{"id":"https://openalex.org/W4407247380","doi":"https://doi.org/10.1109/tase.2025.3539772","title":"Discounted Stable Adaptive Critic Design for Zero-Sum Games With Application Verifications","display_name":"Discounted Stable Adaptive Critic Design for Zero-Sum Games With Application Verifications","publication_year":2025,"publication_date":"2025-01-01","ids":{"openalex":"https://openalex.org/W4407247380","doi":"https://doi.org/10.1109/tase.2025.3539772"},"language":"en","primary_location":{"id":"doi:10.1109/tase.2025.3539772","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tase.2025.3539772","pdf_url":null,"source":{"id":"https://openalex.org/S34881539","display_name":"IEEE Transactions on Automation Science and Engineering","issn_l":"1545-5955","issn":["1545-5955","1558-3783"],"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 Automation Science and Engineering","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/A5074274816","display_name":"Jin Ren","orcid":"https://orcid.org/0000-0001-7812-1521"},"institutions":[{"id":"https://openalex.org/I37796252","display_name":"Beijing University of Technology","ror":"https://ror.org/037b1pp87","country_code":"CN","type":"education","lineage":["https://openalex.org/I37796252"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jin Ren","raw_affiliation_strings":["School of Information Science and Technology, Beijing Key Laboratory of Computational Intelligence and Intelligent System, Beijing Laboratory of Smart Environmental Protection, and Beijing Institute of Artificial Intelligence, Beijing University of Technology, Beijing, China","the Beijing Laboratory of Smart Environmental Protection, and the Beijing Institute of Artificial Intelligence, School of Information Science and Technology, the Beijing Key Laboratory of Computational Intelligence and Intelligent System, Beijing University of Technology, Beijing, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Information Science and Technology, Beijing Key Laboratory of Computational Intelligence and Intelligent System, Beijing Laboratory of Smart Environmental Protection, and Beijing Institute of Artificial Intelligence, Beijing University of Technology, Beijing, China","institution_ids":["https://openalex.org/I37796252"]},{"raw_affiliation_string":"the Beijing Laboratory of Smart Environmental Protection, and the Beijing Institute of Artificial Intelligence, School of Information Science and Technology, the Beijing Key Laboratory of Computational Intelligence and Intelligent System, Beijing University of Technology, Beijing, China","institution_ids":["https://openalex.org/I37796252"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5024549341","display_name":"Ding Wang","orcid":"https://orcid.org/0000-0002-7149-5712"},"institutions":[{"id":"https://openalex.org/I37796252","display_name":"Beijing University of Technology","ror":"https://ror.org/037b1pp87","country_code":"CN","type":"education","lineage":["https://openalex.org/I37796252"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Ding Wang","raw_affiliation_strings":["School of Information Science and Technology, Beijing Key Laboratory of Computational Intelligence and Intelligent System, Beijing Laboratory of Smart Environmental Protection, and Beijing Institute of Artificial Intelligence, Beijing University of Technology, Beijing, China","the Beijing Laboratory of Smart Environmental Protection, and the Beijing Institute of Artificial Intelligence, School of Information Science and Technology, the Beijing Key Laboratory of Computational Intelligence and Intelligent System, Beijing University of Technology, Beijing, China"],"raw_orcid":"https://orcid.org/0000-0002-7149-5712","affiliations":[{"raw_affiliation_string":"School of Information Science and Technology, Beijing Key Laboratory of Computational Intelligence and Intelligent System, Beijing Laboratory of Smart Environmental Protection, and Beijing Institute of Artificial Intelligence, Beijing University of Technology, Beijing, China","institution_ids":["https://openalex.org/I37796252"]},{"raw_affiliation_string":"the Beijing Laboratory of Smart Environmental Protection, and the Beijing Institute of Artificial Intelligence, School of Information Science and Technology, the Beijing Key Laboratory of Computational Intelligence