{"id":"https://openalex.org/W4391341349","doi":"https://doi.org/10.1109/tsmc.2024.3352263","title":"An Improved Level Set Method for Reachability Problems in Differential Games","display_name":"An Improved Level Set Method for Reachability Problems in Differential Games","publication_year":2024,"publication_date":"2024-01-30","ids":{"openalex":"https://openalex.org/W4391341349","doi":"https://doi.org/10.1109/tsmc.2024.3352263"},"language":"en","primary_location":{"id":"doi:10.1109/tsmc.2024.3352263","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsmc.2024.3352263","pdf_url":null,"source":{"id":"https://openalex.org/S4210209078","display_name":"IEEE Transactions on Systems Man and Cybernetics Systems","issn_l":"2168-2216","issn":["2168-2216","2168-2232"],"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 Systems, Man, and Cybernetics: 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/A5010842219","display_name":"Wei Liao","orcid":"https://orcid.org/0000-0003-2778-0572"},"institutions":[{"id":"https://openalex.org/I141649914","display_name":"Nanchang University","ror":"https://ror.org/042v6xz23","country_code":"CN","type":"education","lineage":["https://openalex.org/I141649914"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Wei Liao","raw_affiliation_strings":["Advanced Manufacturing School, Nanchang University, Nanchang, China"],"raw_orcid":"https://orcid.org/0000-0003-2778-0572","affiliations":[{"raw_affiliation_string":"Advanced Manufacturing School, Nanchang University, Nanchang, China","institution_ids":["https://openalex.org/I141649914"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5064604104","display_name":"Taotao Liang","orcid":"https://orcid.org/0000-0001-5355-0856"},"institutions":[{"id":"https://openalex.org/I9842412","display_name":"Nanjing University of Aeronautics and Astronautics","ror":"https://ror.org/01scyh794","country_code":"CN","type":"education","lineage":["https://openalex.org/I9842412"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Taotao Liang","raw_affiliation_strings":["College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing, China"],"raw_orcid":"https://orcid.org/0000-0001-5355-0856","affiliations":[{"raw_affiliation_string":"College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing, China","institution_ids":["https://openalex.org/I9842412"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5001174925","display_name":"Pengwen Xiong","orcid":"https://orcid.org/0000-0002-0623-8592"},"institutions":[{"id":"https://openalex.org/I141649914","display_name":"Nanchang University","ror":"https://ror.org/042v6xz23","country_code":"CN","type":"education","lineage":["https://openalex.org/I141649914"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Pengwen Xiong","raw_affiliation_strings":["Advanced Manufacturing School, Nanchang University, Nanchang, China"],"raw_orcid":"https://orcid.org/0000-0002-0623-8592","affiliations":[{"raw_affiliation_string":"Advanced Manufacturing School, Nanchang University, Nanchang, China","institution_ids":["https://openalex.org/I141649914"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5082942585","display_name":"Chen Wang","orcid":"https://orcid.org/0009-0003-4512-2896"},"institutions":[{"id":"https://openalex.org/I9842412","display_name":"Nanjing University of Aeronautics and Astronautics","ror":"https://ror.org/01scyh794","country_code":"CN","type":"education","lineage":["https://openalex.org/I9842412"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Chen Wang","raw_affiliation_strings":["College of Astronautics, Nanjing University of Aeronautics and Astronautics, Nanjing, China"],"raw_orcid":"https://orcid.org/0009-0003-4512-2896","affiliations":[{"raw_affiliation_string":"College of Astronautics, Nanjing University of Aeronautics and Astronautics, Nanjing, China","institution_ids":["https://openalex.org/I9842412"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5048327458","display_name":"Aiguo Song","orcid":"https://orcid.org/0000-0002-1982-6780"},"institutions":[{"id":"https://openalex.org/I76569877","display_name":"Southeast University","ror":"https://ror.org/04ct4d772","country_code":"CN","type":"education","lineage":["https://openalex.org/I76569877"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Aiguo Song","raw_affiliation_strings":["School of Instrument Science and Engineering, Southeast University, Nanjing, China"],"raw_orcid":"https://orcid.org/0000-0002-1982-6780","affiliations":[{"raw_affiliation_string":"School of Instrument Science and Engineering, Southeast University, Nanjing, China","institution_ids":["https://openalex.org/I76569877"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100659849","display_name":"Peter Liu","orcid":"https://orcid.org/0000-0002-8703-6967"},"institutions":[{"id":"https://openalex.org/I67031392","display_name":"Carleton University","ror":"https://ror.org/02qtvee93","country_code":"CA","type":"education","lineage":["https://openalex.org/I67031392"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Peter X. Liu","raw_affiliation_strings":["Department of Systems and Computer Engineering, Carleton University, Ottawa, Canada"],"raw_orcid":"https://orcid.org/0000-0002-8703-6967","affiliations":[{"raw_affiliation_string":"Department of Systems and Computer Engineering, Carleton University, Ottawa, Canada","institution_ids":["https://openalex.org/I67031392"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":6,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.8749,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.72253483,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"54","issue":"5","first_page":"2907","last_page":"2916"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10586","display_name":"Robotic Path Planning Algorithms","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/T10586","display_name":"Robotic Path Planning Algorithms","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/T12288","display_name":"Optimization and Search Problems","score":0.9954000115394592,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/T10567","display_name":"Vehicle Routing Optimization Methods","score":0.9943000078201294,"subfield":{"id":"https://openalex.org/subfields/2209","display_name":"Industrial and Manufacturing 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":0.9056459665298462},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.681311309337616},{"id":"https://openalex.org/keywords/differential","display_name":"Differential (mechanical device)","score":0.6760474443435669},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5078356862068176},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.40873441100120544},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.36226409673690796},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.27107229828834534},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.15726977586746216},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.10444214940071106},{"id":"https://openalex.org/keywords/aerospace-engineering","display_name":"Aerospace engineering","score":0.05592447519302368}],"concepts":[{"id":"https://openalex.org/C136643341","wikidata":"https://www.wikidata.org/wiki/Q1361526","display_name":"Reachability","level":2,"score":0.9056459665298462},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.681311309337616},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.6760474443435669},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5078356862068176},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.40873441100120544},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.36226409673690796},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.27107229828834534},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.15726977586746216},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.10444214940071106},{"id":"https://openalex.org/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","level":1,"score":0.05592447519302368}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tsmc.2024.3352263","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsmc.2024.3352263","pdf_url":null,"source":{"id":"https://openalex.org/S4210209078","display_name":"IEEE Transactions on Systems Man and Cybernetics Systems","issn_l":"2168-2216","issn":["2168-2216","2168-2232"],"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 Systems, Man, and Cybernetics: Systems","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/13","display_name":"Climate action","score":0.6499999761581421}],"awards":[{"id":"https://openalex.org/G4947412877","display_name":null,"funder_award_id":"62373181","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6949746558","display_name":"\u534a\u81ea\u4e3b\u9065\u64cd\u4f5c\u4e0b\u6838\u7535\u673a\u5668\u4eba\u7684\u8fd0\u52a8\u5206\u6790\u4e0e\u63a7\u5236\u7814\u7a76","funder_award_id":"61663027","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6977814232","display_name":null,"funder_award_id":"62163024","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8939568379","display_name":null,"funder_award_id":"61903175","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":44,"referenced_works":["https://openalex.org/W168874853","https://openalex.org/W1499853177","https://openalex.org/W1544599017","https://openalex.org/W1586383189","https://openalex.org/W1726255445","https://openalex.org/W1908478556","https://openalex.org/W1975236902","https://openalex.org/W1983540877","https://openalex.org/W2024730047","https://openalex.org/W2065533815","https://openalex.org/W2067202372","https://openalex.org/W2090501324","https://openalex.org/W2093834886","https://openalex.org/W2116364955","https://openalex.org/W2123402141","https://openalex.org/W2131441094","https://openalex.org/W2228513190","https://openalex.org/W2314330572","https://openalex.org/W2320516134","https://openalex.org/W2335200202","https://openalex.org/W2608182344","https://openalex.org/W2766658289","https://openalex.org/W2779486833","https://openalex.org/W2792378122","https://openalex.org/W2800806925","https://openalex.org/W2884808385","https://openalex.org/W2907866727","https://openalex.org/W2913142685","https://openalex.org/W2962896691","https://openalex.org/W2963118121","https://openalex.org/W2963606896","https://openalex.org/W3004650008","https://openalex.org/W3009014967","https://openalex.org/W3013660903","https://openalex.org/W3045548741","https://openalex.org/W3080564557","https://openalex.org/W3115515976","https://openalex.org/W3120726845","https://openalex.org/W3127927628","https://openalex.org/W3161426377","https://openalex.org/W4210791600","https://openalex.org/W4212925967","https://openalex.org/W4239369248","https://openalex.org/W6689280993"],"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/W2143461633","https://openalex.org/W2150194458","https://openalex.org/W4321471459","https://openalex.org/W2889071233","https://openalex.org/W2380814829"],"abstract_inverted_index":{"This":[0],"study":[1],"focuses":[2],"on":[3],"reachability":[4],"problems":[5],"in":[6,22],"differential":[7],"games.":[8],"An":[9],"improved":[10],"level":[11],"set":[12,82,95],"(LS)":[13],"method":[14],"for":[15,77,127],"computing":[16],"reachable":[17],"tubes":[18],"(RTs)":[19],"is":[20,27,37,106],"proposed":[21],"this":[23],"article.":[24],"The":[25,171],"RT":[26,112,116],"described":[28],"as":[29,66,109],"a":[30,33,42,57,71,102,110,143],"sub-LS":[31],"of":[32,41,53,60,83,86,134,138,175],"value":[34],"function,":[35],"which":[36,62],"the":[38,51,78,87,93,97,122,128,135,139,152,159,167,176],"viscosity":[39,136],"solution":[40,137],"Hamilton\u2013Jacobi":[43],"(HJ)":[44],"equation":[45,141],"with":[46,154,161],"running":[47,124],"cost.":[48],"We":[49],"generalize":[50],"concept":[52],"RTs":[54,160],"and":[55,80,173],"propose":[56],"new":[58],"class":[59],"RTs,":[61],"are":[63,179],"referred":[64,107],"to":[65,101,108,150],"cost-limited":[67,111],"one.":[68],"In":[69],"particular,":[70],"performance":[72,98],"index":[73,99],"can":[74,91,117,147],"be":[75,118,148],"specified":[76],"system,":[79],"A":[81],"initial":[84],"states":[85],"system\u2019s":[88],"evolutions":[89],"that":[90],"reach":[92],"target":[94],"before":[96],"grows":[100],"given":[103],"allowable":[104,156],"cost":[105,125],"(CRT).":[113],"Such":[114],"an":[115],"obtained":[119],"by":[120],"specifying":[121],"corresponding":[123],"function":[126],"HJ":[129,140],"equation.":[130],"Different":[131],"nonzero":[132],"sub-LSs":[133],"at":[142],"certain":[144],"time":[145,163],"point":[146],"used":[149],"characterize":[151],"CRTs":[153],"different":[155,162],"costs":[157],"(or":[158],"horizons),":[164],"thus":[165],"reducing":[166],"storage":[168],"space":[169],"consumption.":[170],"validity":[172],"accuracy":[174],"suggested":[177],"technique":[178],"demonstrated":[180],"via":[181],"some":[182],"examples.":[183]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}