{"id":"https://openalex.org/W4220671480","doi":"https://doi.org/10.1109/tcns.2022.3161194","title":"A Fully Distributed Nash Equilibrium Seeking Algorithm for N-Coalition Games of Euler\u2013Lagrange Players","display_name":"A Fully Distributed Nash Equilibrium Seeking Algorithm for N-Coalition Games of Euler\u2013Lagrange Players","publication_year":2022,"publication_date":"2022-03-23","ids":{"openalex":"https://openalex.org/W4220671480","doi":"https://doi.org/10.1109/tcns.2022.3161194"},"language":"en","primary_location":{"id":"doi:10.1109/tcns.2022.3161194","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcns.2022.3161194","pdf_url":null,"source":{"id":"https://openalex.org/S2502544478","display_name":"IEEE Transactions on Control of Network Systems","issn_l":"2325-5870","issn":["2325-5870","2372-2533"],"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 Control of Network 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/A5089108915","display_name":"Te Ma","orcid":"https://orcid.org/0000-0001-5733-6160"},"institutions":[{"id":"https://openalex.org/I2801618472","display_name":"PLA Rocket Force University of Engineering","ror":"https://ror.org/00gg5zj35","country_code":"CN","type":"education","lineage":["https://openalex.org/I2801618472"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Te Ma","raw_affiliation_strings":["Rocket Force University of Enginee- ring, Xi’an, China"],"raw_orcid":"https://orcid.org/0000-0001-5733-6160","affiliations":[{"raw_affiliation_string":"Rocket Force University of Enginee- ring, Xi’an, China","institution_ids":["https://openalex.org/I2801618472"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5057995398","display_name":"Zhenhua Deng","orcid":"https://orcid.org/0000-0001-7225-5238"},"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":"Zhenhua Deng","raw_affiliation_strings":["School of Automation, Central South University, Changsha, China"],"raw_orcid":"https://orcid.org/0000-0001-7225-5238","affiliations":[{"raw_affiliation_string":"School of Automation, Central South University, Changsha, China","institution_ids":["https://openalex.org/I139660479"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5018178311","display_name":"Chen Hu","orcid":"https://orcid.org/0000-0001-6587-4225"},"institutions":[{"id":"https://openalex.org/I2801618472","display_name":"PLA Rocket Force University of Engineering","ror":"https://ror.org/00gg5zj35","country_code":"CN","type":"education","lineage":["https://openalex.org/I2801618472"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Chen Hu","raw_affiliation_strings":["Rocket Force University of Enginee- ring, Xi’an, China"],"raw_orcid":"https://orcid.org/0000-0001-6587-4225","affiliations":[{"raw_affiliation_string":"Rocket Force University of Enginee- ring, Xi’an, China","institution_ids":["https://openalex.org/I2801618472"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.7373,"has_fulltext":false,"cited_by_count":29,"citation_normalized_percentile":{"value":0.90054351,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"10","issue":"1","first_page":"205","last_page":"213"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10249","display_name":"Distributed Control Multi-Agent Systems","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/T10249","display_name":"Distributed Control Multi-Agent Systems","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/T12794","display_name":"Adaptive Dynamic Programming Control","score":0.9934999942779541,"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/T10482","display_name":"Mathematical and Theoretical Epidemiology and Ecology Models","score":0.9771999716758728,"subfield":{"id":"https://openalex.org/subfields/2739","display_name":"Public Health, Environmental and Occupational Health"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/nash-equilibrium","display_name":"Nash equilibrium","score":0.6930935382843018},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5793787837028503},{"id":"https://openalex.org/keywords/lyapunov-function","display_name":"Lyapunov function","score":0.5543215870857239},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4902413487434387},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4748782515525818},{"id":"https://openalex.org/keywords/state","display_name":"State (computer science)","score":0.46430259943008423},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.46081632375717163},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.41321006417274475},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.25994545221328735},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.1300155222415924},{"id":"https://openalex.org/keywords/economics","display_name":"Economics","score":0.10431322455406189}],"concepts":[{"id":"https://openalex.org/C46814582","wikidata":"https://www.wikidata.org/wiki/Q23389","display_name":"Nash