{"id":"https://openalex.org/W4387872080","doi":"https://doi.org/10.1109/taes.2023.3326780","title":"Reach-Avoid Games With Two Cooperative Attackers: Value Function and Singular Surfaces","display_name":"Reach-Avoid Games With Two Cooperative Attackers: Value Function and Singular Surfaces","publication_year":2023,"publication_date":"2023-10-23","ids":{"openalex":"https://openalex.org/W4387872080","doi":"https://doi.org/10.1109/taes.2023.3326780"},"language":"en","primary_location":{"id":"doi:10.1109/taes.2023.3326780","is_oa":false,"landing_page_url":"https://doi.org/10.1109/taes.2023.3326780","pdf_url":null,"source":{"id":"https://openalex.org/S193624734","display_name":"IEEE Transactions on Aerospace and Electronic Systems","issn_l":"0018-9251","issn":["0018-9251","1557-9603","2371-9877"],"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 Aerospace and Electronic 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/A5015492944","display_name":"Ruiliang Deng","orcid":"https://orcid.org/0009-0009-1308-3443"},"institutions":[{"id":"https://openalex.org/I99065089","display_name":"Tsinghua University","ror":"https://ror.org/03cve4549","country_code":"CN","type":"education","lineage":["https://openalex.org/I99065089"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Ruiliang Deng","raw_affiliation_strings":["Department of Automation, Tsinghua University, Beijing, China"],"raw_orcid":"https://orcid.org/0009-0009-1308-3443","affiliations":[{"raw_affiliation_string":"Department of Automation, Tsinghua University, Beijing, China","institution_ids":["https://openalex.org/I99065089"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5043045459","display_name":"Zongying Shi","orcid":"https://orcid.org/0000-0002-6805-6858"},"institutions":[{"id":"https://openalex.org/I99065089","display_name":"Tsinghua University","ror":"https://ror.org/03cve4549","country_code":"CN","type":"education","lineage":["https://openalex.org/I99065089"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zongying Shi","raw_affiliation_strings":["Department of Automation, Tsinghua University, Beijing, China"],"raw_orcid":"https://orcid.org/0000-0002-6805-6858","affiliations":[{"raw_affiliation_string":"Department of Automation, Tsinghua University, Beijing, China","institution_ids":["https://openalex.org/I99065089"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101631780","display_name":"Yisheng Zhong","orcid":"https://orcid.org/0000-0001-7871-7317"},"institutions":[{"id":"https://openalex.org/I99065089","display_name":"Tsinghua University","ror":"https://ror.org/03cve4549","country_code":"CN","type":"education","lineage":["https://openalex.org/I99065089"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yisheng Zhong","raw_affiliation_strings":["Department of Automation, Tsinghua University, Beijing, China"],"raw_orcid":"https://orcid.org/0000-0001-7871-7317","affiliations":[{"raw_affiliation_string":"Department of Automation, Tsinghua University, Beijing, China","institution_ids":["https://openalex.org/I99065089"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5015492944"],"corresponding_institution_ids":["https://openalex.org/I99065089"],"apc_list":null,"apc_paid":null,"fwci":9.6647,"has_fulltext":false,"cited_by_count":12,"citation_normalized_percentile":{"value":0.97384263,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":99},"biblio":{"volume":"60","issue":"1","first_page":"558","last_page":"573"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12158","display_name":"Guidance and Control Systems","score":0.9537000060081482,"subfield":{"id":"https://openalex.org/subfields/2202","display_name":"Aerospace 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/T12158","display_name":"Guidance and Control Systems","score":0.9537000060081482,"subfield":{"id":"https://openalex.org/subfields/2202","display_name":"Aerospace 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/function","display_name":"Function (biology)","score":0.6013082265853882},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.551480770111084},{"id":"https://openalex.org/keywords/singular-value","display_name":"Singular value","score":0.5326573252677917},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.4972369968891144},{"id":"https://openalex.org/keywords/value","display_name":"Value (mathematics)","score":0.49419644474983215},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4449955224990845},{"id":"https://openalex.org/keywords/game-theory","display_name":"Game theory","score":0.4319019317626953},{"id":"https://openalex.org/keywords/example-of-a-game-without-a-value","display_name":"Example of a game without a value","score":0.41867581009864807},{"id":"https://openalex.org/keywords/sequential-game","display_name":"Sequential game","score":0.402565062046051},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.302412211894989},{"id":"https://openalex.org/keywords/simultaneous-game","display_name":"Simultaneous game","score":0.24498024582862854},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.23986124992370605},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.09323221445083618}],"concepts":[{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.6013082265853882},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.551480770111084},{"id":"https://openalex.org/C109282560","wikidata":"https://www.wikidata.org/wiki/Q4166054","display_name":"Singular