{"id":"https://openalex.org/W4407574654","doi":"https://doi.org/10.1109/tase.2025.3540401","title":"Optimal Tracking Control for Cyber-Physical Systems Under Mixed Attacks via Game-Theoretical Q-Learning","display_name":"Optimal Tracking Control for Cyber-Physical Systems Under Mixed Attacks via Game-Theoretical Q-Learning","publication_year":2025,"publication_date":"2025-01-01","ids":{"openalex":"https://openalex.org/W4407574654","doi":"https://doi.org/10.1109/tase.2025.3540401"},"language":"en","primary_location":{"id":"doi:10.1109/tase.2025.3540401","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tase.2025.3540401","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/A5039222204","display_name":"Jinyan Li","orcid":"https://orcid.org/0009-0006-8690-7464"},"institutions":[{"id":"https://openalex.org/I139024713","display_name":"Guangdong University of Technology","ror":"https://ror.org/04azbjn80","country_code":"CN","type":"education","lineage":["https://openalex.org/I139024713"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Jinyan Li","raw_affiliation_strings":["School of Automation, Guangdong-Hong Kong Joint Laboratory for Intelligent Decision and Cooperative Control, and Guangdong Provincial Key Laboratory of Intelligent Decision and Cooperative Control, Guangdong University of Technology, Guangzhou, China"],"affiliations":[{"raw_affiliation_string":"School of Automation, Guangdong-Hong Kong Joint Laboratory for Intelligent Decision and Cooperative Control, and Guangdong Provincial Key Laboratory of Intelligent Decision and Cooperative Control, Guangdong University of Technology, Guangzhou, China","institution_ids":["https://openalex.org/I139024713"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5066333390","display_name":"Xiao\u2010Meng Li","orcid":"https://orcid.org/0000-0002-7844-3122"},"institutions":[{"id":"https://openalex.org/I37987034","display_name":"Guangzhou University","ror":"https://ror.org/05ar8rn06","country_code":"CN","type":"education","lineage":["https://openalex.org/I37987034"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiao-Meng Li","raw_affiliation_strings":["School of Mechanical and Electrical Engineering, Guangzhou University, Guangzhou, China"],"affiliations":[{"raw_affiliation_string":"School of Mechanical and Electrical Engineering, Guangzhou University, Guangzhou, China","institution_ids":["https://openalex.org/I37987034"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5015581105","display_name":"Guangdeng Chen","orcid":"https://orcid.org/0000-0001-6586-2494"},"institutions":[{"id":"https://openalex.org/I142108993","display_name":"Southwest University","ror":"https://ror.org/01kj4z117","country_code":"CN","type":"education","lineage":["https://openalex.org/I142108993"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Guangdeng Chen","raw_affiliation_strings":["College of Electronic and Information Engineering, Southwest University, Chongqing, China"],"affiliations":[{"raw_affiliation_string":"College of Electronic and Information Engineering, Southwest University, Chongqing, China","institution_ids":["https://openalex.org/I142108993"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5020309080","display_name":"Xiao\u2010Jie Peng","orcid":"https://orcid.org/0000-0002-7723-162X"},"institutions":[{"id":"https://openalex.org/I142108993","display_name":"Southwest University","ror":"https://ror.org/01kj4z117","country_code":"CN","type":"education","lineage":["https://openalex.org/I142108993"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiao-Jie Peng","raw_affiliation_strings":["College of Electronic and Information Engineering, Southwest University, Chongqing, China"],"affiliations":[{"raw_affiliation_string":"College of Electronic and Information Engineering, Southwest University, Chongqing, China","institution_ids":["https://openalex.org/I142108993"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100413697","display_name":"Hongyi Li","orcid":"https://orcid.org/0000-0002-7590-7411"},"institutions":[{"id":"https://openalex.org/I142108993","display_name":"Southwest University","ror":"https://ror.org/01kj4z117","country_code":"CN","type":"education","lineage":["https://openalex.org/I142108993"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Hongyi Li","raw_affiliation_strings":["College of Electronic and Information Engineering, Southwest University, Chongqing, China"],"affiliations":[{"raw_affiliation_string":"College of Electronic and Information Engineering, Southwest University, Chongqing, China","institution_ids":["https://openalex.org/I142108993"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5039222204"],"corresponding_institution_ids":["https://openalex.org/I139024713"],"apc_list":null,"apc_paid":null,"fwci":9.2935,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.9792106,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":98,"max":99},"biblio":{"volume":"22","issue":null,"first_page":"11944","last_page":"11954"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10917","display_name":"Smart Grid Security and Resilience","score":0.9700999855995178,"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"}},"topics":[{"id":"https://openalex.org/T10917","display_name":"Smart Grid Security and