{"id":"https://openalex.org/W2793015019","doi":"https://doi.org/10.1080/00207179.2018.1441550","title":"Non-zero sum differential graphical game: cluster synchronisation for multi-agents with partially unknown dynamics","display_name":"Non-zero sum differential graphical game: cluster synchronisation for multi-agents with partially unknown dynamics","publication_year":2018,"publication_date":"2018-03-14","ids":{"openalex":"https://openalex.org/W2793015019","doi":"https://doi.org/10.1080/00207179.2018.1441550","mag":"2793015019"},"language":"en","primary_location":{"id":"doi:10.1080/00207179.2018.1441550","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207179.2018.1441550","pdf_url":null,"source":{"id":"https://openalex.org/S88061139","display_name":"International Journal of Control","issn_l":"0020-7179","issn":["0020-7179","1366-5820"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of 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/A5103235005","display_name":"Ni Yang","orcid":"https://orcid.org/0000-0002-6550-3659"},"institutions":[{"id":"https://openalex.org/I47720641","display_name":"Huazhong University of Science and Technology","ror":"https://ror.org/00p991c53","country_code":"CN","type":"education","lineage":["https://openalex.org/I47720641"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Ni Yang","raw_affiliation_strings":["Key Laboratory of Image Processing and Intelligent Control, Huazhong University of Science and Technology, Ministry of Education , Wuhan, China","School of Automation, Huazhong University of Science and Technology , Wuhan, China","Key Laboratory of Image Processing and Intelligent Control, Huazhong University of Science and Technology, Ministry of Education\n, Wuhan, China","School of Automation, Huazhong University of Science and Technology\n, Wuhan, China"],"affiliations":[{"raw_affiliation_string":"Key Laboratory of Image Processing and Intelligent Control, Huazhong University of Science and Technology, Ministry of Education , Wuhan, China","institution_ids":["https://openalex.org/I47720641"]},{"raw_affiliation_string":"School of Automation, Huazhong University of Science and Technology , Wuhan, China","institution_ids":["https://openalex.org/I47720641"]},{"raw_affiliation_string":"Key Laboratory of Image Processing and Intelligent Control, Huazhong University of Science and Technology, Ministry of Education\n, Wuhan, China","institution_ids":["https://openalex.org/I47720641"]},{"raw_affiliation_string":"School of Automation, Huazhong University of Science and Technology\n, Wuhan, China","institution_ids":["https://openalex.org/I47720641"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5043748803","display_name":"Jiang\u2010Wen Xiao","orcid":"https://orcid.org/0000-0002-8708-2920"},"institutions":[{"id":"https://openalex.org/I47720641","display_name":"Huazhong University of Science and Technology","ror":"https://ror.org/00p991c53","country_code":"CN","type":"education","lineage":["https://openalex.org/I47720641"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Jiang-Wen Xiao","raw_affiliation_strings":["Key Laboratory of Image Processing and Intelligent Control, Huazhong University of Science and Technology, Ministry of Education , Wuhan, China","School of Automation, Huazhong University of Science and Technology , Wuhan, China","School of Automation, Huazhong University of Science and Technology\n, Wuhan, China","Key Laboratory of Image Processing and Intelligent Control, Huazhong University of Science and Technology, Ministry of Education\n, Wuhan, China"],"affiliations":[{"raw_affiliation_string":"Key Laboratory of Image Processing and Intelligent Control, Huazhong University of Science and Technology, Ministry of Education , Wuhan, China","institution_ids":["https://openalex.org/I47720641"]},{"raw_affiliation_string":"School of Automation, Huazhong University of Science and Technology , Wuhan, China","institution_ids":["https://openalex.org/I47720641"]},{"raw_affiliation_string":"School of Automation, Huazhong University of Science and Technology\n, Wuhan, China","institution_ids":["https://openalex.org/I47720641"]},{"raw_affiliation_string":"Key Laboratory of Image Processing and Intelligent Control, Huazhong University of Science and Technology, Ministry of Education\n, Wuhan, China","institution_ids":["https://openalex.org/I47720641"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100654885","display_name":"Li