value","level":3,"score":0.5326573252677917},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.4972369968891144},{"id":"https://openalex.org/C2776291640","wikidata":"https://www.wikidata.org/wiki/Q2912517","display_name":"Value (mathematics)","level":2,"score":0.49419644474983215},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4449955224990845},{"id":"https://openalex.org/C177142836","wikidata":"https://www.wikidata.org/wiki/Q44455","display_name":"Game theory","level":2,"score":0.4319019317626953},{"id":"https://openalex.org/C138328387","wikidata":"https://www.wikidata.org/wiki/Q5419308","display_name":"Example of a game without a value","level":5,"score":0.41867581009864807},{"id":"https://openalex.org/C73795354","wikidata":"https://www.wikidata.org/wiki/Q287618","display_name":"Sequential game","level":3,"score":0.402565062046051},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.302412211894989},{"id":"https://openalex.org/C95940807","wikidata":"https://www.wikidata.org/wiki/Q12237274","display_name":"Simultaneous game","level":4,"score":0.24498024582862854},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.23986124992370605},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.09323221445083618},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.0},{"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/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/taes.2023.3326780","is_oa":false,"landing_page_url":"https://doi.org/10.1109/taes.2023.3326780","pdf_url":null,"source":{"id":"https://openalex.org/S193624734","display_name":"IEEE Transactions on Aerospace and Electronic Systems","issn_l":"0018-9251","issn":["0018-9251","1557-9603","2371-9877"],"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 Aerospace and Electronic Systems","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":30,"referenced_works":["https://openalex.org/W369263919","https://openalex.org/W1550828720","https://openalex.org/W1978263382","https://openalex.org/W2009318488","https://openalex.org/W2058737528","https://openalex.org/W2074550675","https://openalex.org/W2078622299","https://openalex.org/W2183469038","https://openalex.org/W2414457428","https://openalex.org/W2761014606","https://openalex.org/W2785598896","https://openalex.org/W2889045701","https://openalex.org/W2913295839","https://openalex.org/W2927557059","https://openalex.org/W2962888568","https://openalex.org/W2969039176","https://openalex.org/W2972260985","https://openalex.org/W2972425740","https://openalex.org/W3005581757","https://openalex.org/W3006321499","https://openalex.org/W3011454388","https://openalex.org/W3011534733","https://openalex.org/W3035782080","https://openalex.org/W3120348026","https://openalex.org/W3123009522","https://openalex.org/W4206607776","https://openalex.org/W4211189800","https://openalex.org/W4239369248","https://openalex.org/W4254199793","https://openalex.org/W4285238151"],"related_works":["https://openalex.org/W2395347989","https://openalex.org/W2067232667","https://openalex.org/W2071306797","https://openalex.org/W4321497886","https://openalex.org/W143065017","https://openalex.org/W651698058","https://openalex.org/W2898418245","https://openalex.org/W2056920506","https://openalex.org/W1994742051","https://openalex.org/W2565239699"],"abstract_inverted_index":{"This":[0,37],"article":[1],"studies":[2],"a":[3,69,85],"zero-sum":[4],"reach-avoid":[5],"game":[6,63,71,130,136],"in":[7,65,75,84,138,162,185],"the":[8,23,28,42,50,62,77,82,99,112,117,122,125,128,134,147,155,159,163,166,175,183,190],"2-D":[9],"plane":[10],"with":[11,107,197],"one":[12],"defender":[13,29,78,176],"and":[14,45,96,154],"two":[15,66],"cooperative":[16],"attackers.":[17],"The":[18,88,103,149],"attackers":[19,83,104,184],"try":[20],"to":[21,32,40,80,116,127,181],"enter":[22],"target":[24],"region":[25],"protected":[26],"by":[27,110],"who":[30],"tries":[31],"capture":[33,81,143,182],"both":[34],"of":[35,52,124,158,165,192],"them.":[36],"work":[38],"aims":[39],"obtain":[41],"value":[43,89,118,160],"function":[44,90,161],"equilibrium":[46,113],"strategies,":[47],"for":[48,146],"which":[49,76,139],"analysis":[51],"singular":[53,150,167,193],"surfaces":[54,151,168,194],"is":[55,73,91,141,172,195],"needed.":[56],"To":[57],"this":[58],"end,":[59],"we":[60,132],"investigate":[61],"problem":[64,137],"steps.":[67],"First,":[68],"constrained":[70],"scenario":[72],"considered":[74],"needs":[79],"predefined":[86,187],"order.":[87,188],"constructed":[92],"using":[93,98],"geometric":[94],"tools":[95],"proved":[97],"viscosity":[100],"solution":[101,126],"method.":[102],"can":[105,177],"cooperate":[106],"each":[108],"other":[109],"adopting":[111],"strategies":[114],"corresponding":[115],"function.":[119],"Second,":[120],"on":[121],"basis":[123],"first":[129],"scenario,":[131],"analyze":[133],"general":[135],"there":[140],"no":[142],"order":[144],"restriction":[145],"defender.":[148],"are":[152,169],"discussed":[153],"local":[156],"properties":[157],"vicinity":[164],"given.":[170],"It":[171],"shown":[173],"that":[174],"perform":[178],"better":[179],"than":[180],"any":[186],"Moreover,":[189],"construction":[191],"illustrated":[196],"numerical":[198],"results.":[199]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":6},{"year":2024,"cited_by_count":3}],"updated_date":"2026-05-06T08:25:59.206177","created_date":"2025-10-10T00:00:00"}
