{"id":"https://openalex.org/W4399511537","doi":"https://doi.org/10.1109/tro.2024.3411850","title":"Value Approximation for Two-Player General-Sum Differential Games With State Constraints","display_name":"Value Approximation for Two-Player General-Sum Differential Games With State Constraints","publication_year":2024,"publication_date":"2024-01-01","ids":{"openalex":"https://openalex.org/W4399511537","doi":"https://doi.org/10.1109/tro.2024.3411850"},"language":"en","primary_location":{"id":"doi:10.1109/tro.2024.3411850","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tro.2024.3411850","pdf_url":null,"source":{"id":"https://openalex.org/S144620930","display_name":"IEEE Transactions on Robotics","issn_l":"1552-3098","issn":["1552-3098","1546-1904","1941-0468"],"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 Robotics","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/A5046800247","display_name":"Lei Zhang","orcid":"https://orcid.org/0009-0004-3023-0306"},"institutions":[{"id":"https://openalex.org/I55732556","display_name":"Arizona State University","ror":"https://ror.org/03efmqc40","country_code":"US","type":"education","lineage":["https://openalex.org/I55732556"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Lei Zhang","raw_affiliation_strings":["Department of Mechanical and Aerospace Engineering, Arizona State University, Tempe, AZ, USA"],"raw_orcid":"https://orcid.org/0009-0004-3023-0306","affiliations":[{"raw_affiliation_string":"Department of Mechanical and Aerospace Engineering, Arizona State University, Tempe, AZ, USA","institution_ids":["https://openalex.org/I55732556"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5060318659","display_name":"Mukesh Ghimire","orcid":"https://orcid.org/0009-0005-5660-5054"},"institutions":[{"id":"https://openalex.org/I55732556","display_name":"Arizona State University","ror":"https://ror.org/03efmqc40","country_code":"US","type":"education","lineage":["https://openalex.org/I55732556"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Mukesh Ghimire","raw_affiliation_strings":["Department of Mechanical and Aerospace Engineering, Arizona State University, Tempe, AZ, USA"],"raw_orcid":"https://orcid.org/0009-0005-5660-5054","affiliations":[{"raw_affiliation_string":"Department of Mechanical and Aerospace Engineering, Arizona State University, Tempe, AZ, USA","institution_ids":["https://openalex.org/I55732556"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100453347","display_name":"Wenlong Zhang","orcid":"https://orcid.org/0000-0002-4046-2213"},"institutions":[{"id":"https://openalex.org/I55732556","display_name":"Arizona State University","ror":"https://ror.org/03efmqc40","country_code":"US","type":"education","lineage":["https://openalex.org/I55732556"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Wenlong Zhang","raw_affiliation_strings":["School of Manufacturing Systems and Networks, Ira A. Fulton Schools of Engineering, Arizona State University, Mesa, AZ, USA"],"raw_orcid":"https://orcid.org/0000-0002-4046-2213","affiliations":[{"raw_affiliation_string":"School of Manufacturing Systems and Networks, Ira A. Fulton Schools of Engineering, Arizona State University, Mesa, AZ, USA","institution_ids":["https://openalex.org/I55732556"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5013789785","display_name":"Zhe Xu","orcid":"https://orcid.org/0000-0002-0440-0912"},"institutions":[{"id":"https://openalex.org/I55732556","display_name":"Arizona State University","ror":"https://ror.org/03efmqc40","country_code":"US","type":"education","lineage":["https://openalex.org/I55732556"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Zhe Xu","raw_affiliation_strings":["Department of Mechanical and Aerospace Engineering, Arizona State University, Tempe, AZ, USA"],"raw_orcid":"https://orcid.org/0000-0002-0440-0912","affiliations":[{"raw_affiliation_string":"Department of Mechanical and Aerospace Engineering, Arizona State University, Tempe, AZ, USA","institution_ids":["https://openalex.org/I55732556"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101812349","display_name":"Yi Ren","orcid":"https://orcid.org/0000-0003-2306-5993"},"institutions":[{"id":"https://openalex.org/I55732556","display_name":"Arizona State