{"id":"https://openalex.org/W3096135216","doi":"https://doi.org/10.1109/tnnls.2020.3030127","title":"Model-Free Adaptive Optimal Control for Unknown Nonlinear Multiplayer Nonzero-Sum Game","display_name":"Model-Free Adaptive Optimal Control for Unknown Nonlinear Multiplayer Nonzero-Sum Game","publication_year":2020,"publication_date":"2020-10-27","ids":{"openalex":"https://openalex.org/W3096135216","doi":"https://doi.org/10.1109/tnnls.2020.3030127","mag":"3096135216","pmid":"https://pubmed.ncbi.nlm.nih.gov/33108297"},"language":"en","primary_location":{"id":"doi:10.1109/tnnls.2020.3030127","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tnnls.2020.3030127","pdf_url":null,"source":{"id":"https://openalex.org/S4210175523","display_name":"IEEE Transactions on Neural Networks and Learning Systems","issn_l":"2162-237X","issn":["2162-237X","2162-2388"],"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 Neural Networks and Learning Systems","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","pubmed"],"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/A5087825639","display_name":"Qinglai Wei","orcid":"https://orcid.org/0000-0001-7002-9800"},"institutions":[{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"government","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I4210100255","display_name":"Beijing Academy of Artificial Intelligence","ror":"https://ror.org/016a74861","country_code":"CN","type":"other","lineage":["https://openalex.org/I4210100255"]},{"id":"https://openalex.org/I4210112150","display_name":"Institute of Automation","ror":"https://ror.org/022c3hy66","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210112150"]},{"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":true,"raw_author_name":"Qinglai Wei","raw_affiliation_strings":["School of Artificial Intelligence, University of Chinese Academy of Sciences, Beijing, China","State Key Laboratory for Management and Control of Complex Systems, Institute of Automation, Chinese Academy of Sciences, Beijing, China"],"affiliations":[{"raw_affiliation_string":"School of Artificial Intelligence, University of Chinese Academy of Sciences, Beijing, China","institution_ids":["https://openalex.org/I4210100255","https://openalex.org/I4210165038"]},{"raw_affiliation_string":"State Key Laboratory for Management and Control of Complex Systems, Institute of Automation, Chinese Academy of Sciences, Beijing, China","institution_ids":["https://openalex.org/I4210112150","https://openalex.org/I19820366"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101847692","display_name":"Liao Zhu","orcid":"https://orcid.org/0000-0002-2120-1755"},"institutions":[{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"government","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I4210100255","display_name":"Beijing Academy of Artificial Intelligence","ror":"https://ror.org/016a74861","country_code":"CN","type":"other","lineage":["https://openalex.org/I4210100255"]},{"id":"https://openalex.org/I4210112150","display_name":"Institute of Automation","ror":"https://ror.org/022c3hy66","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210112150"]},{"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":"Liao Zhu","raw_affiliation_strings":["School of Artificial Intelligence, University of Chinese Academy of Sciences, Beijing, China","State Key Laboratory for Management and Control of Complex Systems, Institute of Automation, Chinese Academy of Sciences, Beijing, China"],"affiliations":[{"raw_affiliation_string":"School of Artificial Intelligence, University of Chinese Academy of Sciences, Beijing, China","institution_ids":["https://openalex.org/I4210100255","https://openalex.org/I4210165038"]},{"raw_affiliation_string":"State Key Laboratory for Management and Control of Complex Systems, Institute of Automation, Chinese Academy of Sciences, Beijing, China","institution_ids":["https://openalex.org/I4210112150","https://openalex.org/I19820366"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5040323322","display_name":"Ruizhuo Song","orcid":"https://orcid.org/0000-0002-6693-2738"},"institutions":[{"id":"https://openalex.org/I92403157","display_name":"University of Science and Technology Beijing","ror":"https://ror.org/02egmk993","country_code":"CN","type":"education","lineage":["https://openalex.org/I92403157"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Ruizhuo Song","raw_affiliation_strings":["School of Automation and Electrical Engineering, University of Science and Technology Beijing, Beijing, China"],"affiliations":[{"raw_affiliation_string":"School of Automation and Electrical Engineering, University of Science and Technology Beijing, Beijing, China","institution_ids":["https://openalex.org/I92403157"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5031222179","display_name":"Pinjia Zhang","orcid":"https://orcid.org/0000-0002-1288-956X"},"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":"Pinjia Zhang","raw_affiliation_strings":["Department of Electrical Engineering, Tsinghua University, Beijing, China"],"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, Tsinghua University, Beijing, China","institution_ids":["https://openalex.org/I99065089"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5004057129","display_name":"Derong Liu","orcid":"https://orcid.org/0000-0003-3715-4778"},"institutions":[{"id":"https://openalex.org/I139024713","display_name":"Guangdong University of Technology","ror":"https://ror.org/04azbjn80","country_code":"CN","type":"education","lineage":["https://openalex.org/I139024713"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Derong