{"id":"https://openalex.org/W3102704006","doi":"https://doi.org/10.1109/tcyb.2020.3028267","title":"A Novel Mean-Field-Game-Type Optimal Control for Very Large-Scale Multiagent Systems","display_name":"A Novel Mean-Field-Game-Type Optimal Control for Very Large-Scale Multiagent Systems","publication_year":2020,"publication_date":"2020-11-18","ids":{"openalex":"https://openalex.org/W3102704006","doi":"https://doi.org/10.1109/tcyb.2020.3028267","mag":"3102704006","pmid":"https://pubmed.ncbi.nlm.nih.gov/33206615"},"language":"en","primary_location":{"id":"doi:10.1109/tcyb.2020.3028267","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcyb.2020.3028267","pdf_url":null,"source":{"id":"https://openalex.org/S4210191041","display_name":"IEEE Transactions on Cybernetics","issn_l":"2168-2267","issn":["2168-2267","2168-2275"],"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 Cybernetics","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/A5088809666","display_name":"Zejian Zhou","orcid":"https://orcid.org/0000-0002-0252-6765"},"institutions":[{"id":"https://openalex.org/I134113660","display_name":"University of Nevada, Reno","ror":"https://ror.org/01keh0577","country_code":"US","type":"education","lineage":["https://openalex.org/I134113660"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Zejian Zhou","raw_affiliation_strings":["Department of Electrical Engineering, University of Nevada, Reno, NV, USA"],"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, University of Nevada, Reno, NV, USA","institution_ids":["https://openalex.org/I134113660"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100717012","display_name":"Hao Xu","orcid":"https://orcid.org/0000-0003-4130-7925"},"institutions":[{"id":"https://openalex.org/I134113660","display_name":"University of Nevada, Reno","ror":"https://ror.org/01keh0577","country_code":"US","type":"education","lineage":["https://openalex.org/I134113660"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Hao Xu","raw_affiliation_strings":["Department of Electrical Engineering, University of Nevada, Reno, NV, USA"],"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, University of Nevada, Reno, NV, USA","institution_ids":["https://openalex.org/I134113660"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5088809666"],"corresponding_institution_ids":["https://openalex.org/I134113660"],"apc_list":null,"apc_paid":null,"fwci":2.3164,"has_fulltext":false,"cited_by_count":31,"citation_normalized_percentile":{"value":0.9107345,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"52","issue":"6","first_page":"5197","last_page":"5208"},"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/T10462","display_name":"Reinforcement Learning in Robotics","score":0.9864000082015991,"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"}},{"id":"https://openalex.org/T10040","display_name":"Adaptive Control of Nonlinear Systems","score":0.9805999994277954,"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/hamilton\u2013jacobi\u2013bellman-equation","display_name":"Hamilton\u2013Jacobi\u2013Bellman equation","score":0.7563429474830627},{"id":"https://openalex.org/keywords/curse-of-dimensionality","display_name":"Curse of dimensionality","score":0.6990883350372314},{"id":"https://openalex.org/keywords/reinforcement-learning","display_name":"Reinforcement learning","score":0.658279538154602},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.6196457147598267},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6063520908355713},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.529789388179779},{"id":"https://openalex.org/keywords/function-approximation","display_name":"Function approximation","score":0.4906250536441803},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.4623855650424957},{"id":"https://openalex.org/keywords/controller","display_name":"Controller (irrigation)","score":0.4571859538555145},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.41364115476608276},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4094022810459137},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.20553499460220337}],"concepts":[{"id":"https://openalex.org/C196978813","wikidata":"https://www.wikidata.org/wiki/Q3302775","display_name":"Hamilton\u2013Jacobi\u2013Bellman