University","ror":"https://ror.org/03efmqc40","country_code":"US","type":"education","lineage":["https://openalex.org/I55732556"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Yi Ren","raw_affiliation_strings":["Department of Mechanical and Aerospace Engineering, Arizona State University, Tempe, AZ, USA"],"raw_orcid":"https://orcid.org/0000-0003-2306-5993","affiliations":[{"raw_affiliation_string":"Department of Mechanical and Aerospace Engineering, Arizona State University, Tempe, AZ, USA","institution_ids":["https://openalex.org/I55732556"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I55732556"],"apc_list":null,"apc_paid":null,"fwci":3.3761,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.93290903,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":97},"biblio":{"volume":"40","issue":null,"first_page":"4631","last_page":"4649"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10991","display_name":"Game Theory and Voting Systems","score":0.9793000221252441,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T10991","display_name":"Game Theory and Voting Systems","score":0.9793000221252441,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T11031","display_name":"Game Theory and Applications","score":0.9610000252723694,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T12158","display_name":"Guidance and Control Systems","score":0.9555000066757202,"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/state","display_name":"State (computer science)","score":0.5926429033279419},{"id":"https://openalex.org/keywords/value","display_name":"Value (mathematics)","score":0.573968768119812},{"id":"https://openalex.org/keywords/differential","display_name":"Differential (mechanical device)","score":0.5443415641784668},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4757761061191559},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4444950819015503},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4437454342842102},{"id":"https://openalex.org/keywords/differential-game","display_name":"Differential game","score":0.4189170002937317},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.39519938826560974},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.36016833782196045},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.23632395267486572},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.12716731429100037},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.1185089647769928}],"concepts":[{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.5926429033279419},{"id":"https://openalex.org/C2776291640","wikidata":"https://www.wikidata.org/wiki/Q2912517","display_name":"Value (mathematics)","level":2,"score":0.573968768119812},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.5443415641784668},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4757761061191559},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4444950819015503},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4437454342842102},{"id":"https://openalex.org/C2779006483","wikidata":"https://www.wikidata.org/wiki/Q1973196","display_name":"Differential game","level":2,"score":0.4189170002937317},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.39519938826560974},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.36016833782196045},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.23632395267486572},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.12716731429100037},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.1185089647769928},{"id":"https://openalex.org/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tro.2024.3411850","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tro.2024.3411850","pdf_url":null,"source":{"id":"https://openalex.org/S144620930","display_name":"IEEE Transactions on Robotics","issn_l":"1552-3098","issn":["1552-3098","1546-1904","1941-0468"],"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 