Xiao","orcid":"https://orcid.org/0000-0002-3063-0869"},"institutions":[{"id":"https://openalex.org/I47720641","display_name":"Huazhong University of Science and Technology","ror":"https://ror.org/00p991c53","country_code":"CN","type":"education","lineage":["https://openalex.org/I47720641"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Li Xiao","raw_affiliation_strings":["Key Laboratory of Image Processing and Intelligent Control, Huazhong University of Science and Technology, Ministry of Education , Wuhan, China","School of Automation, Huazhong University of Science and Technology , Wuhan, China","School of Automation, Huazhong University of Science and Technology\n, Wuhan, China","Key Laboratory of Image Processing and Intelligent Control, Huazhong University of Science and Technology, Ministry of Education\n, Wuhan, China"],"affiliations":[{"raw_affiliation_string":"Key Laboratory of Image Processing and Intelligent Control, Huazhong University of Science and Technology, Ministry of Education , Wuhan, China","institution_ids":["https://openalex.org/I47720641"]},{"raw_affiliation_string":"School of Automation, Huazhong University of Science and Technology , Wuhan, China","institution_ids":["https://openalex.org/I47720641"]},{"raw_affiliation_string":"School of Automation, Huazhong University of Science and Technology\n, Wuhan, China","institution_ids":["https://openalex.org/I47720641"]},{"raw_affiliation_string":"Key Laboratory of Image Processing and Intelligent Control, Huazhong University of Science and Technology, Ministry of Education\n, Wuhan, China","institution_ids":["https://openalex.org/I47720641"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5090447443","display_name":"Yan\u2010Wu Wang","orcid":"https://orcid.org/0000-0002-4722-1332"},"institutions":[{"id":"https://openalex.org/I47720641","display_name":"Huazhong University of Science and Technology","ror":"https://ror.org/00p991c53","country_code":"CN","type":"education","lineage":["https://openalex.org/I47720641"]},{"id":"https://openalex.org/I161350542","display_name":"China Three Gorges University","ror":"https://ror.org/0419nfc77","country_code":"CN","type":"education","lineage":["https://openalex.org/I161350542"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yan-Wu Wang","raw_affiliation_strings":["Hubei Provincial Collaborative Innovation Center for New Energy Microgrid, China Three Gorges University , Yichang, China","Key Laboratory of Image Processing and Intelligent Control, Huazhong University of Science and Technology, Ministry of Education , Wuhan, China","School of Automation, Huazhong University of Science and Technology , Wuhan, China","Key Laboratory of Image Processing and Intelligent Control, Huazhong University of Science and Technology, Ministry of Education\n, Wuhan, China","Hubei Provincial Collaborative Innovation Center for New Energy Microgrid, China Three Gorges University\n, Yichang, China","School of Automation, Huazhong University of Science and Technology\n, Wuhan, China"],"affiliations":[{"raw_affiliation_string":"Hubei Provincial Collaborative Innovation Center for New Energy Microgrid, China Three Gorges University , Yichang, China","institution_ids":["https://openalex.org/I161350542"]},{"raw_affiliation_string":"Key Laboratory of Image Processing and Intelligent Control, Huazhong University of Science and Technology, Ministry of Education , Wuhan, China","institution_ids":["https://openalex.org/I47720641"]},{"raw_affiliation_string":"School of Automation, Huazhong University of Science and Technology , Wuhan, China","institution_ids":["https://openalex.org/I47720641"]},{"raw_affiliation_string":"Key Laboratory of Image Processing and Intelligent Control, Huazhong University of Science and Technology, Ministry of Education\n, Wuhan, China","institution_ids":["https://openalex.org/I47720641"]},{"raw_affiliation_string":"Hubei Provincial Collaborative Innovation Center for New Energy Microgrid, China Three Gorges University\n, Yichang, China","institution_ids":["https://openalex.org/I161350542"]},{"raw_affiliation_string":"School of Automation, Huazhong University of Science and Technology\n, Wuhan, China","institution_ids":["https://openalex.org/I47720641"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5043748803"],"corresponding_institution_ids":["https://openalex.org/I47720641"],"apc_list":null,"apc_paid":null,"fwci":0.4039,"has_fulltext":false,"cited_by_count":12,"citation_normalized_percentile":{"value":0.61531729,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"92","issue":"10","first_page":"2408","last_page":"2419"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12794","display_name":"Adaptive