Resilience","score":0.9700999855995178,"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"}},{"id":"https://openalex.org/T10876","display_name":"Fault Detection and Control Systems","score":0.9692000150680542,"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/cyber-physical-system","display_name":"Cyber-physical system","score":0.707353949546814},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5359504818916321},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.5175725221633911},{"id":"https://openalex.org/keywords/game-theory","display_name":"Game theory","score":0.5122250914573669},{"id":"https://openalex.org/keywords/control-system","display_name":"Control system","score":0.45268574357032776},{"id":"https://openalex.org/keywords/tracking","display_name":"Tracking (education)","score":0.44276660680770874},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.35639679431915283},{"id":"https://openalex.org/keywords/control-engineering","display_name":"Control engineering","score":0.35286247730255127},{"id":"https://openalex.org/keywords/computer-security","display_name":"Computer security","score":0.34053701162338257},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.32470300793647766},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.3078186810016632},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.16589534282684326},{"id":"https://openalex.org/keywords/electrical-engineering","display_name":"Electrical engineering","score":0.11219173669815063}],"concepts":[{"id":"https://openalex.org/C179768478","wikidata":"https://www.wikidata.org/wiki/Q1120057","display_name":"Cyber-physical system","level":2,"score":0.707353949546814},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5359504818916321},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.5175725221633911},{"id":"https://openalex.org/C177142836","wikidata":"https://www.wikidata.org/wiki/Q44455","display_name":"Game theory","level":2,"score":0.5122250914573669},{"id":"https://openalex.org/C17500928","wikidata":"https://www.wikidata.org/wiki/Q959968","display_name":"Control system","level":2,"score":0.45268574357032776},{"id":"https://openalex.org/C2775936607","wikidata":"https://www.wikidata.org/wiki/Q466845","display_name":"Tracking (education)","level":2,"score":0.44276660680770874},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.35639679431915283},{"id":"https://openalex.org/C133731056","wikidata":"https://www.wikidata.org/wiki/Q4917288","display_name":"Control engineering","level":1,"score":0.35286247730255127},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.34053701162338257},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.32470300793647766},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3078186810016632},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.16589534282684326},{"id":"https://openalex.org/C119599485","wikidata":"https://www.wikidata.org/wiki/Q43035","display_name":"Electrical engineering","level":1,"score":0.11219173669815063},{"id":"https://openalex.org/C19417346","wikidata":"https://www.wikidata.org/wiki/Q7922","display_name":"Pedagogy","level":1,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.0},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tase.2025.3540401","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tase.2025.3540401","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/G1064191816","display_name":null,"funder_award_id":"2023B1515120010","funder_id":"https://openalex.org/F4320320671","funder_display_name":"National Research Foundation"},{"id":"https://openalex.org/G2011644497","display_name":null,"funder_award_id":"2022A1515110949","funder_id":"https://openalex.org/F4320320671","funder_display_name":"National Research Foundation"},{"id":"https://openalex.org/G2729922379","display_name":null,"funder_award_id":"62033003, 62433018, 62303125","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5812066096","display_name":null,"funder_award_id":"2023A1515011527","funder_id":"https://openalex.org/F4320320671","funder_display_name":"National Research Foundation"},{"id":"https://openalex.org/G5912275759","display_name":null,"funder_award_id":"62433018","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6266129667","display_name":null,"funder_award_id":"2024M762667","funder_id":"https://openalex.org/F4320321543","funder_display_name":"China Postdoctoral Science Foundation"},{"id":"https://openalex.org/G6351919727","display_name":null,"funder_award_id":"62033003","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6616719906","display_name":null,"funder_award_id":"62303125","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G963353362","display_name":null,"funder_award_id":"2023A1515011527, 2023B1515120010, 2022A1515110949","funder_id":"https://openalex.org/F4320337111","funder_display_name":"Basic and Applied Basic Research Foundation of Guangdong Province"}],"funders":[{"id":"https://openalex.org/F4320320671","display_name":"National Research Foundation","ror":"https://ror.org/05s0g1g46"},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320321543","display_name":"China Postdoctoral Science Foundation","ror":"https://ror.org/0426zh255"},{"id":"https://openalex.org/F4320337111","display_name":"Basic and Applied Basic Research Foundation