Liu","raw_affiliation_strings":["School of Automation, Guangdong University of Technology, Guangzhou, China"],"affiliations":[{"raw_affiliation_string":"School of Automation, Guangdong University of Technology, Guangzhou, China","institution_ids":["https://openalex.org/I139024713"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5076518693","display_name":"Jun Xiao","orcid":"https://orcid.org/0000-0002-1799-3948"},"institutions":[{"id":"https://openalex.org/I4210100255","display_name":"Beijing Academy of Artificial Intelligence","ror":"https://ror.org/016a74861","country_code":"CN","type":"other","lineage":["https://openalex.org/I4210100255"]},{"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":"Jun Xiao","raw_affiliation_strings":["School of Artificial Intelligence, University of Chinese Academy of Sciences, Beijing, China"],"affiliations":[{"raw_affiliation_string":"School of Artificial Intelligence, University of Chinese Academy of Sciences, Beijing, China","institution_ids":["https://openalex.org/I4210100255","https://openalex.org/I4210165038"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":6,"corresponding_author_ids":["https://openalex.org/A5087825639"],"corresponding_institution_ids":["https://openalex.org/I19820366","https://openalex.org/I4210100255","https://openalex.org/I4210112150","https://openalex.org/I4210165038"],"apc_list":null,"apc_paid":null,"fwci":7.08,"has_fulltext":false,"cited_by_count":106,"citation_normalized_percentile":{"value":0.97572977,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":97,"max":100},"biblio":{"volume":"33","issue":"2","first_page":"879","last_page":"892"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12794","display_name":"Adaptive Dynamic Programming Control","score":1.0,"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/T12794","display_name":"Adaptive Dynamic Programming Control","score":1.0,"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/T12277","display_name":"Frequency Control in Power Systems","score":0.968999981880188,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic 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/T14413","display_name":"Advanced Technologies in Various Fields","score":0.951200008392334,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/dynamic-programming","display_name":"Dynamic programming","score":0.5936780571937561},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5849946737289429},{"id":"https://openalex.org/keywords/heuristic","display_name":"Heuristic","score":0.5466727018356323},{"id":"https://openalex.org/keywords/identifier","display_name":"Identifier","score":0.541049599647522},{"id":"https://openalex.org/keywords/lyapunov-function","display_name":"Lyapunov function","score":0.5372115969657898},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5321675539016724},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5151985287666321},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.5109190344810486},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.4722706079483032},{"id":"https://openalex.org/keywords/adaptive-control","display_name":"Adaptive control","score":0.4398096203804016},{"id":"https://openalex.org/keywords/discrete-time-and-continuous-time","display_name":"Discrete time and continuous time","score":0.41763538122177124},{"id":"https://openalex.org/keywords/bellman-equation","display_name":"Bellman equation","score":0.41165655851364136},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.33905333280563354},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.252089262008667},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.18856140971183777}],"concepts":[{"id":"https://openalex.org/C37404715","wikidata":"https://www.wikidata.org/wiki/Q380679","display_name":"Dynamic programming","level":2,"score":0.5936780571937561},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5849946737289429},{"id":"https://openalex.org/C173801870","wikidata":"https://www.wikidata.org/wiki/Q201413","display_name":"Heuristic","level":2,"score":0.5466727018356323},{"id":"https://openalex.org/C154504017","wikidata":"https://www.wikidata.org/wiki/Q853614","display_name":"Identifier","level":2,"score":0.541049599647522},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.5372115969657898},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5321675539016724},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5151985287666321},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.5109190344810486},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.4722706079483032},{"id":"https://openalex.org/C107464732","wikidata":"https://www.wikidata.org/wiki/Q235781","display_name":"Adaptive control","level":3,"score":0.4398096203804016},{"id":"https://openalex.org/C55689738","wikidata":"https://www.wikidata.org/wiki/Q15963867","display_name":"Discrete time and continuous time","level":2,"score":0.41763538122177124},{"id":"https://openalex.org/C14646407","wikidata":"https://www.wikidata.org/wiki/Q1430750","display_name":"Bellman equation","level":2,"score":0.41165655851364136},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.33905333280563354},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.252089262008667},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.18856140971183777},{"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/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tnnls.2020.3030127","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tnnls.2020.3030127","pdf_url":null,"source":{"id":"https://openalex.org/S4210175523","display_name":"IEEE Transactions on Neural Networks and Learning