{"id":"https://openalex.org/W4210704481","doi":"https://doi.org/10.1109/tac.2022.3145632","title":"Linear Quadratic Control Using Model-Free Reinforcement Learning","display_name":"Linear Quadratic Control Using Model-Free Reinforcement Learning","publication_year":2022,"publication_date":"2022-01-25","ids":{"openalex":"https://openalex.org/W4210704481","doi":"https://doi.org/10.1109/tac.2022.3145632"},"language":"en","primary_location":{"id":"doi:10.1109/tac.2022.3145632","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2022.3145632","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"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 Automatic Control","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://liu.diva-portal.org/smash/get/diva2:1749956/FULLTEXT01","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5036304677","display_name":"Farnaz Adib Yaghmaie","orcid":"https://orcid.org/0000-0002-6665-5881"},"institutions":[{"id":"https://openalex.org/I102134673","display_name":"Link\u00f6ping University","ror":"https://ror.org/05ynxx418","country_code":"SE","type":"education","lineage":["https://openalex.org/I102134673"]}],"countries":["SE"],"is_corresponding":true,"raw_author_name":"Farnaz Adib Yaghmaie","raw_affiliation_strings":["Department of Electrical Engineering, Link&#x00F6;ping University, Link&#x00F6;ping, Sweden"],"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, Link&#x00F6;ping University, Link&#x00F6;ping, Sweden","institution_ids":["https://openalex.org/I102134673"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5058002446","display_name":"Fredrik Gustafsson","orcid":"https://orcid.org/0000-0003-3270-171X"},"institutions":[{"id":"https://openalex.org/I102134673","display_name":"Link\u00f6ping University","ror":"https://ror.org/05ynxx418","country_code":"SE","type":"education","lineage":["https://openalex.org/I102134673"]}],"countries":["SE"],"is_corresponding":false,"raw_author_name":"Fredrik Gustafsson","raw_affiliation_strings":["Department of Electrical Engineering, Link&#x00F6;ping University, Link&#x00F6;ping, Sweden"],"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, Link&#x00F6;ping University, Link&#x00F6;ping, Sweden","institution_ids":["https://openalex.org/I102134673"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5078405221","display_name":"Lennart Ljung","orcid":"https://orcid.org/0000-0003-4881-8955"},"institutions":[{"id":"https://openalex.org/I102134673","display_name":"Link\u00f6ping University","ror":"https://ror.org/05ynxx418","country_code":"SE","type":"education","lineage":["https://openalex.org/I102134673"]}],"countries":["SE"],"is_corresponding":false,"raw_author_name":"Lennart Ljung","raw_affiliation_strings":["Department of Electrical Engineering, Link&#x00F6;ping University, Link&#x00F6;ping, Sweden"],"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, Link&#x00F6;ping University, Link&#x00F6;ping, Sweden","institution_ids":["https://openalex.org/I102134673"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5036304677"],"corresponding_institution_ids":["https://openalex.org/I102134673"],"apc_list":null,"apc_paid":null,"fwci":8.1442,"has_fulltext":true,"cited_by_count":57,"citation_normalized_percentile":{"value":0.9811156,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":100},"biblio":{"volume":"68","issue":"2","first_page":"737","last_page":"752"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12794","display_name":"Adaptive Dynamic Programming Control","score":0.9997000098228455,"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":0.9997000098228455,"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/T10675","display_name":"Mechanical Circulatory Support Devices","score":0.9966999888420105,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical 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/T10462","display_name":"Reinforcement Learning in Robotics","score":0.9948999881744385,"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/reinforcement-learning","display_name":"Reinforcement learning","score":0.6076501607894897},{"id":"https://openalex.org/keywords/benchmark","display_name":"Benchmark (surveying)","score":0.5869247317314148},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5420885682106018},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4693613648414612},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.44156646728515625},{"id":"https://openalex.org/keywords/bellman-equation","display_name":"Bellman equation","score":0.4360365867614746},{"id":"https://openalex.org/keywords/variable","display_name":"Variable (mathematics)","score":0.43593481183052063},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.42966705560684204},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.4283723533153534},{"id":"https://openalex.org/keywords/noise","display_name":"Noise (video)","score":0.423086017370224},{"id":"https://openalex.org/keywords/notation","display_name":"Notation","score":0.4119589328765869},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4056384265422821},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3856218159198761},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3606858253479004},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.2917998433113098}],"concepts":[{"id":"https://openalex.org/C97541855","wikidata":"https://www.wikidata.org/wiki/Q830687","display_name":"Reinforcement learning","level":2,"score":0.6076501607894897},{"id":"https://openalex.org/C185798385","wikidata":"https://www.wikidata.org/wiki/Q1161707","display_name":"Benchmark (surveying)","level":2,"score":0.5869247317314148},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5420885682106018},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4693613648414612},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.44156646728515625},{"id":"https://openalex.org/C14646407","wikidata":"https://www.wikidata.org/wiki/Q1430750","display_name":"Bellman