{"id":"https://openalex.org/W4409327176","doi":"https://doi.org/10.1109/tac.2025.3559743","title":"Two-Timescale Distributed Approach to Nash Equilibrium Seeking of Euler\u2013Lagrange Systems in Multicluster Nonconvex Games","display_name":"Two-Timescale Distributed Approach to Nash Equilibrium Seeking of Euler\u2013Lagrange Systems in Multicluster Nonconvex Games","publication_year":2025,"publication_date":"2025-04-10","ids":{"openalex":"https://openalex.org/W4409327176","doi":"https://doi.org/10.1109/tac.2025.3559743"},"language":"en","primary_location":{"id":"doi:10.1109/tac.2025.3559743","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2025.3559743","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"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 Automatic Control","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/A5067257866","display_name":"Banghua Huang","orcid":"https://orcid.org/0009-0000-8196-8977"},"institutions":[{"id":"https://openalex.org/I135237710","display_name":"Zhejiang Normal University","ror":"https://ror.org/01vevwk45","country_code":"CN","type":"education","lineage":["https://openalex.org/I135237710"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Banghua Huang","raw_affiliation_strings":["School of Mathematical Sciences, Zhejiang Normal University, Jinhua, China"],"raw_orcid":"https://orcid.org/0009-0000-8196-8977","affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Zhejiang Normal University, Jinhua, China","institution_ids":["https://openalex.org/I135237710"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Yang Liu","orcid":"https://orcid.org/0000-0003-3761-0104"},"institutions":[{"id":"https://openalex.org/I135237710","display_name":"Zhejiang Normal University","ror":"https://ror.org/01vevwk45","country_code":"CN","type":"education","lineage":["https://openalex.org/I135237710"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yang Liu","raw_affiliation_strings":["Zhejiang Key Laboratory of Intelligent Education Technology and Application, School of Mathematical Sciences, Zhejiang Normal University, Jinhua, China"],"raw_orcid":"https://orcid.org/0000-0003-3761-0104","affiliations":[{"raw_affiliation_string":"Zhejiang Key Laboratory of Intelligent Education Technology and Application, School of Mathematical Sciences, Zhejiang Normal University, Jinhua, China","institution_ids":["https://openalex.org/I135237710"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5049482611","display_name":"Jianquan Lu","orcid":"https://orcid.org/0000-0003-4423-6034"},"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":"Jianquan Lu","raw_affiliation_strings":["School of Mathematics, Southeast University, Nanjing, China"],"raw_orcid":"https://orcid.org/0000-0003-4423-6034","affiliations":[{"raw_affiliation_string":"School of Mathematics, Southeast University, Nanjing, China","institution_ids":["https://openalex.org/I76569877"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Yunliang Jiang","orcid":"https://orcid.org/0000-0003-4500-5836"},"institutions":[{"id":"https://openalex.org/I135237710","display_name":"Zhejiang Normal University","ror":"https://ror.org/01vevwk45","country_code":"CN","type":"education","lineage":["https://openalex.org/I135237710"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yunliang Jiang","raw_affiliation_strings":["Zhejiang Key Laboratory of Intelligent Education Technology and Application, School of Computer Science and Technology, Zhejiang Normal University, Jinhua, China"],"raw_orcid":"https://orcid.org/0000-0003-4500-5836","affiliations":[{"raw_affiliation_string":"Zhejiang Key Laboratory of Intelligent Education Technology and Application, School of Computer Science and Technology, Zhejiang Normal University, Jinhua, China","institution_ids":["https://openalex.org/I135237710"]}]},{"author_position":"last","author":{"id":null,"display_name":"Weihua Gui","orcid":"https://orcid.org/0000-0003-0312-436X"},"institutions":[{"id":"https://openalex.org/I139660479","display_name":"Central South University","ror":"https://ror.org/00f1zfq44","country_code":"CN","type":"education","lineage":["https://openalex.org/I139660479"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Weihua Gui","raw_affiliation_strings":["School of Automation, Central South University, Changsha, China"],"raw_orcid":"https://orcid.org/0000-0003-0312-436X","affiliations":[{"raw_affiliation_string":"School of Automation, Central South University, Changsha, China","institution_ids":["https://openalex.org/I139660479"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":8.8538,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.9798544,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":98,"max":99},"biblio":{"volume":"70","issue":"9","first_page":"6323","last_page":"6330"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.964900016784668,"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/T10545","display_name":"Optimization and Variational Analysis","score":0.964900016784668,"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/T12158","display_name":"Guidance and Control Systems","score":0.9592999815940857,"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"}},{"id":"https://openalex.org/T12137","display_name":"Economic theories and models","score":0.9473999738693237,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/nash-equilibrium","display_name":"Nash equilibrium","score":0.7398971319198608},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.49872493743896484},{"id":"https://openalex.org/keywords/cluster","display_name":"Cluster (spacecraft)","score":0.47289812564849854},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4636095464229584},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.4461897611618042},{"id":"https://openalex.org/keywords/epsilon-equilibrium","display_name":"Epsilon-equilibrium","score":0.41931307315826416},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.40129318833351135},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3674110472202301},{"id":"https://openalex.org/keywords/best-response","display_name":"Best