{"id":"https://openalex.org/W2997938989","doi":"https://doi.org/10.1109/tsmc.2019.2957000","title":"Reinforcement Q-Learning Algorithm for H<sub>\u221e</sub> Tracking Control of Unknown Discrete-Time Linear Systems","display_name":"Reinforcement Q-Learning Algorithm for H<sub>\u221e</sub> Tracking Control of Unknown Discrete-Time Linear Systems","publication_year":2019,"publication_date":"2019-12-24","ids":{"openalex":"https://openalex.org/W2997938989","doi":"https://doi.org/10.1109/tsmc.2019.2957000","mag":"2997938989"},"language":"en","primary_location":{"id":"doi:10.1109/tsmc.2019.2957000","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsmc.2019.2957000","pdf_url":null,"source":{"id":"https://openalex.org/S4210209078","display_name":"IEEE Transactions on Systems Man and Cybernetics Systems","issn_l":"2168-2216","issn":["2168-2216","2168-2232"],"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 Systems, Man, and Cybernetics: 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/A5000624513","display_name":"Yunjian Peng","orcid":"https://orcid.org/0000-0002-6066-3979"},"institutions":[{"id":"https://openalex.org/I90610280","display_name":"South China University of Technology","ror":"https://ror.org/0530pts50","country_code":"CN","type":"education","lineage":["https://openalex.org/I90610280"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Yunjian Peng","raw_affiliation_strings":["School of Automation Science and Engineering, South China University of Technology, Guangzhou, China"],"raw_orcid":"https://orcid.org/0000-0002-6066-3979","affiliations":[{"raw_affiliation_string":"School of Automation Science and Engineering, South China University of Technology, Guangzhou, China","institution_ids":["https://openalex.org/I90610280"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5015464852","display_name":"Qian Chen","orcid":"https://orcid.org/0000-0001-7118-1695"},"institutions":[{"id":"https://openalex.org/I90610280","display_name":"South China University of Technology","ror":"https://ror.org/0530pts50","country_code":"CN","type":"education","lineage":["https://openalex.org/I90610280"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Qian Chen","raw_affiliation_strings":["School of Automation Science and Engineering, South China University of Technology, Guangzhou, China"],"raw_orcid":"https://orcid.org/0000-0001-7118-1695","affiliations":[{"raw_affiliation_string":"School of Automation Science and Engineering, South China University of Technology, Guangzhou, China","institution_ids":["https://openalex.org/I90610280"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5007988261","display_name":"Weijie Sun","orcid":"https://orcid.org/0000-0002-6148-6783"},"institutions":[{"id":"https://openalex.org/I90610280","display_name":"South China University of Technology","ror":"https://ror.org/0530pts50","country_code":"CN","type":"education","lineage":["https://openalex.org/I90610280"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Weijie Sun","raw_affiliation_strings":["School of Automation Science and Engineering, South China University of Technology, Guangzhou, China"],"raw_orcid":"https://orcid.org/0000-0002-6148-6783","affiliations":[{"raw_affiliation_string":"School of Automation Science and Engineering, South China University of Technology, Guangzhou, China","institution_ids":["https://openalex.org/I90610280"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5000624513"],"corresponding_institution_ids":["https://openalex.org/I90610280"],"apc_list":null,"apc_paid":null,"fwci":3.2338,"has_fulltext":false,"cited_by_count":72,"citation_normalized_percentile":{"value":0.92938387,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":100},"biblio":{"volume":"50","issue":"11","first_page":"4109","last_page":"4122"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12794","display_name":"Adaptive Dynamic Programming Control","score":1.0,"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":1.0,"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/T10462","display_name":"Reinforcement Learning in Robotics","score":0.973800003528595,"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"}},{"id":"https://openalex.org/T10040","display_name":"Adaptive Control of Nonlinear Systems","score":0.9650999903678894,"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/reinforcement-learning","display_name":"Reinforcement learning","score":0.8021637201309204},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.5675427317619324},{"id":"https://openalex.org/keywords/bellman-equation","display_name":"Bellman