{"id":"https://openalex.org/W7117310817","doi":"https://doi.org/10.1109/tase.2025.3648417","title":"A Learnable LQR Controller for Uncertain Systems: Hybrid-Driven Recurrent Learning","display_name":"A Learnable LQR Controller for Uncertain Systems: Hybrid-Driven Recurrent Learning","publication_year":2025,"publication_date":"2025-12-26","ids":{"openalex":"https://openalex.org/W7117310817","doi":"https://doi.org/10.1109/tase.2025.3648417"},"language":null,"primary_location":{"id":"doi:10.1109/tase.2025.3648417","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tase.2025.3648417","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/A5062453311","display_name":"Xucun Yan","orcid":"https://orcid.org/0000-0001-6772-4618"},"institutions":[{"id":"https://openalex.org/I4210148107","display_name":"Space Engineering University","ror":"https://ror.org/04rj1td02","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210148107"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Xucun Yan","raw_affiliation_strings":["Space Engineering University, Beijing, China"],"affiliations":[{"raw_affiliation_string":"Space Engineering University, Beijing, China","institution_ids":["https://openalex.org/I4210148107"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101423831","display_name":"Wei Zhang","orcid":"https://orcid.org/0000-0001-6496-849X"},"institutions":[{"id":"https://openalex.org/I4210148107","display_name":"Space Engineering University","ror":"https://ror.org/04rj1td02","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210148107"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Wei Zhang","raw_affiliation_strings":["Space Engineering University, Beijing, China"],"affiliations":[{"raw_affiliation_string":"Space Engineering University, Beijing, China","institution_ids":["https://openalex.org/I4210148107"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5103128481","display_name":"Yiwen Jiao","orcid":"https://orcid.org/0000-0002-9060-9703"},"institutions":[{"id":"https://openalex.org/I4210148107","display_name":"Space Engineering University","ror":"https://ror.org/04rj1td02","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210148107"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yiwen Jiao","raw_affiliation_strings":["Space Engineering University, Beijing, China"],"affiliations":[{"raw_affiliation_string":"Space Engineering University, Beijing, China","institution_ids":["https://openalex.org/I4210148107"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101475266","display_name":"Tao Wu","orcid":"https://orcid.org/0000-0002-7506-2914"},"institutions":[{"id":"https://openalex.org/I4210148107","display_name":"Space Engineering University","ror":"https://ror.org/04rj1td02","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210148107"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Tao Wu","raw_affiliation_strings":["Space Engineering University, Beijing, China"],"affiliations":[{"raw_affiliation_string":"Space Engineering University, Beijing, China","institution_ids":["https://openalex.org/I4210148107"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5121353694","display_name":"Guixin Li","orcid":null},"institutions":[{"id":"https://openalex.org/I4210148107","display_name":"Space Engineering University","ror":"https://ror.org/04rj1td02","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210148107"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Guixin Li","raw_affiliation_strings":["Space Engineering University, Beijing, China"],"affiliations":[{"raw_affiliation_string":"Space Engineering University, Beijing, China","institution_ids":["https://openalex.org/I4210148107"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5121119780","display_name":"Hong Ma","orcid":null},"institutions":[{"id":"https://openalex.org/I4210148107","display_name":"Space Engineering University","ror":"https://ror.org/04rj1td02","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210148107"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Hong Ma","raw_affiliation_strings":["Space Engineering University, Beijing, China"],"affiliations":[{"raw_affiliation_string":"Space Engineering University, Beijing, China","institution_ids":["https://openalex.org/I4210148107"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5121226009","display_name":"Hongbin Ma","orcid":null},"institutions":[{"id":"https://openalex.org/I4210148107","display_name":"Space Engineering University","ror":"https://ror.org/04rj1td02","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210148107"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Hongbin Ma","raw_affiliation_strings":["Space Engineering University, Beijing, China"],"affiliations":[{"raw_affiliation_string":"Space Engineering University, Beijing, China","institution_ids":["https://openalex.org/I4210148107"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5121363736","display_name":"You Cui","orcid":null},"institutions":[{"id":"https://openalex.org/I4210118099","display_name":"China Design Group (China)","ror":"https://ror.org/02mnaa826","country_code":"CN","type":"company","lineage":["https://openalex.org/I4210118099"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"You Cui","raw_affiliation_strings":["China Aerospace Planning and Design Group Company Ltd., Beijing, China"],"affiliations":[{"raw_affiliation_string":"China Aerospace Planning and Design Group Company Ltd., Beijing, China","institution_ids":["https://openalex.org/I4210118099"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5121321621","display_name":"Zihuai Lin","orcid":null},"institutions":[{"id":"https://openalex.org/I129604602","display_name":"The