equation","level":3,"score":0.7563429474830627},{"id":"https://openalex.org/C111030470","wikidata":"https://www.wikidata.org/wiki/Q1430460","display_name":"Curse of dimensionality","level":2,"score":0.6990883350372314},{"id":"https://openalex.org/C97541855","wikidata":"https://www.wikidata.org/wiki/Q830687","display_name":"Reinforcement learning","level":2,"score":0.658279538154602},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.6196457147598267},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6063520908355713},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.529789388179779},{"id":"https://openalex.org/C91873725","wikidata":"https://www.wikidata.org/wiki/Q3445816","display_name":"Function approximation","level":3,"score":0.4906250536441803},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.4623855650424957},{"id":"https://openalex.org/C203479927","wikidata":"https://www.wikidata.org/wiki/Q5165939","display_name":"Controller (irrigation)","level":2,"score":0.4571859538555145},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.41364115476608276},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4094022810459137},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.20553499460220337},{"id":"https://openalex.org/C6557445","wikidata":"https://www.wikidata.org/wiki/Q173113","display_name":"Agronomy","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.0}],"mesh":[{"descriptor_ui":"D000465","descriptor_name":"Algorithms","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D000465","descriptor_name":"Algorithms","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D000465","descriptor_name":"Algorithms","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D003198","descriptor_name":"Computer Simulation","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D003198","descriptor_name":"Computer Simulation","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D003198","descriptor_name":"Computer Simulation","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D012054","descriptor_name":"Reinforcement, Psychology","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D012054","descriptor_name":"Reinforcement, Psychology","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D012054","descriptor_name":"Reinforcement, Psychology","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D016571","descriptor_name":"Neural Networks, Computer","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D016571","descriptor_name":"Neural Networks, Computer","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D016571","descriptor_name":"Neural Networks, Computer","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D017711","descriptor_name":"Nonlinear Dynamics","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D017711","descriptor_name":"Nonlinear Dynamics","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D017711","descriptor_name":"Nonlinear Dynamics","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true}],"locations_count":2,"locations":[{"id":"doi:10.1109/tcyb.2020.3028267","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcyb.2020.3028267","pdf_url":null,"source":{"id":"https://openalex.org/S4210191041","display_name":"IEEE Transactions on Cybernetics","issn_l":"2168-2267","issn":["2168-2267","2168-2275"],"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 Cybernetics","raw_type":"journal-article"},{"id":"pmid:33206615","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/33206615","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 cybernetics","raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G5262290504","display_name":null,"funder_award_id":"FA8750-15-2-0119","funder_id":"https://openalex.org/F4320333578","funder_display_name":"Office of the Under Secretary of Defense"}],"funders":[{"id":"https://openalex.org/F4320333578","display_name":"Office of the Under Secretary of