{"id":"https://openalex.org/W4297626836","doi":"https://doi.org/10.1137/20m1379605","title":"A Q-Learning Algorithm for Discrete-Time Linear-Quadratic Control with Random Parameters of Unknown Distribution: Convergence and Stabilization","display_name":"A Q-Learning Algorithm for Discrete-Time Linear-Quadratic Control with Random Parameters of Unknown Distribution: Convergence and Stabilization","publication_year":2022,"publication_date":"2022-07-07","ids":{"openalex":"https://openalex.org/W4297626836","doi":"https://doi.org/10.1137/20m1379605"},"language":"en","primary_location":{"id":"doi:10.1137/20m1379605","is_oa":false,"landing_page_url":"https://doi.org/10.1137/20m1379605","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Control and Optimization","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/A5043464993","display_name":"Kai Du","orcid":"https://orcid.org/0000-0002-3117-0307"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Kai Du","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5102014477","display_name":"Qingxin Meng","orcid":"https://orcid.org/0000-0003-4020-5679"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Qingxin Meng","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5016969742","display_name":"Zhang Fu","orcid":"https://orcid.org/0000-0002-3968-0870"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Fu Zhang","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0002-3968-0870","affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.0116,"has_fulltext":false,"cited_by_count":14,"citation_normalized_percentile":{"value":0.88297001,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"60","issue":"4","first_page":"1991","last_page":"2015"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12794","display_name":"Adaptive Dynamic Programming Control","score":0.9991999864578247,"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":0.9991999864578247,"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/T10791","display_name":"Advanced Control Systems Optimization","score":0.9948999881744385,"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/T10046","display_name":"Stability and Control of Uncertain Systems","score":0.9936000108718872,"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/mathematics","display_name":"Mathematics","score":0.8297595977783203},{"id":"https://openalex.org/keywords/independent-and-identically-distributed-random-variables","display_name":"Independent and identically distributed random variables","score":0.7384554743766785},{"id":"https://openalex.org/keywords/algebraic-riccati-equation","display_name":"Algebraic Riccati equation","score":0.7214564085006714},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.6432771682739258},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.540521502494812},{"id":"https://openalex.org/keywords/riccati-equation","display_name":"Riccati equation","score":0.5097007751464844},{"id":"https://openalex.org/keywords/equivalence","display_name":"Equivalence (formal languages)","score":0.508129358291626},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.49770811200141907},{"id":"https://openalex.org/keywords/linear-quadratic-gaussian-control","display_name":"Linear-quadratic-Gaussian control","score":0.47774165868759155},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.42602190375328064},{"id":"https://openalex.org/keywords/distribution","display_name":"Distribution (mathematics)","score":0.424834668636322},{"id":"https://openalex.org/keywords/random-variable","display_name":"Random variable","score":0.3334195017814636},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3208373188972473},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.2389574944972992},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1492486596107483},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.13339072465896606}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8297595977783203},{"id":"https://openalex.org/C141513077","wikidata":"https://www.wikidata.org/wiki/Q378542","display_name":"Independent and identically distributed random variables","level":3,"score":0.7384554743766785},{"id":"https://openalex.org/C13847129","wikidata":"https://www.wikidata.org/wiki/Q4723989","display_name":"Algebraic Riccati equation","level":4,"score":0.7214564085006714},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.6432771682739258},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.540521502494812},{"id":"https://openalex.org/C45473103","wikidata":"https://www.wikidata.org/wiki/Q851503","display_name":"Riccati equation","level":3,"score":0.5097007751464844},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.508129358291626},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.49770811200141907},{"id":"https://openalex.org/C204495892","wikidata":"https://www.wikidata.org/wiki/Q1798304","display_name":"Linear-quadratic-Gaussian control","level":3,"score":0.47774165868759155},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.42602190375328064},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.424834668636322},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.3334195017814636},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3208373188972473},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2389574944972992},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1492486596107483},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.13339072465896606},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/20m1379605","is_oa":false,"landing_page_url":"https://doi.org/10.1137/20m1379605","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Control