University of Sydney","ror":"https://ror.org/0384j8v12","country_code":"AU","type":"education","lineage":["https://openalex.org/I129604602"]},{"id":"https://openalex.org/I3045169105","display_name":"Southern University of Science and Technology","ror":"https://ror.org/049tv2d57","country_code":"CN","type":"education","lineage":["https://openalex.org/I3045169105"]}],"countries":["AU","CN"],"is_corresponding":false,"raw_author_name":"Zihuai Lin","raw_affiliation_strings":["School of Automation and Intelligent Manufacturing, and Guangdong Provincial Key Laboratory of Fully Actuated System Control Theory and Technology, Southern University of Science and Technology, Shenzhen, China","School of Electrical and Information Engineering, The University of Sydney, Sydney, NSW, Australia"],"affiliations":[{"raw_affiliation_string":"School of Automation and Intelligent Manufacturing, and Guangdong Provincial Key Laboratory of Fully Actuated System Control Theory and Technology, Southern University of Science and Technology, Shenzhen, China","institution_ids":["https://openalex.org/I3045169105"]},{"raw_affiliation_string":"School of Electrical and Information Engineering, The University of Sydney, Sydney, NSW, Australia","institution_ids":["https://openalex.org/I129604602"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5121314308","display_name":"Zhiyun Lin","orcid":null},"institutions":[{"id":"https://openalex.org/I129604602","display_name":"The University of Sydney","ror":"https://ror.org/0384j8v12","country_code":"AU","type":"education","lineage":["https://openalex.org/I129604602"]},{"id":"https://openalex.org/I3045169105","display_name":"Southern University of Science and Technology","ror":"https://ror.org/049tv2d57","country_code":"CN","type":"education","lineage":["https://openalex.org/I3045169105"]}],"countries":["AU","CN"],"is_corresponding":false,"raw_author_name":"Zhiyun Lin","raw_affiliation_strings":["School of Automation and Intelligent Manufacturing, and Guangdong Provincial Key Laboratory of Fully Actuated System Control Theory and Technology, Southern University of Science and Technology, Shenzhen, China","School of Electrical and Information Engineering, The University of Sydney, Sydney, NSW, Australia"],"affiliations":[{"raw_affiliation_string":"School of Automation and Intelligent Manufacturing, and Guangdong Provincial Key Laboratory of Fully Actuated System Control Theory and Technology, Southern University of Science and Technology, Shenzhen, China","institution_ids":["https://openalex.org/I3045169105"]},{"raw_affiliation_string":"School of Electrical and Information Engineering, The University of Sydney, Sydney, NSW, Australia","institution_ids":["https://openalex.org/I129604602"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":10,"corresponding_author_ids":["https://openalex.org/A5062453311"],"corresponding_institution_ids":["https://openalex.org/I4210148107"],"apc_list":null,"apc_paid":null,"fwci":1.42,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.8851831,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":96,"max":98},"biblio":{"volume":"23","issue":null,"first_page":"1546","last_page":"1560"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12794","display_name":"Adaptive Dynamic Programming Control","score":0.71670001745224,"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":0.71670001745224,"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":0.19339999556541443,"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/T11206","display_name":"Model Reduction and Neural Networks","score":0.02280000038444996,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/reinforcement-learning","display_name":"Reinforcement learning","score":0.6984000205993652},{"id":"https://openalex.org/keywords/linear-quadratic-regulator","display_name":"Linear-quadratic regulator","score":0.6304000020027161},{"id":"https://openalex.org/keywords/controller","display_name":"Controller (irrigation)","score":0.5407000184059143},{"id":"https://openalex.org/keywords/key","display_name":"Key (lock)","score":0.5321000218391418},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.5210999846458435},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.5041999816894531},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.4560000002384186},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.3950999975204468}],"concepts":[{"id":"https://openalex.org/C97541855","wikidata":"https://www.wikidata.org/wiki/Q830687","display_name":"Reinforcement learning","level":2,"score":0.6984000205993652},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6453999876976013},{"id":"https://openalex.org/C98779006","wikidata":"https://www.wikidata.org/wiki/Q2520550","display_name":"Linear-quadratic regulator","level":3,"score":0.6304000020027161},{"id":"https://openalex.org/C203479927","wikidata":"https://www.wikidata.org/wiki/Q5165939","display_name":"Controller (irrigation)","level":2,"score":0.5407000184059143},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.5321000218391418},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.5210999846458435},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.5041999816894531},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.4560000002384186},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.41940000653266907},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.3950999975204468},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.3790999948978424},{"id":"https://openalex.org/C17500928","wikidata":"https://www.wikidata.org/wiki/Q959968","display_name":"Control