{"id":"https://openalex.org/W4210333886","doi":"https://doi.org/10.1109/cdc45484.2021.9683555","title":"Reach-Avoid Analysis for Delay Differential Equations","display_name":"Reach-Avoid Analysis for Delay Differential Equations","publication_year":2021,"publication_date":"2021-12-14","ids":{"openalex":"https://openalex.org/W4210333886","doi":"https://doi.org/10.1109/cdc45484.2021.9683555"},"language":"en","primary_location":{"id":"doi:10.1109/cdc45484.2021.9683555","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc45484.2021.9683555","pdf_url":null,"source":{"id":"https://openalex.org/S4363607724","display_name":"2021 60th IEEE 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":"2021 60th IEEE 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/A5100781916","display_name":"Xue Bai","orcid":"https://orcid.org/0000-0001-9717-846X"},"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"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Bai Xue","raw_affiliation_strings":["State Key Lab. of Computer Science, Institute of Software, CAS","Univ. of Chinese Academy of Sciences, Beijing, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"State Key Lab. of Computer Science, Institute of Software, CAS","institution_ids":["https://openalex.org/I4210128818"]},{"raw_affiliation_string":"Univ. of Chinese Academy of Sciences, Beijing, China","institution_ids":["https://openalex.org/I4210165038"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5113000496","display_name":"Yunjun Bai","orcid":null},"institutions":[{"id":"https://openalex.org/I194716290","display_name":"China Academy of Space Technology","ror":"https://ror.org/025397a59","country_code":"CN","type":"government","lineage":["https://openalex.org/I194716290","https://openalex.org/I2802615301"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yunjun Bai","raw_affiliation_strings":["China Academy of Space Technology, Beijing Institute of Control Engineering, Beijing, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"China Academy of Space Technology, Beijing Institute of Control Engineering, Beijing, China","institution_ids":["https://openalex.org/I194716290"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5026435847","display_name":"Naijun Zhan","orcid":"https://orcid.org/0000-0003-3298-3817"},"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"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Naijun Zhan","raw_affiliation_strings":["State Key Lab. of Computer Science, Institute of Software, CAS","Univ. of Chinese Academy of Sciences, Beijing, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"State Key Lab. of Computer Science, Institute of Software, CAS","institution_ids":["https://openalex.org/I4210128818"]},{"raw_affiliation_string":"Univ. of Chinese Academy of Sciences, Beijing, China","institution_ids":["https://openalex.org/I4210165038"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5084214906","display_name":"Wenyou Liu","orcid":null},"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"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Wenyou Liu","raw_affiliation_strings":["State Key Lab. of Computer Science, Institute of Software, CAS","Univ. of Chinese Academy of Sciences, Beijing, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"State Key Lab. of Computer Science, Institute of Software, CAS","institution_ids":["https://openalex.org/I4210128818"]},{"raw_affiliation_string":"Univ. of Chinese Academy of Sciences, Beijing, China","institution_ids":["https://openalex.org/I4210165038"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100419499","display_name":"Jiao Li","orcid":"https://orcid.org/0000-0002-8027-5877"},"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"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Li Jiao","raw_affiliation_strings":["State Key Lab. of Computer Science, Institute of Software, CAS","Univ. of Chinese Academy of Sciences, Beijing, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"State Key Lab. of Computer Science, Institute of Software, CAS","institution_ids":["https://openalex.org/I4210128818"]},{"raw_affiliation_string":"Univ. of Chinese Academy of Sciences, Beijing, China","institution_ids":["https://openalex.org/I4210165038"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":5,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.25876851,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"1301","last_page":"1307"},"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":0.9958999752998352,"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":0.9958999752998352,"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/T11416","display_name":"Numerical methods for differential equations","score":0.9921000003814697,"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/T14083","display_name":"Extremum Seeking Control Systems","score":0.989799976348877,"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/set","display_name":"Set (abstract data type)","score":0.7422246932983398},{"id":"https://openalex.org/keywords/delay-differential-equation","display_name":"Delay differential equation","score":0.6871832609176636},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5973916053771973},{"id":"https://openalex.org/keywords/differential","display_name":"Differential (mechanical device)","score":0.5585572123527527},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5038923621177673},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.5003652572631836},{"id":"https://openalex.org/keywords/reduction","display_name":"Reduction (mathematics)","score":0.486374169588089},{"id":"https://openalex.org/keywords/connection","display_name":"Connection (principal bundle)","score":0.4547107517719269},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.44538676738739014},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.39793384075164795},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.36626672744750977},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3514190912246704},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3290495276451111},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.10242190957069397},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.06834164261817932}],"concepts":[{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.7422246932983398},{"id":"https://openalex.org/C147504518","wikidata":"https://www.wikidata.org/wiki/Q2146125","display_name":"Delay differential equation","level":3,"score":0.6871832609176636},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5973916053771973},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.5585572123527527},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5038923621177673},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.5003652572631836},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.486374169588089},{"id":"https://openalex.org/C13355873","wikidata":"https://www.wikidata.org/wiki/Q2920850","display_name":"Connection (principal bundle)","level":2,"score":0.4547107517719269},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.44538676738739014},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.39793384075164795},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.36626672744750977},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3514190912246704},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3290495276451111},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.10242190957069397},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.06834164261817932},{"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/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","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},{"id":"https://openalex.org/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","level":1,"score":0.0},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/cdc45484.2021.9683555","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc45484.2021.9683555","pdf_url":null,"source":{"id":"https://openalex.org/S4363607724","display_name":"2021 60th IEEE 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":"2021 60th IEEE 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":22,"referenced_works":["https://openalex.org/W1499853177","https://openalex.org/W1506119886","https://openalex.org/W1577525693","https://openalex.org/W1963790880","https://openalex.org/W1982535910","https://openalex.org/W2029608738","https://openalex.org/W2134590937","https://openalex.org/W2136224174","https://openalex.org/W2149971042","https://openalex.org/W2474433838","https://openalex.org/W2483544051","https://openalex.org/W2536620281","https://openalex.org/W2741978752","https://openalex.org/W2884955533","https://openalex.org/W2932827394","https://openalex.org/W2960231273","https://openalex.org/W3009072669","https://openalex.org/W3119044986","https://openalex.org/W3210839039","https://openalex.org/W4301046466","https://openalex.org/W6722145564","https://openalex.org/W6753623554"],"related_works":["https://openalex.org/W1261320338","https://openalex.org/W1675687971","https://openalex.org/W2942981489","https://openalex.org/W2924035449","https://openalex.org/W2954452568","https://openalex.org/W4226042226","https://openalex.org/W2086307616","https://openalex.org/W2903509708","https://openalex.org/W4388044483","https://openalex.org/W2753150188"],"abstract_inverted_index":{"Time-delay":[0],"systems":[1,35],"are":[2,142],"ubiquitous":[3],"in":[4,8,134],"nature":[5],"and":[6,17,101,108],"occur":[7],"connection":[9],"with":[10,140],"various":[11],"aspects":[12],"of":[13,46,55,63,96,126,132,148],"physical,":[14],"chemical,":[15],"biological":[16],"economic":[18],"systems.":[19],"In":[20,88],"this":[21],"paper":[22],"we":[23,91],"propose":[24,110],"a":[25,56,73,80,111],"semi-definite":[26,112],"programming":[27],"method":[28],"to":[29,49,70,144],"address":[30],"reach-avoid":[31,44,57,117],"problems":[32],"for":[33,104,114],"time-delay":[34,68,106],"modeled":[36],"by":[37],"polynomial":[38],"delay":[39],"differential":[40],"equations":[41],"(DDEs).":[42],"The":[43,124],"problem":[45],"interest":[47],"is":[48,60],"compute":[50],"an":[51,94],"inner-approximation":[52],"(i.e.,":[53],"sub-set)":[54],"set,":[58],"which":[59],"the":[61,67,85,105,116,121,130,146],"set":[62,76,83,118],"initial":[64],"functions":[65],"enabling":[66],"system":[69],"eventually":[71],"enter":[72],"desirable":[74],"target":[75,86],"while":[77],"remaining":[78],"inside":[79],"specified":[81],"safe":[82],"till":[84],"hit.":[87],"our":[89,149],"approach":[90],"first":[92],"derive":[93],"estimate":[95],"discrepancies":[97],"between":[98],"current":[99],"states":[100],"delayed":[102],"ones":[103],"system,":[107],"then":[109],"program":[113],"inner-approximating":[115],"via":[119],"incorporating":[120],"discrepancy":[122,127],"estimate.":[123],"incorporation":[125],"estimates":[128],"facilitates":[129],"reduction":[131],"conservativeness":[133],"computing":[135],"inner-approximations.":[136],"Finally,":[137],"three":[138],"examples":[139],"comparisons":[141],"presented":[143],"demonstrate":[145],"performance":[147],"approach.":[150]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}