinese Academy of Sciences, Beijing, China","institution_ids":["https://openalex.org/I4210128818","https://openalex.org/I19820366"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5005541177"],"corresponding_institution_ids":["https://openalex.org/I19820366","https://openalex.org/I4210128818","https://openalex.org/I4210165038","https://openalex.org/I4391767820"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.23432343,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"3839","last_page":"3845"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10142","display_name":"Formal Methods in Verification","score":0.9980000257492065,"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"}},"topics":[{"id":"https://openalex.org/T10142","display_name":"Formal Methods in Verification","score":0.9980000257492065,"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/T10791","display_name":"Advanced Control Systems Optimization","score":0.9929999709129333,"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/T11435","display_name":"Polynomial and algebraic computation","score":0.9897000193595886,"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/set","display_name":"Set (abstract data type)","score":0.6643803715705872},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.606930136680603},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.597325325012207},{"id":"https://openalex.org/keywords/complement","display_name":"Complement (music)","score":0.5774069428443909},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5322591662406921},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.442219614982605},{"id":"https://openalex.org/keywords/explained-sum-of-squares","display_name":"Explained sum of squares","score":0.42164182662963867},{"id":"https://openalex.org/keywords/dynamic-programming","display_name":"Dynamic programming","score":0.41915401816368103},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.41789355874061584}],"concepts":[{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.6643803715705872},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.606930136680603},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.597325325012207},{"id":"https://openalex.org/C112313634","wikidata":"https://www.wikidata.org/wiki/Q7886648","display_name":"Complement (music)","level":5,"score":0.5774069428443909},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5322591662406921},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.442219614982605},{"id":"https://openalex.org/C49847556","wikidata":"https://www.wikidata.org/wiki/Q3964631","display_name":"Explained sum of squares","level":2,"score":0.42164182662963867},{"id":"https://openalex.org/C37404715","wikidata":"https://www.wikidata.org/wiki/Q380679","display_name":"Dynamic programming","level":2,"score":0.41915401816368103},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.41789355874061584},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"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/C127716648","wikidata":"https://www.wikidata.org/wiki/Q104053","display_name":"Phenotype","level":3,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"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/C188082640","wikidata":"https://www.wikidata.org/wiki/Q1780899","display_name":"Complementation","level":4,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/cdc51059.2022.9993391","is_oa":false,"landing_page_url":"http://dx.doi.org/10.1109/cdc51059.2022.9993391","pdf_url":null,"source":{"id":"https://openalex.org/S4363607710","display_name":"2022 IEEE 61st Conference on Decision and Control (CDC)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"conference"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2022 IEEE 61st Conference on Decision and Control (CDC)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W1489501223","https://openalex.org/W1963790880","https://openalex.org/W1964345118","https://openalex.org/W1975236902","https://openalex.org/W1982535910","https://openalex.org/W2025669802","https://openalex.org/W2034773561","https://openalex.org/W2045814149","https://openalex.org/W2057789475","https://openalex.org/W2093350522","https://openalex.org/W2106816694","https://openalex.org/W2149626391","https://openalex.org/W2288883172","https://openalex.org/W2375099263","https://openalex.org/W2528933731","https://openalex.org/W2536620281","https://openalex.org/W2884548887","https://openalex.org/W2964102294","https://openalex.org/W2964208569","https://openalex.org/W3119044986","https://openalex.org/W3150266660","https://openalex.org/W3171227993","https://openalex.org/W4210812484","https://openalex.org/W6796699647"],"related_works":["https://openalex.org/W2382566571","https://openalex.org/W2349321798","https://openalex.org/W2366686860","https://openalex.org/W3036520466","https://openalex.org/W3013085049","https://openalex.org/W2350859087","https://openalex.org/W2289860960","https://openalex.org/W2762413806","https://openalex.org/W3093984754","https://openalex.org/W2230915131"],"abstract_inverted_index":{"In":[0],"this":[1,94],"paper":[2],"we":[3,122,143],"propose":[4],"a":[5,31,56,65,75,96,112,141,148,174],"semi-definite":[6,175],"programming":[7],"method":[8,204],"for":[9,101,181],"computing":[10],"outer-approximations":[11,208],"(i.e.,":[12],"super-sets)":[13],"of":[14,18,33,52,98,114,151,162,168,202,209],"controlled":[15,27,87,104,137,210],"reach-avoid":[16,28,88,105,138,211],"sets":[17,212],"discrete-time":[19],"polynomial":[20,194],"systems":[21],"subject":[22],"to":[23,54,111,159],"control":[24,43],"inputs.":[25],"The":[26,165],"set":[29,32,59,68,97,106,113,150,167],"is":[30,72,90,107,154],"all":[34],"initial":[35],"states":[36],"that":[37,124],"there":[38],"exists":[39],"at":[40],"least":[41],"one":[42],"policy":[44],"which":[45,153,184],"steers":[46],"the":[47,70,85,103,160,178,200],"system":[48],"starting":[49],"from":[50],"each":[51,125,133],"them":[53,145],"enter":[55],"specified":[57],"target":[58,71],"in":[60,116,135,193],"finite":[61],"time":[62],"while":[63],"avoiding":[64],"given":[66],"unsafe":[67],"till":[69],"hit.":[73],"First,":[74],"Bellman":[76],"type":[77],"equation,":[78,95],"whose":[79],"unique":[80],"bounded":[81],"solution":[82],"can":[83,131,170,185],"characterize":[84],"exact":[86],"set,":[89],"derived.":[91],"By":[92],"relaxing":[93],"quantified":[99],"inequalities":[100],"outer-approximating":[102,136],"obtained.":[108],"Via":[109],"comparing":[110],"constraints":[115,169],"state-of-the-art":[117],"methods":[118,192],"on":[119,205],"occupation":[120],"measures,":[121],"find":[123],"has":[126],"its":[127],"own":[128],"strengths":[129],"and":[130,146,156],"complement":[132],"other":[134],"sets.":[139],"As":[140],"consequence,":[142],"integrate":[144],"obtain":[147],"new":[149],"constraints,":[152],"weaker":[155],"thus":[157],"contributes":[158],"gain":[161],"tighter":[163,207],"outer-approximations.":[164],"resulting":[166],"be":[171,186],"encoded":[172],"into":[173],"program":[176],"via":[177,189],"sum-of-squares":[179],"decomposition":[180],"multivariate":[182],"variables,":[183],"solved":[187],"efficiently":[188],"interior":[190],"point":[191],"time.":[195],"Finally,":[196],"several":[197],"examples":[198],"demonstrate":[199],"benefits":[201],"our":[203],"gaining":[206],"over":[213],"existing":[214],"methods.":[215]},"counts_by_year":[],"updated_date":"2025-12-21T01:58:51.020947","created_date":"2025-10-10T00:00:00"}