Robotics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":60,"referenced_works":["https://openalex.org/W44423733","https://openalex.org/W153353184","https://openalex.org/W315739085","https://openalex.org/W1582899597","https://openalex.org/W2008588420","https://openalex.org/W2041700247","https://openalex.org/W2055300044","https://openalex.org/W2087599797","https://openalex.org/W2088710292","https://openalex.org/W2091510786","https://openalex.org/W2113108728","https://openalex.org/W2142332594","https://openalex.org/W2296073425","https://openalex.org/W2484646121","https://openalex.org/W2588978360","https://openalex.org/W2789029145","https://openalex.org/W2800727637","https://openalex.org/W2803629276","https://openalex.org/W2883548334","https://openalex.org/W2889522259","https://openalex.org/W2891385160","https://openalex.org/W2899283552","https://openalex.org/W2899507754","https://openalex.org/W2948551291","https://openalex.org/W2953931148","https://openalex.org/W2959078751","https://openalex.org/W2963146412","https://openalex.org/W2972723147","https://openalex.org/W2980176926","https://openalex.org/W2990116160","https://openalex.org/W2990653181","https://openalex.org/W3006784013","https://openalex.org/W3027682703","https://openalex.org/W3047245470","https://openalex.org/W3080564557","https://openalex.org/W3082030075","https://openalex.org/W3089576059","https://openalex.org/W3093786597","https://openalex.org/W3120409696","https://openalex.org/W3171832434","https://openalex.org/W3205025130","https://openalex.org/W3206190169","https://openalex.org/W4200574011","https://openalex.org/W4206101760","https://openalex.org/W4226065362","https://openalex.org/W4230684562","https://openalex.org/W4239369248","https://openalex.org/W4250744658","https://openalex.org/W4288083537","https://openalex.org/W4293399525","https://openalex.org/W4383066412","https://openalex.org/W4383108404","https://openalex.org/W4391741307","https://openalex.org/W6744562401","https://openalex.org/W6755977528","https://openalex.org/W6779265984","https://openalex.org/W6779753539","https://openalex.org/W6809713462","https://openalex.org/W6847191943","https://openalex.org/W6855980189"],"related_works":["https://openalex.org/W4287869118","https://openalex.org/W3005585050","https://openalex.org/W1984343254","https://openalex.org/W3126195429","https://openalex.org/W2354473585","https://openalex.org/W2070267559","https://openalex.org/W2800797998","https://openalex.org/W2315034291","https://openalex.org/W4256290860","https://openalex.org/W2030449225"],"abstract_inverted_index":{"Solving":[0],"Hamilton\u2013Jacobi\u2013Isaacs":[1],"(HJI)":[2],"PDEs":[3],"numerically":[4],"enables":[5],"equilibrial":[6],"feedback":[7],"control":[8],"in":[9,28,31,38,150],"two-player":[10],"differential":[11],"games,":[12],"yet":[13],"faces":[14],"the":[15,53,91,110,116,121,145,162,169],"curse":[16],"of":[17,52,101,152,160,172],"dimensionality":[18],"(CoD).":[19],"While":[20],"physics-informed":[21],"neural":[22],"networks":[23],"(PINNs)":[24],"have":[25],"shown":[26],"promise":[27],"alleviating":[29],"CoD":[30],"solving":[32],"PDEs,":[33],"vanilla":[34],"PINNs":[35],"fall":[36],"short":[37],"learning":[39,81],"discontinuous":[40,59],"solutions":[41,74],"due":[42,60],"to":[43,48,61,75,123],"their":[44],"sampling":[45],"nature,":[46],"leading":[47],"poor":[49],"safety":[50,155],"performance":[51,156],"resulting":[54],"policies":[55],"when":[56],"values":[57,165],"are":[58,103],"state":[62,127],"or":[63],"temporal":[64],"logic":[65],"constraints.":[66],"In":[67],"this":[68,76],"study,":[69],"we":[70],"explore":[71],"three":[72],"potential":[73],"challenge:":[77],"1)":[78],"a":[79,95,99,124],"hybrid":[80,146],"method":[82,97,147],"that":[83,119,144],"is":[84],"guided":[85],"by":[86,157],"both":[87,161],"supervisory":[88,163],"equilibria":[89],"and":[90,114,136,139,154,166,168],"HJI":[92],"PDE,":[93],"2)":[94],"value-hardening":[96],"where":[98,129],"sequence":[100],"HJIs":[102],"solved":[104],"with":[105],"increasing":[106],"Lipschitz":[107],"constant":[108],"on":[109],"constraint":[111],"violation":[112],"penalty,":[113],"3)":[115],"epigraphical":[117],"technique":[118],"lifts":[120],"value":[122],"higher":[125],"dimensional":[126],"space":[128],"it":[130],"becomes":[131],"continuous.":[132],"Evaluations":[133],"through":[134],"5-D":[135],"9-D":[137],"vehicle":[138],"13-D":[140],"drone":[141],"simulations":[142],"reveal":[143],"outperforms":[148],"others":[149],"terms":[151],"generalization":[153],"taking":[158],"advantage":[159],"equilibrium":[164],"co-states,":[167],"low":[170],"cost":[171],"PINN":[173],"loss":[174],"gradients.":[175]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":3}],"updated_date":"2025-12-26T23:08:49.675405","created_date":"2025-10-10T00:00:00"}