Systems","issn_l":"2162-237X","issn":["2162-237X","2162-2388"],"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 Neural Networks and Learning Systems","raw_type":"journal-article"},{"id":"pmid:33108297","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/33108297","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE transactions on neural networks and learning systems","raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.41999998688697815,"display_name":"Partnerships for the goals","id":"https://metadata.un.org/sdg/17"}],"awards":[{"id":"https://openalex.org/G5552542783","display_name":null,"funder_award_id":"61673054","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5938002141","display_name":null,"funder_award_id":"62073321","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6603537307","display_name":null,"funder_award_id":"61722312","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7163010157","display_name":null,"funder_award_id":"61533017","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8272745707","display_name":null,"funder_award_id":"2018YFB1702300","funder_id":"https://openalex.org/F4320335777","funder_display_name":"National Key Research and Development Program of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320335777","display_name":"National Key Research and Development Program of China","ror":null}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":52,"referenced_works":["https://openalex.org/W132264163","https://openalex.org/W560518094","https://openalex.org/W1513689897","https://openalex.org/W1517236425","https://openalex.org/W1559261542","https://openalex.org/W1570487003","https://openalex.org/W1986278072","https://openalex.org/W1994860132","https://openalex.org/W1995097018","https://openalex.org/W2005675298","https://openalex.org/W2007640554","https://openalex.org/W2019338681","https://openalex.org/W2050838777","https://openalex.org/W2060605484","https://openalex.org/W2068949505","https://openalex.org/W2073540225","https://openalex.org/W2074229485","https://openalex.org/W2136064843","https://openalex.org/W2137092694","https://openalex.org/W2165726932","https://openalex.org/W2203860294","https://openalex.org/W2329769476","https://openalex.org/W2345200935","https://openalex.org/W2475651303","https://openalex.org/W2476930474","https://openalex.org/W2484646121","https://openalex.org/W2522967535","https://openalex.org/W2529203006","https://openalex.org/W2561946193","https://openalex.org/W2570494446","https://openalex.org/W2727450595","https://openalex.org/W2735449579","https://openalex.org/W2756081914","https://openalex.org/W2762211190","https://openalex.org/W2777247237","https://openalex.org/W2779055119","https://openalex.org/W2782656687","https://openalex.org/W2803973384","https://openalex.org/W2883806155","https://openalex.org/W2897507137","https://openalex.org/W2903851759","https://openalex.org/W2949510088","https://openalex.org/W2963350146","https://openalex.org/W2981394297","https://openalex.org/W2998579696","https://openalex.org/W2998774248","https://openalex.org/W2999953156","https://openalex.org/W3014535293","https://openalex.org/W3034966130","https://openalex.org/W3039492319","https://openalex.org/W3150098721","https://openalex.org/W6804409665"],"related_works":["https://openalex.org/W4255265352","https://openalex.org/W4239477580","https://openalex.org/W2952594763","https://openalex.org/W4285537323","https://openalex.org/W1932159282","https://openalex.org/W2090698372","https://openalex.org/W4383890581","https://openalex.org/W2921905705","https://openalex.org/W4233178034","https://openalex.org/W2602009922"],"abstract_inverted_index":{"In":[0],"this":[1],"article,":[2],"an":[3,64],"online":[4,65,114],"adaptive":[5,11,66],"optimal":[6,101],"control":[7],"algorithm":[8,68],"based":[9,115,133],"on":[10,116,134],"dynamic":[12,34],"programming":[13,35],"is":[14,38,48,69,131],"developed":[15,70,149],"to":[16,40,57,71,96,143],"solve":[17,41,72],"the":[18,42,59,73,77,107,121,127,135,145,148],"multiplayer":[19],"nonzero-sum":[20],"game":[21],"(MP-NZSG)":[22],"for":[23,103],"discrete-time":[24],"unknown":[25],"nonlinear":[26],"systems.":[27],"First,":[28],"a":[29,86],"model-free":[30],"coupled":[31],"globalized":[32],"dual-heuristic":[33],"(GDHP)":[36],"structure":[37],"designed":[39],"MP-NZSG":[43],"problem,":[44],"in":[45,55],"which":[46],"there":[47],"no":[49],"model":[50],"network":[51,109],"or":[52],"identifier.":[53],"Second,":[54],"order":[56],"relax":[58],"requirement":[60],"of":[61,80,88,126,147],"systems":[62],"dynamics,":[63],"learning":[67],"Hamilton-Jacobi":[74],"equation":[75],"using":[76],"system":[78,118],"states":[79],"two":[81],"adjacent":[82],"time":[83],"steps.":[84],"Third,":[85],"series":[87],"critic":[89],"networks":[90,93],"and":[91,100],"action":[92],"are":[94,112,141],"used":[95],"approximate":[97],"value":[98],"functions":[99],"policies":[102],"all":[104],"players.":[105],"All":[106],"neural":[108],"(NN)":[110],"weights":[111],"updated":[113],"real-time":[117],"states.":[119],"Fourth,":[120],"uniformly":[122],"ultimate":[123],"boundedness":[124],"analysis":[125],"NN":[128],"approximation":[129],"errors":[130],"proved":[132],"Lyapunov":[136],"approach.":[137],"Finally,":[138],"simulation":[139],"results":[140],"given":[142],"demonstrate":[144],"effectiveness":[146],"scheme.":[150]},"counts_by_year":[{"year":2026,"cited_by_count":4},{"year":2025,"cited_by_count":24},{"year":2024,"cited_by_count":29},{"year":2023,"cited_by_count":23},{"year":2022,"cited_by_count":22},{"year":2021,"cited_by_count":4}],"updated_date":"2026-04-09T08:11:56.329763","created_date":"2025-10-10T00:00:00"}
