{"id":"https://openalex.org/W4388676586","doi":"https://doi.org/10.1109/tcns.2023.3332747","title":"Formation Tracking in Noncooperative Game-Theoretic Framework","display_name":"Formation Tracking in Noncooperative Game-Theoretic Framework","publication_year":2023,"publication_date":"2023-11-14","ids":{"openalex":"https://openalex.org/W4388676586","doi":"https://doi.org/10.1109/tcns.2023.3332747"},"language":"en","primary_location":{"id":"doi:10.1109/tcns.2023.3332747","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcns.2023.3332747","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/A5066466328","display_name":"Cheng Yuwen","orcid":"https://orcid.org/0000-0001-8456-1646"},"institutions":[{"id":"https://openalex.org/I9842412","display_name":"Nanjing University of Aeronautics and Astronautics","ror":"https://ror.org/01scyh794","country_code":"CN","type":"education","lineage":["https://openalex.org/I9842412"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Cheng Yuwen","raw_affiliation_strings":["College of Automatic Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing, China"],"raw_orcid":"https://orcid.org/0000-0001-8456-1646","affiliations":[{"raw_affiliation_string":"College of Automatic Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing, China","institution_ids":["https://openalex.org/I9842412"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5016583158","display_name":"Ziyang Zhen","orcid":"https://orcid.org/0000-0002-8498-7206"},"institutions":[{"id":"https://openalex.org/I9842412","display_name":"Nanjing University of Aeronautics and Astronautics","ror":"https://ror.org/01scyh794","country_code":"CN","type":"education","lineage":["https://openalex.org/I9842412"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Ziyang Zhen","raw_affiliation_strings":["College of Automatic Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing, China"],"raw_orcid":"https://orcid.org/0000-0002-8498-7206","affiliations":[{"raw_affiliation_string":"College of Automatic Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing, China","institution_ids":["https://openalex.org/I9842412"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5000618529","display_name":"Liangdong Wen","orcid":"https://orcid.org/0000-0003-4688-9477"},"institutions":[{"id":"https://openalex.org/I9842412","display_name":"Nanjing University of Aeronautics and Astronautics","ror":"https://ror.org/01scyh794","country_code":"CN","type":"education","lineage":["https://openalex.org/I9842412"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Liangdong Wen","raw_affiliation_strings":["College of Automatic Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing, China"],"raw_orcid":"https://orcid.org/0000-0003-4688-9477","affiliations":[{"raw_affiliation_string":"College of Automatic Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing, China","institution_ids":["https://openalex.org/I9842412"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5066466328"],"corresponding_institution_ids":["https://openalex.org/I9842412"],"apc_list":null,"apc_paid":null,"fwci":1.1805,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.80558783,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":98},"biblio":{"volume":"11","issue":"2","first_page":"1056","last_page":"1066"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10249","display_name":"Distributed Control Multi-Agent Systems","score":0.9998999834060669,"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":0.9998999834060669,"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/T10482","display_name":"Mathematical and Theoretical Epidemiology and Ecology Models","score":0.9988999962806702,"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"}},{"id":"https://openalex.org/T11829","display_name":"Mathematical Biology Tumor Growth","score":0.9980999827384949,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/nash-equilibrium","display_name":"Nash equilibrium","score":0.8640820980072021},{"id":"https://openalex.org/keywords/lyapunov-function","display_name":"Lyapunov function","score":0.5781232714653015},{"id":"https://openalex.org/keywords/epsilon-equilibrium","display_name":"Epsilon-equilibrium","score":0.56830233335495},{"id":"https://openalex.org/keywords/sequential-game","display_name":"Sequential game","score":0.5506972670555115},{"id":"https://openalex.org/keywords/equilibrium-selection","display_name":"Equilibrium selection","score":0.5425399541854858},{"id":"https://openalex.org/keywords/equilibrium-point","display_name":"Equilibrium point","score":0.5075536966323853},{"id":"https://openalex.org/keywords/double-integrator","display_name":"Double integrator","score":0.4969201385974884},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4959579408168793},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.48715898394584656},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4770737886428833},{"id":"https://openalex.org/keywords/best-response","display_name":"Best response","score":0.4737741947174072},{"id":"https://openalex.org/keywords/game-theory","display_name":"Game theory","score":0.46556758880615234},{"id":"https://openalex.org/keywords/system-dynamics","display_name":"System dynamics","score":0.428242027759552},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.41082876920700073},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.38579219579696655},{"id":"https://openalex.org/keywords/repeated-game","display_name":"Repeated game","score":0.38381722569465637},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.37434542179107666},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.24284490942955017},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.11452507972717285},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.06966224312782288}],"concepts":[{"id":"https://openalex.org/C46814582","wikidata":"https://www.wikidata.org/wiki/Q23389","display_name":"Nash equilibrium","level":2,"score":0.8640820980072021},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.5781232714653015},{"id":"https://openalex.org/C141824439","wikidata":"https://www.wikidata.org/wiki/Q307521","display_name":"Epsilon-equilibrium","level":4,"score":0.56830233335495},{"id":"https://openalex.org/C73795354","wikidata":"https://www.wikidata.org/wiki/Q287618","display_name":"Sequential