equation","level":2,"score":0.4360365867614746},{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.43593481183052063},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.42966705560684204},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.4283723533153534},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.423086017370224},{"id":"https://openalex.org/C45357846","wikidata":"https://www.wikidata.org/wiki/Q2001982","display_name":"Notation","level":2,"score":0.4119589328765869},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4056384265422821},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3856218159198761},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3606858253479004},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.2917998433113098},{"id":"https://openalex.org/C13280743","wikidata":"https://www.wikidata.org/wiki/Q131089","display_name":"Geodesy","level":1,"score":0.0},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"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/C205649164","wikidata":"https://www.wikidata.org/wiki/Q1071","display_name":"Geography","level":0,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"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/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tac.2022.3145632","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2022.3145632","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"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 Automatic Control","raw_type":"journal-article"},{"id":"pmh:oai:DiVA.org:liu-192951","is_oa":true,"landing_page_url":"http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-192951","pdf_url":"https://liu.diva-portal.org/smash/get/diva2:1749956/FULLTEXT01","source":{"id":"https://openalex.org/S4306401559","display_name":"KTH Publication Database DiVA (KTH Royal Institute of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:DiVA.org:liu-192951","is_oa":true,"landing_page_url":"http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-192951","pdf_url":"https://liu.diva-portal.org/smash/get/diva2:1749956/FULLTEXT01","source":{"id":"https://openalex.org/S4306401559","display_name":"KTH Publication Database DiVA (KTH Royal Institute of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[{"score":0.46000000834465027,"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4210704481.pdf"},"referenced_works_count":39,"referenced_works":["https://openalex.org/W8452924","https://openalex.org/W41554520","https://openalex.org/W118183761","https://openalex.org/W178056938","https://openalex.org/W1876438114","https://openalex.org/W1972243698","https://openalex.org/W2011866373","https://openalex.org/W2072931156","https://openalex.org/W2090167557","https://openalex.org/W2105739999","https://openalex.org/W2107726111","https://openalex.org/W2151966330","https://openalex.org/W2152161277","https://openalex.org/W2165418472","https://openalex.org/W2165726932","https://openalex.org/W2169209873","https://openalex.org/W2331243380","https://openalex.org/W2580629550","https://openalex.org/W2586680856","https://openalex.org/W2822752092","https://openalex.org/W2900809720","https://openalex.org/W2926824550","https://openalex.org/W2951568559","https://openalex.org/W2966348706","https://openalex.org/W2974120149","https://openalex.org/W3011550305","https://openalex.org/W4298300677","https://openalex.org/W4298857966","https://openalex.org/W4312258136","https://openalex.org/W6637967152","https://openalex.org/W6684205842","https://openalex.org/W6704571135","https://openalex.org/W6746722099","https://openalex.org/W6752646424","https://openalex.org/W6753610117","https://openalex.org/W6754297394","https://openalex.org/W6757029329","https://openalex.org/W6773051451","https://openalex.org/W6775030691"],"related_works":["https://openalex.org/W2386410636","https://openalex.org/W3038962357","https://openalex.org/W2025663273","https://openalex.org/W3099153698","https://openalex.org/W1859185863","https://openalex.org/W2964126589","https://openalex.org/W4285537323","https://openalex.org/W1932159282","https://openalex.org/W4307691181","https://openalex.org/W3016225735"],"abstract_inverted_index":{"In":[0],"this":[1,232],"article,":[2],"we":[3,61],"consider":[4],"linear":[5,40],"quadratic":[6],"(LQ)":[7],"control":[8,160],"problem":[9,19,161],"with":[10,86,184],"process":[11],"and":[12,26,44,110,129,157,179,195,212,222],"measurement":[13,117],"noises.":[14],"We":[15,33,95,112,138,173,199],"analyze":[16,97,113],"the":[17,23,27,30,36,39,49,58,69,82,89,98,101,107,114,120,123,126,130,152,158,166,170,185,188,196,209,219,223,238],"LQ":[18,70],"in":[20],"terms":[21],"of":[22,29,38,48,57,77,91,100,106,116,122,151],"average":[24,90],"cost":[25],"structure":[28],"value":[31],"function.":[32],"assume":[34],"that":[35,165,201],"dynamics":[37],"system":[41,154],"is":[42,84,155,162,169],"unknown":[43],"only":[45],"noisy":[46,55],"measurements":[47,56],"state":[50,59],"variable":[51],"are":[52,75],"available.":[53],"Using":[54],"variable,":[60],"propose":[62],"two":[63],"model-free":[64],"iterative":[65],"algorithms":[66,74,183,217,230],"to":[67,88,177,208],"solve":[68],"problem.":[71],"The":[72],"proposed":[73,102,124,182,214],"variants":[76],"policy":[78,83,197,215],"iteration":[79],"routine":[80],"where":[81,148],"greedy":[85],"respect":[87],"all":[92],"previous":[93],"iterations.":[94],"rigorously":[96],"properties":[99],"algorithms,":[103,125],"including":[104],"stability":[105],"generated":[108],"controllers":[109],"convergence.":[111],"effect":[115],"noise":[118],"on":[119,231],"performance":[121],"classical":[127,131,186,189,220,224],"off-policy,":[128,187],"<inline-formula":[132,190,225],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[133,191,226],"xmlns:xlink=\"http://www.w3.org/1999/xlink\"><tex-math":[134,192,227],"notation=\"LaTeX\">$Q$</tex-math></inline-formula>":[135,193,228],"-learning":[136,229],"routines.":[137],"also":[139],"investigate":[140],"a":[141,149,175],"model-building":[142,203,239],"approach,":[143],"inspired":[144],"by":[145],"adaptive":[146],"control,":[147],"model":[150,168],"dynamical":[153],"estimated":[156,167],"optimal":[159],"solved":[163],"assuming":[164],"true":[171],"model.":[172],"use":[174],"benchmark":[176,233],"evaluate":[178],"compare":[180],"our":[181,202,213],"-learning,":[194],"gradient.":[198],"show":[200],"approach":[204],"performs":[205],"nearly":[206],"identical":[207],"analytical":[210],"solution":[211],"iteration-based":[216],"outperform":[218,237],"off-policy":[221],"but":[234],"do":[235],"not":[236],"approach.":[240]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":22},{"year":2024,"cited_by_count":19},{"year":2023,"cited_by_count":10},{"year":2022,"cited_by_count":3}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