equation","score":0.5553073287010193},{"id":"https://openalex.org/keywords/riccati-equation","display_name":"Riccati equation","score":0.5524687170982361},{"id":"https://openalex.org/keywords/algebraic-riccati-equation","display_name":"Algebraic Riccati equation","score":0.5444887280464172},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.489332377910614},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4690221846103668},{"id":"https://openalex.org/keywords/controller","display_name":"Controller (irrigation)","score":0.4596218168735504},{"id":"https://openalex.org/keywords/discrete-time-and-continuous-time","display_name":"Discrete time and continuous time","score":0.4316684305667877},{"id":"https://openalex.org/keywords/state","display_name":"State (computer science)","score":0.42577311396598816},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3443368673324585},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.26298877596855164},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.2442876398563385},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.12383848428726196},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.08830699324607849},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.08526143431663513}],"concepts":[{"id":"https://openalex.org/C97541855","wikidata":"https://www.wikidata.org/wiki/Q830687","display_name":"Reinforcement learning","level":2,"score":0.8021637201309204},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5675427317619324},{"id":"https://openalex.org/C14646407","wikidata":"https://www.wikidata.org/wiki/Q1430750","display_name":"Bellman equation","level":2,"score":0.5553073287010193},{"id":"https://openalex.org/C45473103","wikidata":"https://www.wikidata.org/wiki/Q851503","display_name":"Riccati equation","level":3,"score":0.5524687170982361},{"id":"https://openalex.org/C13847129","wikidata":"https://www.wikidata.org/wiki/Q4723989","display_name":"Algebraic Riccati equation","level":4,"score":0.5444887280464172},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.489332377910614},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4690221846103668},{"id":"https://openalex.org/C203479927","wikidata":"https://www.wikidata.org/wiki/Q5165939","display_name":"Controller (irrigation)","level":2,"score":0.4596218168735504},{"id":"https://openalex.org/C55689738","wikidata":"https://www.wikidata.org/wiki/Q15963867","display_name":"Discrete time and continuous time","level":2,"score":0.4316684305667877},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.42577311396598816},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3443368673324585},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.26298877596855164},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.2442876398563385},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.12383848428726196},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.08830699324607849},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.08526143431663513},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"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/C6557445","wikidata":"https://www.wikidata.org/wiki/Q173113","display_name":"Agronomy","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tsmc.2019.2957000","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsmc.2019.2957000","pdf_url":null,"source":{"id":"https://openalex.org/S4210209078","display_name":"IEEE Transactions on Systems Man and Cybernetics Systems","issn_l":"2168-2216","issn":["2168-2216","2168-2232"],"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 Systems, Man, and Cybernetics: Systems","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2081057477","display_name":null,"funder_award_id":"61573154","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G313084318","display_name":null,"funder_award_id":"2015A010106003","funder_id":"https://openalex.org/F4320335795","funder_display_name":"Science and Technology Planning Project of Guangdong Province"},{"id":"https://openalex.org/G5489165093","display_name":null,"funder_award_id":"2017A010101009","funder_id":"https://openalex.org/F4320335795","funder_display_name":"Science and Technology Planning Project of Guangdong Province"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320335795","display_name":"Science and Technology Planning Project of Guangdong