equilibrium","level":2,"score":0.6930935382843018},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5793787837028503},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.5543215870857239},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4902413487434387},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4748782515525818},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.46430259943008423},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.46081632375717163},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.41321006417274475},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.25994545221328735},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.1300155222415924},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.10431322455406189},{"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tcns.2022.3161194","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcns.2022.3161194","pdf_url":null,"source":{"id":"https://openalex.org/S2502544478","display_name":"IEEE Transactions on Control of Network Systems","issn_l":"2325-5870","issn":["2325-5870","2372-2533"],"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 Control of Network Systems","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16","score":0.4699999988079071}],"awards":[{"id":"https://openalex.org/G5084387563","display_name":null,"funder_award_id":"61803385","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5897570712","display_name":null,"funder_award_id":"2019JJ50754","funder_id":"https://openalex.org/F4320322843","funder_display_name":"Natural Science Foundation of\u00a0Hunan Province"},{"id":"https://openalex.org/G8578155771","display_name":null,"funder_award_id":"61403120406","funder_id":"https://openalex.org/F4320325551","funder_display_name":"National Defense Pre-Research 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/F4320322843","display_name":"Natural Science Foundation of\u00a0Hunan Province","ror":null},{"id":"https://openalex.org/F4320325551","display_name":"National Defense Pre-Research Foundation of China","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":37,"referenced_works":["https://openalex.org/W1195279777","https://openalex.org/W1490458594","https://openalex.org/W1977794212","https://openalex.org/W2007926026","https://openalex.org/W2042860072","https://openalex.org/W2053842902","https://openalex.org/W2056226204","https://openalex.org/W2057929279","https://openalex.org/W2089940759","https://openalex.org/W2117618281","https://openalex.org/W2128658178","https://openalex.org/W2137435346","https://openalex.org/W2140208620","https://openalex.org/W2251632681","https://openalex.org/W2282594424","https://openalex.org/W2345998142","https://openalex.org/W2592202249","https://openalex.org/W2611964096","https://openalex.org/W2805316908","https://openalex.org/W2901460157","https://openalex.org/W2915026742","https://openalex.org/W2919725712","https://openalex.org/W2981565778","https://openalex.org/W3021573557","https://openalex.org/W3039554471","https://openalex.org/W3088637899","https://openalex.org/W3094173350","https://openalex.org/W3102274955","https://openalex.org/W3104002866","https://openalex.org/W3120365745","https://openalex.org/W3128815919","https://openalex.org/W4238591275","https://openalex.org/W4245550013","https://openalex.org/W4249513058","https://openalex.org/W4301791716","https://openalex.org/W4321441990","https://openalex.org/W6782991008"],"related_works":["https://openalex.org/W4210735314","https://openalex.org/W2092374696","https://openalex.org/W1705316893","https://openalex.org/W1517908938","https://openalex.org/W2129581964","https://openalex.org/W4315489088","https://openalex.org/W2375947969","https://openalex.org/W2047874730","https://openalex.org/W2142757154","https://openalex.org/W1518233575"],"abstract_inverted_index":{"This":[0],"article":[1],"investigates":[2],"the":[3,11,41,48,51,56,59,87,117,122,136,139],"N-coalition":[4,109],"games":[5,110],"of":[6,16,19,30,43,47,70,89,116,138],"Euler\u2013Lagrange":[7],"(EL)":[8],"systems.":[9],"In":[10],"games,":[12],"every":[13],"coalition":[14,32,60],"consists":[15],"a":[17,101],"group":[18],"players,":[20],"whose":[21],"dynamics":[22],"are":[23],"formulated":[24],"as":[25],"EL":[26],"equations.":[27],"The":[28,67,113],"objective":[29],"each":[31,71],"is":[33,40,73,111,119,132],"to":[34,76,134],"minimize":[35,62],"its":[36,83],"cost":[37,45,65,68],"function,":[38],"which":[39],"sum":[42],"local":[44],"functions":[46],"players":[49,57],"in":[50,129],"corresponding":[52],"coalition.":[53],"That":[54],"is,":[55],"within":[58],"collaboratively":[61],"their":[63],"coalition\u2019s":[64],"function.":[66],"function":[69],"player":[72],"only":[74,82],"available":[75],"itself":[77],"and":[78,98],"depends":[79],"on":[80,93],"not":[81],"decision,":[84],"but":[85],"also":[86],"aggregate":[88],"all":[90],"decisions.":[91],"Based":[92],"gradient":[94],"descent,":[95],"consensus":[96],"technique,":[97],"state":[99],"feedback,":[100],"fully":[102],"distributed":[103],"Nash":[104],"equilibrium":[105],"seeking":[106],"algorithm":[107,118],"for":[108],"proposed.":[112],"exponential":[114],"convergence":[115],"analyzed":[120],"by":[121],"Lyapunov":[123],"stability":[124],"theorem.":[125],"A":[126],"numerical":[127],"example":[128],"smart":[130],"grids":[131],"given":[133],"illustrate":[135],"effectiveness":[137],"proposed":[140],"algorithm.":[141]},"counts_by_year":[{"year":2026,"cited_by_count":5},{"year":2025,"cited_by_count":9},{"year":2024,"cited_by_count":12},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1}],"updated_date":"2026-08-08T07:41:36.138363","created_date":"2025-10-10T00:00:00"}