Dynamic Programming Control","score":0.9998999834060669,"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":0.9998999834060669,"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/T11347","display_name":"Neural Networks Stability and Synchronization","score":0.9894000291824341,"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/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.9840999841690063,"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":0.6624971032142639},{"id":"https://openalex.org/keywords/nash-equilibrium","display_name":"Nash equilibrium","score":0.6210654377937317},{"id":"https://openalex.org/keywords/residual","display_name":"Residual","score":0.5639622211456299},{"id":"https://openalex.org/keywords/zero-sum-game","display_name":"Zero-sum game","score":0.5528490543365479},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5517942905426025},{"id":"https://openalex.org/keywords/differential-game","display_name":"Differential game","score":0.49874305725097656},{"id":"https://openalex.org/keywords/controller","display_name":"Controller (irrigation)","score":0.4966731667518616},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4883977770805359},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.48073673248291016},{"id":"https://openalex.org/keywords/cluster","display_name":"Cluster (spacecraft)","score":0.4760308563709259},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.4418773949146271},{"id":"https://openalex.org/keywords/zero","display_name":"Zero (linguistics)","score":0.43755874037742615},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.3050714135169983},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.24118572473526},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.12102991342544556}],"concepts":[{"id":"https://openalex.org/C196978813","wikidata":"https://www.wikidata.org/wiki/Q3302775","display_name":"Hamilton\u2013Jacobi\u2013Bellman equation","level":3,"score":0.6624971032142639},{"id":"https://openalex.org/C46814582","wikidata":"https://www.wikidata.org/wiki/Q23389","display_name":"Nash equilibrium","level":2,"score":0.6210654377937317},{"id":"https://openalex.org/C155512373","wikidata":"https://www.wikidata.org/wiki/Q287450","display_name":"Residual","level":2,"score":0.5639622211456299},{"id":"https://openalex.org/C136356330","wikidata":"https://www.wikidata.org/wiki/Q156612","display_name":"Zero-sum game","level":3,"score":0.5528490543365479},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5517942905426025},{"id":"https://openalex.org/C2779006483","wikidata":"https://www.wikidata.org/wiki/Q1973196","display_name":"Differential game","level":2,"score":0.49874305725097656},{"id":"https://openalex.org/C203479927","wikidata":"https://www.wikidata.org/wiki/Q5165939","display_name":"Controller (irrigation)","level":2,"score":0.4966731667518616},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4883977770805359},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.48073673248291016},{"id":"https://openalex.org/C164866538","wikidata":"https://www.wikidata.org/wiki/Q367351","display_name":"Cluster (spacecraft)","level":2,"score":0.4760308563709259},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.4418773949146271},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.43755874037742615},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.3050714135169983},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.24118572473526},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.12102991342544556},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"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/C6557445","wikidata":"https://www.wikidata.org/wiki/Q173113","display_name":"Agronomy","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/00207179.2018.1441550","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207179.2018.1441550","pdf_url":null,"source":{"id":"https://openalex.org/S88061139","display_name":"International Journal of Control","issn_l":"0020-7179","issn":["0020-7179","1366-5820"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Control","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G5314092097","display_name":null,"funder_award_id":"**","funder_id":"https://openalex.org/F4320321760","funder_display_name":"Henan