of Guangdong Province","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":48,"referenced_works":["https://openalex.org/W1980568723","https://openalex.org/W2005437559","https://openalex.org/W2792111770","https://openalex.org/W2807176303","https://openalex.org/W2977733636","https://openalex.org/W3004943475","https://openalex.org/W3092252985","https://openalex.org/W3128089553","https://openalex.org/W4285605593","https://openalex.org/W4285773432","https://openalex.org/W4308246097","https://openalex.org/W4313291108","https://openalex.org/W4319866759","https://openalex.org/W4321609142","https://openalex.org/W4327704802","https://openalex.org/W4379531887","https://openalex.org/W4380046748","https://openalex.org/W4382119200","https://openalex.org/W4385144976","https://openalex.org/W4385152096","https://openalex.org/W4385819645","https://openalex.org/W4386025725","https://openalex.org/W4386320531","https://openalex.org/W4386869636","https://openalex.org/W4389331490","https://openalex.org/W4389579542","https://openalex.org/W4391936224","https://openalex.org/W4392544396","https://openalex.org/W4392563584","https://openalex.org/W4392667157","https://openalex.org/W4392948334","https://openalex.org/W4394994803","https://openalex.org/W4399297660","https://openalex.org/W4399989878","https://openalex.org/W4400352538","https://openalex.org/W4400678981","https://openalex.org/W4401163471","https://openalex.org/W4401326291","https://openalex.org/W4402052386","https://openalex.org/W4402618490","https://openalex.org/W4402805840","https://openalex.org/W4403210026","https://openalex.org/W4403445906","https://openalex.org/W4404520559","https://openalex.org/W4404644816","https://openalex.org/W4407669976","https://openalex.org/W4408231922","https://openalex.org/W6879637531"],"related_works":["https://openalex.org/W2615607975","https://openalex.org/W2192101006","https://openalex.org/W2116800748","https://openalex.org/W2638730922","https://openalex.org/W2190465783","https://openalex.org/W2027827693","https://openalex.org/W2381267592","https://openalex.org/W4241033836","https://openalex.org/W2053371515","https://openalex.org/W2518504198"],"abstract_inverted_index":{"This":[0],"paper":[1],"investigates":[2],"the":[3,17,34,46,51,55,82,89,101,104,107,118,127,140,148,154,160,164,175,179,187,203,214,240,262,266],"optimal":[4,56,119,232],"tracking":[5,41,233,270],"control":[6,35,57,77,90,120,205,234],"problem":[7],"for":[8,129,250],"cyber-physical":[9],"systems":[10],"(CPSs)":[11],"under":[12,264],"mixed":[13,37,86,243],"attacks":[14,87,192,196,244],"based":[15,44],"on":[16,45,88,208,245],"Stackelberg":[18,47,225],"game":[19,48,226],"strategy.":[20],"First,":[21],"an":[22,110,231],"improved":[23,111],"value":[24],"function":[25],"is":[26,114,145,167,221,236],"designed":[27],"to":[28,99,106,116,131,173,190,238,260],"meet":[29],"performance":[30,91,271],"criteria":[31],"by":[32,67,169],"considering":[33],"signal,":[36,39],"attack":[38,63,254],"and":[40,50,59,134,153,197,219],"performance.":[42],"Then,":[43],"theory":[49],"principle":[52],"of":[53,85,92,103,156,182,202,242,253],"optimality,":[54],"strategy":[58,78],"false":[60],"data":[61],"injection":[62],"policy":[64],"are":[65,97,151,255],"derived":[66],"solving":[68],"a":[69,224],"coupled":[70],"algebraic":[71],"Riccati":[72],"equation":[73],"(CARE).":[74],"The":[75,200],"proposed":[76,115,165,237],"can":[79,158],"effectively":[80],"alleviate":[81],"adverse":[83],"impact":[84,241],"CPSs.":[93,246],"Subsequently,":[94],"sufficient":[95,248],"conditions":[96,249,263],"provided":[98],"guarantee":[100],"existence":[102],"solution":[105],"CARE.":[108],"Additionally,":[109],"Q-learning":[112],"algorithm":[113,235],"learn":[117],"scheme":[121],"through":[122],"state":[123,132],"reconstruction,":[124],"which":[125,257,265],"avoids":[126],"need":[128],"access":[130],"vectors":[133],"facilitates":[135],"data-based":[136],"controller":[137],"design.":[138],"Using":[139],"Lyapunov":[141],"stability":[142],"theory,":[143],"it":[144],"demonstrated":[146],"that":[147],"presented":[149],"algorithms":[150],"convergent":[152],"output":[155],"CPSs":[157],"track":[159],"reference":[161],"trajectory.":[162],"Finally,":[163],"approach":[166],"validated":[168],"numerical":[170],"simulations.":[171],"Note":[172],"Practitioners\u2014In":[174],"engineering":[176],"application":[177],"scenarios,":[178],"sharing":[180],"feature":[181],"network":[183],"communication":[184],"may":[185,272],"expose":[186],"controlled":[188],"system":[189],"malicious":[191],"(such":[193],"as":[194],"DoS":[195],"FDI":[198],"attacks).":[199],"majority":[201],"current":[204],"methods":[206],"focus":[207],"one-sided":[209],"analyses.":[210],"In":[211],"this":[212,229],"paper,":[213],"dynamic":[215],"interaction":[216],"between":[217],"attackers":[218],"defenders":[220],"described":[222],"using":[223],"model.":[227],"Within":[228],"model,":[230],"mitigate":[239],"Moreover,":[247],"tolerable":[251],"probability":[252],"derived,":[256],"enables":[258],"practitioners":[259],"determine":[261],"attacked":[267],"system\u2019s":[268],"stable":[269],"still":[273],"be":[274],"maintained.":[275]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":6}],"updated_date":"2026-04-09T08:11:56.329763","created_date":"2025-10-10T00:00:00"}