and Intelligent System, Beijing University of Technology, Beijing, China","institution_ids":["https://openalex.org/I37796252"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101711547","display_name":"Menghua Li","orcid":"https://orcid.org/0000-0002-7231-7555"},"institutions":[{"id":"https://openalex.org/I37796252","display_name":"Beijing University of Technology","ror":"https://ror.org/037b1pp87","country_code":"CN","type":"education","lineage":["https://openalex.org/I37796252"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Menghua Li","raw_affiliation_strings":["School of Information Science and Technology, Beijing Key Laboratory of Computational Intelligence and Intelligent System, Beijing Laboratory of Smart Environmental Protection, and Beijing Institute of Artificial Intelligence, Beijing University of Technology, Beijing, China","the Beijing Laboratory of Smart Environmental Protection, and the Beijing Institute of Artificial Intelligence, School of Information Science and Technology, the Beijing Key Laboratory of Computational Intelligence and Intelligent System, Beijing University of Technology, Beijing, China"],"raw_orcid":"https://orcid.org/0000-0002-7231-7555","affiliations":[{"raw_affiliation_string":"School of Information Science and Technology, Beijing Key Laboratory of Computational Intelligence and Intelligent System, Beijing Laboratory of Smart Environmental Protection, and Beijing Institute of Artificial Intelligence, Beijing University of Technology, Beijing, China","institution_ids":["https://openalex.org/I37796252"]},{"raw_affiliation_string":"the Beijing Laboratory of Smart Environmental Protection, and the Beijing Institute of Artificial Intelligence, School of Information Science and Technology, the Beijing Key Laboratory of Computational Intelligence and Intelligent System, Beijing University of Technology, Beijing, China","institution_ids":["https://openalex.org/I37796252"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5113852585","display_name":"Junfei Qiao","orcid":"https://orcid.org/0000-0003-0950-7900"},"institutions":[{"id":"https://openalex.org/I37796252","display_name":"Beijing University of Technology","ror":"https://ror.org/037b1pp87","country_code":"CN","type":"education","lineage":["https://openalex.org/I37796252"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Junfei Qiao","raw_affiliation_strings":["School of Information Science and Technology, Beijing Key Laboratory of Computational Intelligence and Intelligent System, Beijing Laboratory of Smart Environmental Protection, and Beijing Institute of Artificial Intelligence, Beijing University of Technology, Beijing, China","the Beijing Laboratory of Smart Environmental Protection, and the Beijing Institute of Artificial Intelligence, School of Information Science and Technology, the Beijing Key Laboratory of Computational Intelligence and Intelligent System, Beijing University of Technology, Beijing, China"],"raw_orcid":"https://orcid.org/0000-0003-0950-7900","affiliations":[{"raw_affiliation_string":"School of Information Science and Technology, Beijing Key Laboratory of Computational Intelligence and Intelligent System, Beijing Laboratory of Smart Environmental Protection, and Beijing Institute of Artificial Intelligence, Beijing University of Technology, Beijing, China","institution_ids":["https://openalex.org/I37796252"]},{"raw_affiliation_string":"the Beijing Laboratory of Smart Environmental Protection, and the Beijing Institute of Artificial Intelligence, School of Information Science and Technology, the Beijing Key Laboratory of Computational Intelligence and Intelligent System, Beijing University of Technology, Beijing, China","institution_ids":["https://openalex.org/I37796252"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I37796252"],"apc_list":null,"apc_paid":null,"fwci":6.7251,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.95108579,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":95,"max":96},"biblio":{"volume":"22","issue":null,"first_page":"11706","last_page":"11716"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12158","display_name":"Guidance and Control Systems","score":0.9858999848365784,"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"}},"topics":[{"id":"https://openalex.org/T12158","display_name":"Guidance