Province","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":48,"referenced_works":["https://openalex.org/W69446332","https://openalex.org/W601144718","https://openalex.org/W1500134124","https://openalex.org/W1530596433","https://openalex.org/W1559261542","https://openalex.org/W1614417283","https://openalex.org/W1765365314","https://openalex.org/W1972243698","https://openalex.org/W1972972294","https://openalex.org/W1976956127","https://openalex.org/W1977788021","https://openalex.org/W1996941060","https://openalex.org/W1998361253","https://openalex.org/W2005437559","https://openalex.org/W2011310556","https://openalex.org/W2011866373","https://openalex.org/W2013895638","https://openalex.org/W2019338681","https://openalex.org/W2024303516","https://openalex.org/W2048687352","https://openalex.org/W2050838777","https://openalex.org/W2078977470","https://openalex.org/W2139416664","https://openalex.org/W2148439597","https://openalex.org/W2151966330","https://openalex.org/W2253274025","https://openalex.org/W2278308097","https://openalex.org/W2295495433","https://openalex.org/W2312229020","https://openalex.org/W2484646121","https://openalex.org/W2580629550","https://openalex.org/W2591999327","https://openalex.org/W2752879615","https://openalex.org/W2761264428","https://openalex.org/W2766143943","https://openalex.org/W2783964454","https://openalex.org/W2802990478","https://openalex.org/W2805779274","https://openalex.org/W2807176303","https://openalex.org/W2883464943","https://openalex.org/W2883806155","https://openalex.org/W2901756453","https://openalex.org/W2907823935","https://openalex.org/W2914172002","https://openalex.org/W2917945410","https://openalex.org/W2922358507","https://openalex.org/W2929647494","https://openalex.org/W4405938501"],"related_works":["https://openalex.org/W2005019312","https://openalex.org/W2105459831","https://openalex.org/W1546579375","https://openalex.org/W1563296412","https://openalex.org/W2127238600","https://openalex.org/W2096105566","https://openalex.org/W2114791549","https://openalex.org/W16457797","https://openalex.org/W2792258377","https://openalex.org/W1987193149"],"abstract_inverted_index":{"This":[0],"article":[1],"addresses":[2],"the":[3,26,30,58,69,74,77,95,103,115,127,133,143,153,158,162,171,177,185,197,217,220],"online":[4],"reinforcement":[5,96,122],"Q-learning":[6,97,123,144,222],"algorithms":[7,124],"to":[8,42,57,72,101,105,152,170,194,215],"design":[9],"H":[10,78,106],"<sub":[11,79,107],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[12,80,108],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">\u221e</sub>":[13,81,109],"tracking":[14,82,110],"controller":[15],"for":[16,68],"unknown":[17],"discrete-time":[18],"linear":[19],"systems.":[20],"An":[21],"augmented":[22],"system":[23,28,116,199],"composed":[24],"of":[25,54,76,150,219],"original":[27],"and":[29,35,62,120,167],"command":[31],"generator":[32],"is":[33,40,66,89,99,140,181,213],"constructed,":[34],"a":[36,44,55,63,208],"discounted":[37,45,173],"performance":[38],"function":[39,135],"introduced":[41],"establish":[43],"game":[46],"algebraic":[47],"Riccati":[48],"equation":[49,88,156],"(GARE).":[50],"The":[51,85],"existence":[52],"conditions":[53],"solution":[56,104,151],"GARE":[59,174],"are":[60,130],"proposed":[61,178,221],"lower":[64],"bound":[65],"found":[67],"discount":[70],"factor":[71],"assure":[73],"stability":[75],"control":[83,111,128],"solution.":[84,175],"Q-function":[86,154],"Bellman":[87,155],"then":[90],"derived,":[91],"based":[92],"on":[93],"which":[94],"algorithm":[98],"developed":[100],"learn":[102],"problem":[112],"without":[113],"knowing":[114],"dynamics.":[117],"Both":[118],"state-data-driven":[119,186],"output-data-driven":[121,179],"toward":[125],"finding":[126],"policies":[129],"proposed.":[131],"Unlike":[132],"value":[134],"approximation":[136],"(VFA)-based":[137],"approach,":[138],"it":[139,189],"proved":[141],"that":[142],"scheme":[145],"brings":[146],"out":[147],"no":[148],"bias":[149],"under":[157],"probing":[159],"noise":[160],"satisfying":[161],"persistent":[163],"excitation":[164],"(PE)":[165],"condition,":[166],"therefore,":[168],"converges":[169],"nominal":[172],"Moreover,":[176],"method":[180,187],"more":[182],"powerful":[183],"than":[184],"as":[188],"may":[190],"not":[191],"be":[192],"available":[193],"completely":[195],"measure":[196],"full":[198],"states":[200],"in":[201],"practical":[202],"applications.":[203],"A":[204],"simulation":[205],"example":[206],"with":[207],"single-phase":[209],"voltage-source":[210],"UPS":[211],"inverter":[212],"used":[214],"verify":[216],"effectiveness":[218],"algorithms.":[223]},"counts_by_year":[{"year":2026,"cited_by_count":7},{"year":2025,"cited_by_count":15},{"year":2024,"cited_by_count":21},{"year":2023,"cited_by_count":13},{"year":2022,"cited_by_count":8},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":2}],"updated_date":"2026-05-07T13:39:58.223016","created_date":"2025-10-10T00:00:00"}