Defense","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":39,"referenced_works":["https://openalex.org/W1167633088","https://openalex.org/W1808956822","https://openalex.org/W1979905340","https://openalex.org/W1983321045","https://openalex.org/W1983523797","https://openalex.org/W1994186360","https://openalex.org/W2019338681","https://openalex.org/W2035608030","https://openalex.org/W2074060273","https://openalex.org/W2099618002","https://openalex.org/W2103496339","https://openalex.org/W2108286682","https://openalex.org/W2117539524","https://openalex.org/W2151966330","https://openalex.org/W2152161277","https://openalex.org/W2160643434","https://openalex.org/W2191948661","https://openalex.org/W2338351427","https://openalex.org/W2460802106","https://openalex.org/W2787070120","https://openalex.org/W2791992027","https://openalex.org/W2795156925","https://openalex.org/W2908261578","https://openalex.org/W2941038413","https://openalex.org/W2962951766","https://openalex.org/W2963368541","https://openalex.org/W2976686511","https://openalex.org/W3000132382","https://openalex.org/W3000179003","https://openalex.org/W3003662551","https://openalex.org/W3011347165","https://openalex.org/W3013793781","https://openalex.org/W3019152138","https://openalex.org/W3019217877","https://openalex.org/W3021053030","https://openalex.org/W3032565176","https://openalex.org/W3046072112","https://openalex.org/W4298044389","https://openalex.org/W6747941106"],"related_works":["https://openalex.org/W2290858160","https://openalex.org/W1552483862","https://openalex.org/W2112014346","https://openalex.org/W4251016492","https://openalex.org/W2164674108","https://openalex.org/W2174882787","https://openalex.org/W2028614848","https://openalex.org/W2126977748","https://openalex.org/W3149091143","https://openalex.org/W4226145367"],"abstract_inverted_index":{"In":[0,112],"this":[1],"article,":[2],"a":[3,28,99,186,195],"decentralized":[4,62,164],"adaptive":[5],"optimal":[6,63,146,165,177],"controller":[7],"based":[8,205],"on":[9,206],"the":[10,39,45,61,76,78,113,127,135,138,145,151,163,169,176,182,202,207,212,223,226],"emerging":[11,51],"mean-field":[12],"game":[13],"(MFG)":[14],"and":[15,31,43,83,158,171,192,211],"self-organizing":[16,55,109,187],"neural":[17],"networks":[18],"(NNs)":[19],"has":[20,68,104,119,189,218],"been":[21,69,105,190,219],"developed":[22,106,114,196,227],"for":[23,65],"multiagent":[24],"systems":[25],"(MASs)":[26],"with":[27,54,108,156,175],"large":[29],"population":[30],"uncertain":[32],"dynamics.":[33],"This":[34],"design":[35],"can":[36,200],"effectively":[37],"break":[38],"\"curse":[40],"of":[41,137,225],"dimensionality\"":[42],"reduce":[44,181],"computational":[46,184],"complexity":[47],"by":[48,167],"appropriately":[49],"integrating":[50],"MFG":[52],"theory":[53],"NNs-based":[56],"reinforcement":[57],"learning":[58,126,150,209],"techniques.":[59],"First,":[60],"control":[64,166,178],"massive":[66],"MASs":[67],"formulated":[70],"into":[71,194],"an":[72],"MFG.":[73],"To":[74,180],"unfold":[75],"MFG,":[77],"coupled":[79],"Hamilton-Jacobian-Bellman":[80],"(HJB)":[81],"equation":[82,86,153],"Fokker-Planck-Kolmogorov":[84],"(FPK)":[85],"needed":[87],"to":[88,221],"be":[89],"solved":[90],"simultaneously,":[91],"which":[92],"is":[93],"challenging":[94],"in":[95],"real":[96],"time.":[97],"Therefore,":[98],"novel":[100],"actor-critic-mass":[101],"(ACM)":[102],"structure":[103,198],"along":[107,155,174],"NNs":[110,173],"subsequently.":[111],"ACM":[115,197],"structure,":[116],"each":[117],"agent":[118],"three":[120],"NNs,":[121],"including:":[122],"1)":[123],"mass":[124,128,172],"NN":[125,143,161,188],"MAS's":[129],"overall":[130],"behavior":[131],"via":[132],"online":[133],"estimating":[134,162],"solution":[136,154],"FPK":[139],"equation;":[140],"2)":[141],"critic":[142,170],"obtaining":[144],"cost":[147],"function":[148],"through":[149],"HJB":[152],"time;":[157],"3)":[159],"actor":[160],"using":[168],"theory.":[179],"NNs'":[183,203,208],"complexity,":[185],"adopted":[191],"integrated":[193],"that":[199],"adjust":[201],"architecture":[204],"performance":[210],"computation":[213],"cost.":[214],"Finally,":[215],"numerical":[216],"simulation":[217],"provided":[220],"demonstrate":[222],"effectiveness":[224],"schemes.":[228]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":8},{"year":2023,"cited_by_count":7},{"year":2022,"cited_by_count":7},{"year":2021,"cited_by_count":2}],"updated_date":"2026-04-03T22:45:19.894376","created_date":"2025-10-10T00:00:00"}