response","score":0.2989037036895752}],"concepts":[{"id":"https://openalex.org/C46814582","wikidata":"https://www.wikidata.org/wiki/Q23389","display_name":"Nash equilibrium","level":2,"score":0.7398971319198608},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.49872493743896484},{"id":"https://openalex.org/C164866538","wikidata":"https://www.wikidata.org/wiki/Q367351","display_name":"Cluster (spacecraft)","level":2,"score":0.47289812564849854},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4636095464229584},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.4461897611618042},{"id":"https://openalex.org/C141824439","wikidata":"https://www.wikidata.org/wiki/Q307521","display_name":"Epsilon-equilibrium","level":4,"score":0.41931307315826416},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.40129318833351135},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3674110472202301},{"id":"https://openalex.org/C32407928","wikidata":"https://www.wikidata.org/wiki/Q2733833","display_name":"Best response","level":3,"score":0.2989037036895752},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tac.2025.3559743","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2025.3559743","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"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 Automatic Control","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1150634568","display_name":null,"funder_award_id":"U22A20102","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G455596764","display_name":null,"funder_award_id":"623B2018","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7323475582","display_name":null,"funder_award_id":"BK20240009","funder_id":"https://openalex.org/F4320322769","funder_display_name":"Natural Science Foundation of Jiangsu Province"},{"id":"https://openalex.org/G8498166285","display_name":null,"funder_award_id":"62173308","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"},{"id":"https://openalex.org/F4320322769","display_name":"Natural Science Foundation of Jiangsu Province","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":47,"referenced_works":["https://openalex.org/W1516681311","https://openalex.org/W1886742781","https://openalex.org/W1977794212","https://openalex.org/W2128658178","https://openalex.org/W2132450099","https://openalex.org/W2275030070","https://openalex.org/W2611964096","https://openalex.org/W2766719770","https://openalex.org/W2801481166","https://openalex.org/W2805316908","https://openalex.org/W2915026742","https://openalex.org/W2962910407","https://openalex.org/W2968630554","https://openalex.org/W3011550106","https://openalex.org/W3013955056","https://openalex.org/W3039554471","https://openalex.org/W3041493239","https://openalex.org/W3116605176","https://openalex.org/W3128631749","https://openalex.org/W3128815919","https://openalex.org/W3135910512","https://openalex.org/W3174070171","https://openalex.org/W3175177495","https://openalex.org/W3213724282","https://openalex.org/W3216879630","https://openalex.org/W3217547593","https://openalex.org/W4210243579","https://openalex.org/W4210505829","https://openalex.org/W4213421918","https://openalex.org/W4226362429","https://openalex.org/W4288708237","https://openalex.org/W4293254212","https://openalex.org/W4312782641","https://openalex.org/W4312928653","https://openalex.org/W4319866015","https://openalex.org/W4320018417","https://openalex.org/W4320170208","https://openalex.org/W4361758024","https://openalex.org/W4365516025","https://openalex.org/W4379659740","https://openalex.org/W4384080289","https://openalex.org/W4384819646","https://openalex.org/W4385782893","https://openalex.org/W4390576316","https://openalex.org/W4390970494","https://openalex.org/W4398226311","https://openalex.org/W4399485094"],"related_works":["https://openalex.org/W4302558842","https://openalex.org/W1554758635","https://openalex.org/W2282604764","https://openalex.org/W2500870930","https://openalex.org/W1721270588","https://openalex.org/W2569414037","https://openalex.org/W4389370903","https://openalex.org/W2803931294","https://openalex.org/W3125137934","https://openalex.org/W2010679956"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3],"investigate":[4],"a":[5,51,61,79,91,122,125,133],"distributed":[6],"generalized":[7],"Nash":[8],"equilibrium":[9],"(GNE)":[10],"seeking":[11],"problem":[12,127],"for":[13,84],"multi-cluster":[14,29,33,85],"games,":[15],"where":[16],"each":[17],"cluster":[18,52],"consists":[19],"of":[20,26,74,107,115,140],"multiple":[21],"players.":[22],"Different":[23],"from":[24],"most":[25],"the":[27,32,71,105,108,116,138,141],"existing":[28],"game":[30,135],"studies,":[31],"games":[34],"considered":[35],"nonconvex":[36,39,86],"cost":[37,72],"functions,":[38],"(coupled)":[40,45],"inequality":[41],"constraints,":[42],"and":[43,54,132],"nonaffine":[44],"equality":[46],"constraints.":[47],"Each":[48],"player":[49],"in":[50,94,128],"communicates":[53],"cooperates":[55],"with":[56,110],"other":[57],"players":[58,96],"based":[59],"on":[60,121],"directed":[62],"connected":[63],"network":[64],"to":[65,113,136],"make":[66],"optimal":[67],"actions":[68],"that":[69],"minimize":[70],"function":[73],"their":[75],"cluster.":[76],"We":[77,88,103,119],"propose":[78,90],"two-timescale":[80,92],"multi-agent":[81],"system":[82],"(MAS)":[83],"games.":[87],"further":[89],"MAS":[93,109],"which":[95],"are":[97],"formulated":[98],"by":[99],"Euler-Lagrange":[100],"(EL)":[101],"dynamics.":[102],"prove":[104],"convergence":[106],"derived":[111],"conditions":[112],"one":[114],"local":[117],"GNEs.":[118],"elaborate":[120],"numerical":[123],"example,":[124],"price-bidding":[126],"an":[129],"electricity":[130],"market,":[131],"Nash-Cournot":[134],"illustrate":[137],"characteristics":[139],"proposed":[142],"approach.":[143]},"counts_by_year":[{"year":2026,"cited_by_count":5},{"year":2025,"cited_by_count":5}],"updated_date":"2026-03-27T05:58:40.876381","created_date":"2025-10-10T00:00:00"}