and Control Systems","score":0.9858999848365784,"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/T11195","display_name":"Simulation Techniques and Applications","score":0.9793999791145325,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T11574","display_name":"Artificial Intelligence in Games","score":0.9743000268936157,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/zero","display_name":"Zero (linguistics)","score":0.5993642210960388},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.49471399188041687},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4851025342941284},{"id":"https://openalex.org/keywords/zero-sum-game","display_name":"Zero-sum game","score":0.4707520604133606},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4413682520389557},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.42994725704193115},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.34435194730758667},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.17648857831954956},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.14140677452087402},{"id":"https://openalex.org/keywords/nash-equilibrium","display_name":"Nash equilibrium","score":0.1322959065437317}],"concepts":[{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.5993642210960388},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.49471399188041687},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4851025342941284},{"id":"https://openalex.org/C136356330","wikidata":"https://www.wikidata.org/wiki/Q156612","display_name":"Zero-sum game","level":3,"score":0.4707520604133606},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4413682520389557},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.42994725704193115},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.34435194730758667},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.17648857831954956},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.14140677452087402},{"id":"https://openalex.org/C46814582","wikidata":"https://www.wikidata.org/wiki/Q23389","display_name":"Nash equilibrium","level":2,"score":0.1322959065437317},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tase.2025.3539772","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tase.2025.3539772","pdf_url":null,"source":{"id":"https://openalex.org/S34881539","display_name":"IEEE Transactions on Automation Science and Engineering","issn_l":"1545-5955","issn":["1545-5955","1558-3783"],"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 Automation Science and Engineering","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1638800125","display_name":null,"funder_award_id":"62473012","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3929591211","display_name":null,"funder_award_id":"62021003","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4553196225","display_name":null,"funder_award_id":"62222301","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G679485329","display_name":null,"funder_award_id":"2021ZD0112302","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G890763551","display_name":null,"funder_award_id":"2021ZD0112301","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"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":43,"referenced_works":["https://openalex.org/W1680219837","https://openalex.org/W1988523476","https://openalex.org/W2004735053","https://openalex.org/W2005437559","https://openalex.org/W2052399669","https://openalex.org/W2131502866","https://openalex.org/W2132858840","https://openalex.org/W2152161277","https://openalex.org/W2550394442","https://openalex.org/W2581606339","https://openalex.org/W2955358943","https://openalex.org/W2962974451","https://openalex.org/W3009014967","https://openalex.org/W3036186095","https://openalex.org/W3111327451","https://openalex.org/W3196924932","https://openalex.org/W3200299012","https://openalex.org/W3200354666","https://openalex.org/W4200329055","https://openalex.org/W4205172873","https://openalex.org/W4205939747","https://openalex.org/W4210556448","https://openalex.org/W4214821607","https://openalex.org/W4283727098","https://openalex.org/W4295832240","https://openalex.org/W4312721382","https://openalex.org/W4319996361","https://openalex.org/W4327521999","https://openalex.org/W4377145631","https://openalex.org/W4377224182","https://openalex