{"id":"https://openalex.org/W3114329882","doi":"https://doi.org/10.1109/tnnls.2020.3042589","title":"Model-Free Reinforcement Learning by Embedding an Auxiliary System for Optimal Control of Nonlinear Systems","display_name":"Model-Free Reinforcement Learning by Embedding an Auxiliary System for Optimal Control of Nonlinear Systems","publication_year":2020,"publication_date":"2020-12-21","ids":{"openalex":"https://openalex.org/W3114329882","doi":"https://doi.org/10.1109/tnnls.2020.3042589","mag":"3114329882","pmid":"https://pubmed.ncbi.nlm.nih.gov/33347416"},"language":"en","primary_location":{"id":"doi:10.1109/tnnls.2020.3042589","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tnnls.2020.3042589","pdf_url":null,"source":{"id":"https://openalex.org/S4210175523","display_name":"IEEE Transactions on Neural Networks and Learning Systems","issn_l":"2162-237X","issn":["2162-237X","2162-2388"],"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 Neural Networks and Learning Systems","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","pubmed"],"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/A5100729868","display_name":"Zhenhui Xu","orcid":"https://orcid.org/0000-0003-1378-6164"},"institutions":[{"id":"https://openalex.org/I42999171","display_name":"Sophia University","ror":"https://ror.org/01nckkm68","country_code":"JP","type":"education","lineage":["https://openalex.org/I42999171"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"Zhenhui Xu","raw_affiliation_strings":["Department of Engineering and Applied Sciences, Sophia University, Tokyo, Japan"],"affiliations":[{"raw_affiliation_string":"Department of Engineering and Applied Sciences, Sophia University, Tokyo, Japan","institution_ids":["https://openalex.org/I42999171"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5015056057","display_name":"Tielong Shen","orcid":"https://orcid.org/0000-0002-2183-9978"},"institutions":[{"id":"https://openalex.org/I42999171","display_name":"Sophia University","ror":"https://ror.org/01nckkm68","country_code":"JP","type":"education","lineage":["https://openalex.org/I42999171"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Tielong Shen","raw_affiliation_strings":["Department of Engineering and Applied Sciences, Sophia University, Tokyo, Japan"],"affiliations":[{"raw_affiliation_string":"Department of Engineering and Applied Sciences, Sophia University, Tokyo, Japan","institution_ids":["https://openalex.org/I42999171"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5020035625","display_name":"Daizhan Cheng","orcid":"https://orcid.org/0000-0001-5088-3209"},"institutions":[{"id":"https://openalex.org/I4210120485","display_name":"Academy of Mathematics and Systems Science","ror":"https://ror.org/02jkmyk67","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210120485"]},{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"funder","lineage":["https://openalex.org/I19820366"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Daizhan Cheng","raw_affiliation_strings":["Key Laboratory of Systems and Control, Academy of Mathematics and Systems Sciences, Chinese Academy of Sciences, Beijing, China"],"affiliations":[{"raw_affiliation_string":"Key Laboratory of Systems and Control, Academy of Mathematics and Systems Sciences, Chinese Academy of Sciences, Beijing, China","institution_ids":["https://openalex.org/I4210120485","https://openalex.org/I19820366"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5100729868"],"corresponding_institution_ids":["https://openalex.org/I42999171"],"apc_list":null,"apc_paid":null,"fwci":1.6885,"has_fulltext":false,"cited_by_count":21,"citation_normalized_percentile":{"value":0.8815803,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":95,"max":99},"biblio":{"volume":"33","issue":"4","first_page":"1520","last_page":"1534"},"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":0.9794999957084656,"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/T10675","display_name":"Mechanical Circulatory Support Devices","score":0.9740999937057495,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/reinforcement-learning","display_name":"Reinforcement learning","score":0.7942785620689392},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.6852083206176758},{"id":"https://openalex.org/keywords/embedding","display_name":"Embedding","score":0.6251257061958313},{"id":"https://openalex.org/keywords/trajectory","display_name":"Trajectory","score":0.6221259832382202},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6178229451179504},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.6020307540893555},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5733124017715454},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.5649560689926147},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.5587871670722961},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.48623552918434143},{"id":"https://openalex.org/keywords/state","display_name":"State (computer science)","score":0.47786587476730347},{"id":"https://openalex.org/keywords/noise","display_name":"Noise (video)","score":0.41637271642684937},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.36467814445495605},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3246302604675293},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3078400194644928},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.27086353302001953},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.2073984146118164},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.08061820268630981}],"concepts":[{"id":"https://openalex.org/C97541855","wikidata":"https://www.wikidata.org/wiki/Q830687","display_name":"Reinforcement