game","level":3,"score":0.5506972670555115},{"id":"https://openalex.org/C164407509","wikidata":"https://www.wikidata.org/wiki/Q5384490","display_name":"Equilibrium selection","level":4,"score":0.5425399541854858},{"id":"https://openalex.org/C94766913","wikidata":"https://www.wikidata.org/wiki/Q1530271","display_name":"Equilibrium point","level":3,"score":0.5075536966323853},{"id":"https://openalex.org/C2779323837","wikidata":"https://www.wikidata.org/wiki/Q5300045","display_name":"Double integrator","level":3,"score":0.4969201385974884},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4959579408168793},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.48715898394584656},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4770737886428833},{"id":"https://openalex.org/C32407928","wikidata":"https://www.wikidata.org/wiki/Q2733833","display_name":"Best response","level":3,"score":0.4737741947174072},{"id":"https://openalex.org/C177142836","wikidata":"https://www.wikidata.org/wiki/Q44455","display_name":"Game theory","level":2,"score":0.46556758880615234},{"id":"https://openalex.org/C77405623","wikidata":"https://www.wikidata.org/wiki/Q598451","display_name":"System dynamics","level":2,"score":0.428242027759552},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.41082876920700073},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.38579219579696655},{"id":"https://openalex.org/C202556891","wikidata":"https://www.wikidata.org/wiki/Q1584646","display_name":"Repeated game","level":3,"score":0.38381722569465637},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.37434542179107666},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.24284490942955017},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.11452507972717285},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.06966224312782288},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"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/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","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},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tcns.2023.3332747","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcns.2023.3332747","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":[{"score":0.699999988079071,"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16"}],"awards":[{"id":"https://openalex.org/G8339948675","display_name":null,"funder_award_id":"61973158","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8903107056","display_name":null,"funder_award_id":"NZ2019008","funder_id":"https://openalex.org/F4320335787","funder_display_name":"Fundamental Research Funds for the Central Universities"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320335787","display_name":"Fundamental Research Funds for the Central Universities","ror":null}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":32,"referenced_works":["https://openalex.org/W1630241696","https://openalex.org/W1658402581","https://openalex.org/W1970786657","https://openalex.org/W1972221945","https://openalex.org/W1977098392","https://openalex.org/W1981826826","https://openalex.org/W2008516441","https://openalex.org/W2036571133","https://openalex.org/W2088995751","https://openalex.org/W2092374696","https://openalex.org/W2099175737","https://openalex.org/W2105555541","https://openalex.org/W2107306424","https://openalex.org/W2119120935","https://openalex.org/W2119955255","https://openalex.org/W2121039643","https://openalex.org/W2141359401","https://openalex.org/W2478654971","https://openalex.org/W2501656778","https://openalex.org/W2611964096","https://openalex.org/W2727450595","https://openalex.org/W2780412706","https://openalex.org/W2883642126","https://openalex.org/W2909993591","https://openalex.org/W2962910407","https://openalex.org/W2971931235","https://openalex.org/W2999611204","https://openalex.org/W3104002866","https://openalex.org/W3116605176","https://openalex.org/W3134697742","https://openalex.org/W4226017528","https://openalex.org/W4229706427"],"related_works":["https://openalex.org/W1853631319","https://openalex.org/W2013767790","https://openalex.org/W4221157020","https://openalex.org/W4315489088","https://openalex.org/W4299551322","https://openalex.org/W4302558842","https://openalex.org/W211718035","https://openalex.org/W2025767136","https://openalex.org/W3125812435","https://openalex.org/W1554758635"],"abstract_inverted_index":{"This":[0],"paper":[1],"addresses":[2],"a":[3],"class":[4],"of":[5,9,15,24,91,117,130],"formation":[6,65,74],"tracking":[7],"problems":[8],"multiple":[10],"agents":[11],"from":[12],"the":[13,19,21,40,53,56,59,64,69,72,78,83,89,101,107,115,123,131],"perspective":[14],"game":[16],"theory.":[17],"In":[18],"game,":[20],"private":[22],"interests":[23],"all":[25,118],"followers":[26,57,119],"are":[27,97],"permitted.":[28],"Each":[29],"follower":[30,45],"aims":[31],"to":[32,51,99,122],"minimize":[33],"its":[34,49],"own":[35],"objective":[36,54],"function":[37],"by":[38,136],"updating":[39],"control":[41],"input.":[42],"When":[43],"each":[44],"cannot":[46],"unilaterally":[47],"change":[48],"state":[50],"reduce":[52],"function,":[55],"reach":[58],"dynamic":[60,79,102,124],"Nash":[61,80,103,125],"equilibrium,":[62],"and":[63,85],"is":[66,112,134],"achieved":[67],"in":[68,88],"meanwhile.":[70],"Specifically,":[71],"resultant":[73],"geometry":[75],"depends":[76],"on":[77,106],"equilibrium.":[81,104],"Considering":[82],"single-integrator":[84],"double-integrator":[86],"dynamics":[87],"form":[90],"Newton's":[92],"second":[93],"law,":[94],"some":[95,137],"strategies":[96,133],"proposed":[98,132],"seek":[100],"Based":[105],"Lyapunov":[108],"analysis":[109],"technique,":[110],"it":[111],"proved":[113],"that":[114],"states":[116],"converge":[120],"exponentially":[121],"equilibrium":[126],"point.":[127],"The":[128],"effectiveness":[129],"demonstrated":[135],"numerical":[138],"examples.":[139]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