.org/W4382931108","https://openalex.org/W4384789633","https://openalex.org/W4385833430","https://openalex.org/W4386523235","https://openalex.org/W4387385622","https://openalex.org/W4387886187","https://openalex.org/W4387889537","https://openalex.org/W4388579564","https://openalex.org/W4390776948","https://openalex.org/W4393079544","https://openalex.org/W4394874555","https://openalex.org/W4396629508","https://openalex.org/W6804409665"],"related_works":["https://openalex.org/W1982160337","https://openalex.org/W1971380437","https://openalex.org/W1983548084","https://openalex.org/W2739681863","https://openalex.org/W3170723600","https://openalex.org/W4287122294","https://openalex.org/W2039187327","https://openalex.org/W4307291161","https://openalex.org/W1877069894","https://openalex.org/W1994737592"],"abstract_inverted_index":{"In":[0,230],"this":[1,226],"paper,":[2],"an":[3,181],"adaptive":[4,218],"critic":[5],"design":[6],"with":[7,21,161,174,225,273],"performance":[8,203,274,304],"guarantee":[9],"is":[10,32,221,246,252,290,299],"established":[11,98],"based":[12],"on":[13,59,234,265],"the":[14,22,36,41,48,64,67,71,74,78,87,91,103,112,117,123,127,134,138,145,148,165,186,201,205,212,235,239,243,250,253,266,280,288,293,297,303,306,319,324],"discounted":[15],"value":[16,79,215],"iteration":[17,31,80,216],"algorithm":[18],"to":[19,34,40,99,116,143,152,211,223,232,262,278],"settle":[20],"optimal":[23,38,105,118,189,267,282],"regulation":[24,268],"problem":[25],"for":[26,44,53,93,133,312],"discrete-time":[27,270],"zero-sum":[28,166,191,271],"games.":[29],"Value":[30],"implemented":[33],"obtain":[35,279],"approximate":[37],"solutions":[39],"Hamilton-Jacobi-Isaacs":[42],"equation":[43,52],"nonlinear":[45],"systems":[46,160,176],"and":[47,70,90,137,163,292,321],"game":[49,167],"algebraic":[50],"Riccati":[51],"linear":[54],"systems.":[55],"Then,":[56],"we":[57,259],"focus":[58],"system":[60,95,136,140,202,240,298],"stability":[61,96,125,241,251,289,295],"affected":[62],"by":[63],"introduction":[65],"of":[66,73,86,126,147,158,188,207,228,237,255,269,287,296,305,323],"discount":[68,88],"factor":[69,89],"admissibility":[72],"policy":[75,106,196,283],"pairs":[76,197],"in":[77,101,185,204,217],"process.":[81],"The":[82],"appropriate":[83],"selection":[84],"range":[85],"criteria":[92],"ensuring":[94],"are":[97,141,169,260,315],"assist":[100],"obtaining":[102],"stabilized":[104],"pair,":[107],"which":[108,276,301,317],"not":[109],"only":[110],"makes":[111],"cost":[113],"function":[114],"converge":[115],"value,":[119],"but":[120],"also":[121],"guarantees":[122],"asymptotic":[124,294],"closed-loop":[128],"system.":[129],"Finally,":[130],"practical":[131,313],"examples":[132],"power":[135],"ball-beam":[139],"conducted":[142],"demonstrate":[144],"effectiveness":[146,322],"presented":[149],"method.":[150],"Note":[151],"Practitioners\u2014Since":[153],"there":[154],"exist":[155],"a":[156],"multitude":[157],"dynamic":[159,175,219],"uncertainty":[162],"interference,":[164],"problems":[168],"ubiquitous,":[170],"especially":[171],"when":[172],"dealing":[173],"featuring":[177],"antagonistic":[178],"properties.":[179],"As":[180],"important":[182],"research":[183],"direction":[184],"field":[187],"control,":[190],"games":[192,272],"usually":[193],"involve":[194],"designing":[195],"that":[198],"can":[199],"optimize":[200],"presence":[206],"adversarial":[208],"disturbances.":[209],"Due":[210],"excellent":[213],"adaptability,":[214],"programming":[220],"employed":[222],"deal":[224],"kind":[227],"issues.":[229],"addition":[231],"focusing":[233],"optimality":[236],"policies,":[238],"during":[242],"control":[244,326],"process":[245],"equally":[247],"significance,":[248],"where":[249],"premise":[254],"all":[256],"operations.":[257],"Therefore,":[258],"dedicated":[261],"providing":[263],"guidance":[264],"guarantee,":[275],"contributes":[277],"stable":[281],"pair.":[284],"Theoretical":[285],"analysis":[286],"provided":[291],"ensured,":[300],"improves":[302],"designed":[307],"controller.":[308],"Furthermore,":[309],"simulation":[310],"experiments":[311],"applications":[314],"conducted,":[316],"verify":[318],"feasibility":[320],"proposed":[325],"design.":[327]},"counts_by_year":[{"year":2025,"cited_by_count":2}],"updated_date":"2025-12-23T23:11:35.936235","created_date":"2025-10-10T00:00:00"}