learning","level":2,"score":0.7942785620689392},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6852083206176758},{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.6251257061958313},{"id":"https://openalex.org/C13662910","wikidata":"https://www.wikidata.org/wiki/Q193139","display_name":"Trajectory","level":2,"score":0.6221259832382202},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6178229451179504},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.6020307540893555},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5733124017715454},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5649560689926147},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.5587871670722961},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.48623552918434143},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.47786587476730347},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.41637271642684937},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.36467814445495605},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3246302604675293},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3078400194644928},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.27086353302001953},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.2073984146118164},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.08061820268630981},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","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},{"id":"https://openalex.org/C1276947","wikidata":"https://www.wikidata.org/wiki/Q333","display_name":"Astronomy","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}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tnnls.2020.3042589","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tnnls.2020.3042589","pdf_url":null,"source":{"id":"https://openalex.org/S4210175523","display_name":"IEEE Transactions on Neural Networks and Learning Systems","issn_l":"2162-237X","issn":["2162-237X","2162-2388"],"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 Neural Networks and Learning Systems","raw_type":"journal-article"},{"id":"pmid:33347416","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/33347416","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE transactions on neural networks and learning systems","raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Peace, Justice and strong institutions","score":0.550000011920929,"id":"https://metadata.un.org/sdg/16"}],"awards":[{"id":"https://openalex.org/G1939058816","display_name":null,"funder_award_id":"(B)17H03284","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"}],"funders":[{"id":"https://openalex.org/F4320334764","display_name":"Japan Society for the Promotion of Science","ror":"https://ror.org/00hhkn466"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":36,"referenced_works":["https://openalex.org/W5108103","https://openalex.org/W132264163","https://openalex.org/W162622153","https://openalex.org/W234738007","https://openalex.org/W1492186721","https://openalex.org/W1508405709","https://openalex.org/W1515851193","https://openalex.org/W1527736490","https://openalex.org/W1548148540","https://openalex.org/W1599132769","https://openalex.org/W1854776945","https://openalex.org/W1907796993","https://openalex.org/W1965687381","https://openalex.org/W1983523797","https://openalex.org/W2005229381","https://openalex.org/W2011694027","https://openalex.org/W2027197837","https://openalex.org/W2034806307","https://openalex.org/W2046386580","https://openalex.org/W2047090868","https://openalex.org/W2057484415","https://openalex.org/W2073591687","https://openalex.org/W2073990179","https://openalex.org/W2081514674","https://openalex.org/W2083283377","https://openalex.org/W2093831009","https://openalex.org/W2098432798","https://openalex.org/W2104843094","https://openalex.org/W2108286682","https://openalex.org/W2132858840","https://openalex.org/W2148439597","https://openalex.org/W2149481490","https://openalex.org/W2160561608","https://openalex.org/W2165501837","https://openalex.org/W3103456419","https://openalex.org/W6799835771"],"related_works":["https://openalex.org/W2081900870","https://openalex.org/W4306904969","https://openalex.org/W2138720691","https://openalex.org/W4362501864","https://openalex.org/W4323768008","https://openalex.org/W1941703695","https://openalex.org/W4380318855","https://openalex.org/W3084456289","https://openalex.org/W2024136090","https://openalex.org/W3131574667"],"abstract_inverted_index":{"In":[0],"this":[1],"article,":[2],"a":[3,87],"novel":[4],"integral":[5],"reinforcement":[6],"learning":[7,30],"(IRL)":[8],"algorithm":[9,92,138,169],"is":[10,31,55,70,93,114,121,139],"proposed":[11,189],"to":[12,33,61,72,109,128,183],"solve":[13],"the":[14,35,39,47,63,67,74,78,84,96,101,110,124,130,133,137,142,149,155,162,168,171,174,185,188],"optimal":[15,64,111],"control":[16],"problem":[17],"for":[18],"continuous-time":[19],"nonlinear":[20],"systems":[21],"with":[22],"unknown":[23],"dynamics.":[24,135],"The":[25,145,165],"main":[26],"challenging":[27],"issue":[28,48],"in":[29],"how":[32],"reject":[34],"oscillation":[36],"caused":[37],"by":[38,49,82,161],"externally":[40],"added":[41],"probing":[42],"noise.":[43],"This":[44],"article":[45],"challenges":[46],"embedding":[50],"an":[51,58,117],"auxiliary":[52,68],"trajectory":[53,69,76],"that":[54,116],"designed":[56],"as":[57],"exciting":[59],"signal":[60],"learn":[62],"solution.":[65,112],"First,":[66],"used":[71],"decompose":[73],"state":[75],"of":[77,132,148,167,173,187],"controlled":[79],"system.":[80],"Then,":[81],"using":[83],"decoupled":[85],"trajectories,":[86],"model-free":[88],"policy":[89,97,102,125],"iteration":[90],"(PI)":[91],"developed,":[94],"where":[95],"evaluation":[98],"step":[99,104,127],"and":[100,154,170],"improvement":[103,126],"are":[105,158,177,181],"alternated":[106],"until":[107],"convergence":[108,166],"It":[113],"noted":[115],"appropriate":[118],"external":[119],"input":[120],"introduced":[122],"at":[123],"eliminate":[129],"requirement":[131],"input-to-state":[134],"Finally,":[136],"implemented":[140],"on":[141],"actor-critic":[143],"structure.":[144],"output":[146],"weights":[147],"critic":[150],"neural":[151],"network":[152],"(NN)":[153],"actor":[156],"NN":[157],"updated":[159],"sequentially":[160],"least-squares":[163],"methods.":[164],"stability":[172],"closed-loop":[175],"system":[176],"guaranteed.":[178],"Two":[179],"examples":[180],"given":[182],"show":[184],"effectiveness":[186],"algorithm.":[190]},"counts_by_year":[{"year":2025,"cited_by_count":6},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":6},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}