and Optimization","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1138586619","display_name":null,"funder_award_id":"11701369","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2818004746","display_name":"\u65e0\u9650\u7ef4\u5e73\u5747\u573a\u6b63\u5012\u5411\u968f\u673a\u53d1\u5c55\u7cfb\u7edf\u7406\u8bba\u53ca\u5176\u5e94\u7528","funder_award_id":"LZ22A010005","funder_id":"https://openalex.org/F4320338464","funder_display_name":"Natural Science Foundation of Zhejiang Province"},{"id":"https://openalex.org/G4532882392","display_name":"\u6781\u7aef\u6ce2\u52a8\u4e0e\u4f20\u67d3\u5e02\u573a\u73af\u5883\u4e2d\u6295\u8d44\u8fde\u7ed3\u578b\u5bff\u9669\u4ea7\u54c1\u7684\u82e5\u5e72\u95ee\u9898\u7814\u7a76","funder_award_id":"11871121","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5059117279","display_name":null,"funder_award_id":"11801084","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5764032034","display_name":null,"funder_award_id":"LY21A010001","funder_id":"https://openalex.org/F4320338464","funder_display_name":"Natural Science Foundation of Zhejiang Province"},{"id":"https://openalex.org/G7385022006","display_name":null,"funder_award_id":"12071292","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/F4320324174","display_name":"Natural Science Foundation of Shandong Province","ror":null},{"id":"https://openalex.org/F4320336023","display_name":"Program for Professor of Special Appointment (Eastern Scholar) at Shanghai Institutions of Higher Learning","ror":null},{"id":"https://openalex.org/F4320338464","display_name":"Natural Science Foundation of Zhejiang Province","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":35,"referenced_works":["https://openalex.org/W767279938","https://openalex.org/W1527117384","https://openalex.org/W1754942779","https://openalex.org/W1964350975","https://openalex.org/W1964592180","https://openalex.org/W1965083998","https://openalex.org/W1974495488","https://openalex.org/W1992948049","https://openalex.org/W1994616650","https://openalex.org/W1996731752","https://openalex.org/W2042856298","https://openalex.org/W2043880592","https://openalex.org/W2072007764","https://openalex.org/W2075549445","https://openalex.org/W2077728023","https://openalex.org/W2092642106","https://openalex.org/W2112284360","https://openalex.org/W2113159675","https://openalex.org/W2119567691","https://openalex.org/W2120871244","https://openalex.org/W2121863487","https://openalex.org/W2123486671","https://openalex.org/W2124614463","https://openalex.org/W2132021973","https://openalex.org/W2137850460","https://openalex.org/W2165131254","https://openalex.org/W2173931892","https://openalex.org/W2313568470","https://openalex.org/W2344252730","https://openalex.org/W2911495555","https://openalex.org/W2997572556","https://openalex.org/W3015621283","https://openalex.org/W4233151592","https://openalex.org/W4233696721","https://openalex.org/W4243772471"],"related_works":["https://openalex.org/W2005019312","https://openalex.org/W2105459831","https://openalex.org/W1546579375","https://openalex.org/W2127238600","https://openalex.org/W1563296412","https://openalex.org/W2114791549","https://openalex.org/W16457797","https://openalex.org/W2792258377","https://openalex.org/W1530596433","https://openalex.org/W2096105566"],"abstract_inverted_index":{"This":[0],"paper":[1],"studies":[2],"an":[3,36,57],"infinite":[4],"horizon":[5],"optimal":[6],"control":[7,99,117,131],"problem":[8,132],"for":[9,65],"discrete-time":[10],"linear":[11],"systems":[12],"and":[13,23,44,101],"quadratic":[14],"criteria,":[15],"both":[16],"with":[17,26],"random":[18,71],"parameters":[19,74],"which":[20],"are":[21,137],"independent":[22],"identically":[24],"distributed":[25],"respect":[27],"to":[28,34,139],"time.":[29],"A":[30],"classical":[31],"approach":[32],"is":[33,133],"solve":[35],"algebraic":[37,106],"Riccati":[38,107],"equation":[39],"that":[40,113],"involves":[41],"mathematical":[42],"expectations":[43],"requires":[45],"certain":[46],"statistical":[47],"information":[48],"of":[49,63,73,86,91,97,104,120],"the":[50,61,66,84,89,92,95,98,102,105,114,121,125,130],"parameters.":[51],"In":[52],"this":[53],"paper,":[54],"we":[55],"propose":[56],"iterative":[58],"algorithm":[59],"in":[60,118],"spirit":[62],"Q-learning":[64],"situation":[67],"where":[68],"only":[69],"one":[70],"sample":[72],"emerges":[75],"at":[76],"each":[77],"time":[78],"step.":[79],"The":[80,109],"first":[81],"theorem":[82,111],"proves":[83],"equivalence":[85],"three":[87],"properties:":[88],"convergence":[90],"learning":[93,122],"sequence,":[94],"well-posedness":[96],"problem,":[100],"solvability":[103],"equation.":[108],"second":[110],"shows":[112],"adaptive":[115],"feedback":[116],"terms":[119],"sequence":[123],"stabilizes":[124],"system":[126],"as":[127,129],"long":[128],"well-posed.":[134],"Numerical":[135],"examples":[136],"presented":[138],"illustrate":[140],"our":[141],"results.":[142]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":8},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":1}],"updated_date":"2026-07-13T07:31:44.756512","created_date":"2025-10-10T00:00:00"}