University of Science and Technology"},{"id":"https://openalex.org/G6684674032","display_name":null,"funder_award_id":"2017CFA035","funder_id":"https://openalex.org/F4320322186","funder_display_name":"Natural Science Foundation of Hubei Province"},{"id":"https://openalex.org/G7154922941","display_name":null,"funder_award_id":"61572210, 61773172, 51537003","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/F4320321760","display_name":"Henan University of Science and Technology","ror":"https://ror.org/05d80kz58"},{"id":"https://openalex.org/F4320322186","display_name":"Natural Science Foundation of Hubei Province","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":46,"referenced_works":["https://openalex.org/W620104706","https://openalex.org/W1581842928","https://openalex.org/W1659904137","https://openalex.org/W1689905572","https://openalex.org/W1985131825","https://openalex.org/W1997603681","https://openalex.org/W2009702937","https://openalex.org/W2019338681","https://openalex.org/W2020688906","https://openalex.org/W2032631296","https://openalex.org/W2045719273","https://openalex.org/W2047202704","https://openalex.org/W2052399669","https://openalex.org/W2058626170","https://openalex.org/W2086977346","https://openalex.org/W2088103590","https://openalex.org/W2092715413","https://openalex.org/W2100276679","https://openalex.org/W2108383324","https://openalex.org/W2112103082","https://openalex.org/W2132468772","https://openalex.org/W2151852050","https://openalex.org/W2195304191","https://openalex.org/W2198330444","https://openalex.org/W2203860294","https://openalex.org/W2214195367","https://openalex.org/W2214884926","https://openalex.org/W2249513906","https://openalex.org/W2299109138","https://openalex.org/W2320262435","https://openalex.org/W2331370928","https://openalex.org/W2342560477","https://openalex.org/W2342894696","https://openalex.org/W2405379562","https://openalex.org/W2417285541","https://openalex.org/W2467991260","https://openalex.org/W2489475604","https://openalex.org/W2499611642","https://openalex.org/W2511759575","https://openalex.org/W2531648764","https://openalex.org/W2539264244","https://openalex.org/W2556654037","https://openalex.org/W2767784613","https://openalex.org/W2963609304","https://openalex.org/W3016369786","https://openalex.org/W3103127108"],"related_works":["https://openalex.org/W4251016492","https://openalex.org/W2112014346","https://openalex.org/W2767031889","https://openalex.org/W2174882787","https://openalex.org/W2028614848","https://openalex.org/W2126977748","https://openalex.org/W2978027790","https://openalex.org/W4226145367","https://openalex.org/W3035072031","https://openalex.org/W3011680666"],"abstract_inverted_index":{"This":[0],"paper":[1],"investigates":[2],"the":[3,26,35,39,46,52,56,63,67,92,95,101,108,113,120,126,136,139],"cluster":[4,27,42],"synchronisation":[5,28],"problem":[6,58,64],"for":[7],"multi-agent":[8,53],"non-zero":[9],"sum":[10],"differential":[11],"game":[12],"with":[13,84,97,107],"partially":[14,98],"unknown":[15,99],"dynamics.":[16],"The":[17],"objective":[18],"is":[19,82,132],"to":[20,24,30,134],"design":[21],"a":[22,77],"controller":[23],"achieve":[25],"and":[29,45,119],"ensure":[31],"local":[32],"optimality":[33],"of":[34,41,48,65,94,103,116,138],"performance":[36],"index.":[37],"With":[38],"definition":[40],"tracking":[43],"error":[44],"concept":[47],"Nash":[49],"equilibrium":[50],"in":[51,91],"system":[54,109,117],"(MAS),":[55],"previous":[57],"can":[59],"be":[60],"transformed":[61],"into":[62],"solving":[66],"coupled":[68],"Hamilton\u2013Jacobi\u2013Bellman":[69],"(HJB)":[70],"equations.":[71],"To":[72],"solve":[73],"these":[74],"HJB":[75],"equations,":[76],"data-based":[78],"policy":[79],"iteration":[80],"algorithm":[81],"proposed":[83,140],"an":[85],"actor\u2013critic":[86],"neural":[87],"network":[88],"(NN)":[89],"structure":[90],"case":[93],"MAS":[96],"dynamics;":[100],"weights":[102],"NNs":[104],"are":[105,123],"updated":[106],"data":[110],"rather":[111],"than":[112],"complete":[114],"knowledge":[115],"dynamics":[118],"residual":[121],"errors":[122],"minimised":[124],"using":[125],"least-square":[127],"approach.":[128,141],"A":[129],"simulation":[130],"example":[131],"provided":[133],"verify":[135],"effectiveness":[137]},"counts_by_year":[{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":3},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