system","level":2,"score":0.36899998784065247},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3628000020980835},{"id":"https://openalex.org/C2164484","wikidata":"https://www.wikidata.org/wiki/Q5170150","display_name":"Core (optical fiber)","level":2,"score":0.3610000014305115},{"id":"https://openalex.org/C22607594","wikidata":"https://www.wikidata.org/wiki/Q5375150","display_name":"Enabling","level":2,"score":0.34470000863075256},{"id":"https://openalex.org/C82327864","wikidata":"https://www.wikidata.org/wiki/Q835100","display_name":"Intelligent control","level":2,"score":0.32010000944137573},{"id":"https://openalex.org/C81845259","wikidata":"https://www.wikidata.org/wiki/Q290117","display_name":"Quadratic programming","level":2,"score":0.30149999260902405},{"id":"https://openalex.org/C196340769","wikidata":"https://www.wikidata.org/wiki/Q7698910","display_name":"Temporal difference learning","level":3,"score":0.299699991941452},{"id":"https://openalex.org/C133731056","wikidata":"https://www.wikidata.org/wiki/Q4917288","display_name":"Control engineering","level":1,"score":0.27399998903274536},{"id":"https://openalex.org/C147168706","wikidata":"https://www.wikidata.org/wiki/Q1457734","display_name":"Recurrent neural network","level":3,"score":0.2556000053882599},{"id":"https://openalex.org/C519536355","wikidata":"https://www.wikidata.org/wiki/Q21021151","display_name":"Repurposing","level":2,"score":0.25529998540878296}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tase.2025.3648417","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tase.2025.3648417","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/G524267663","display_name":null,"funder_award_id":"U23A20325","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8618877991","display_name":null,"funder_award_id":"2024B1212010002","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":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":41,"referenced_works":["https://openalex.org/W1606233807","https://openalex.org/W1964710473","https://openalex.org/W1973978840","https://openalex.org/W2001808786","https://openalex.org/W2012087716","https://openalex.org/W2134569556","https://openalex.org/W2145952809","https://openalex.org/W2158663867","https://openalex.org/W2323490143","https://openalex.org/W2343912161","https://openalex.org/W2509524967","https://openalex.org/W2597866042","https://openalex.org/W2790506641","https://openalex.org/W2798405286","https://openalex.org/W2822752092","https://openalex.org/W2854640194","https://openalex.org/W2885195348","https://openalex.org/W2897702175","https://openalex.org/W2903410452","https://openalex.org/W2919774326","https://openalex.org/W2978980369","https://openalex.org/W3004259300","https://openalex.org/W3088521775","https://openalex.org/W3094844886","https://openalex.org/W3095394819","https://openalex.org/W3133254695","https://openalex.org/W4205981124","https://openalex.org/W4225128020","https://openalex.org/W4226169791","https://openalex.org/W4312567063","https://openalex.org/W4312713104","https://openalex.org/W4385062410","https://openalex.org/W4389065345","https://openalex.org/W4389609868","https://openalex.org/W4392308954","https://openalex.org/W4396878038","https://openalex.org/W4401246379","https://openalex.org/W4401506952","https://openalex.org/W4404562711","https://openalex.org/W4409537054","https://openalex.org/W4409581531"],"related_works":[],"abstract_inverted_index":{"The":[0,51],"Linear":[1],"Quadratic":[2],"Regulator":[3],"(LQR)":[4],"problem":[5],"for":[6,157],"systems":[7],"with":[8,44],"uncertainty":[9],"is":[10,55,62,78,123],"challenging:":[11],"model-based":[12,41],"design":[13],"loses":[14],"optimality,":[15],"while":[16,74],"prevailing":[17],"reinforcement":[18],"learning":[19,46],"methods":[20],"demand":[21],"prohibitive":[22],"data":[23],"and":[24,130,154],"computation.":[25],"This":[26,89],"paper":[27],"introduces":[28],"a":[29,48,56,83,92,97,107,117,151],"Hybrid-Driven":[30],"Recurrent":[31],"Learning":[32],"(HDRL)":[33],"framework":[34],"that":[35,148],"bridges":[36],"this":[37],"gap":[38],"by":[39,64,80],"synergizing":[40],"optimal":[42,158],"control":[43,159],"data-driven":[45],"in":[47],"novel":[49],"way.":[50],"core":[52],"of":[53,142],"HDRL":[54,105,149],"hybrid":[57],"training":[58,138],"strategy:":[59],"the":[60,68,75,113,143],"policy":[61,76,95],"evaluated":[63],"rolling":[65],"out":[66],"on":[67],"actual":[69],"uncertain":[70],"system":[71],"(forward":[72],"pass),":[73],"gradient":[77],"computed":[79],"backpropagating":[81],"through":[82],"deterministic":[84],"nominal":[85],"model":[86],"(backward":[87],"pass).":[88],"approach":[90],"creates":[91],"low-variance,":[93],"model-guided":[94],"gradient,":[96],"fundamental":[98],"departure":[99],"from":[100],"high-variance":[101],"model-free":[102],"estimators.":[103],"Architecturally,":[104],"employs":[106],"recurrent":[108],"neural":[109],"network-like":[110],"structure,":[111],"repurposing":[112],"LQR":[114],"cost":[115],"as":[116],"self-supervised":[118],"loss.":[119],"A":[120],"key":[121],"enabler":[122],"our":[124],"method":[125],"to":[126],"convert":[127],"both":[128],"additive":[129,135],"structured":[131],"uncertainties":[132],"into":[133],"an":[134],"signal,":[136],"making":[137],"feasible":[139],"without":[140],"knowledge":[141],"perturbed":[144],"dynamics.":[145],"Simulations":[146],"demonstrate":[147],"provides":[150],"robust,":[152],"sample-efficient,":[153],"practical":[155],"solution":[156],"under":[160],"uncertainty.":[161]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-04-09T08:11:56.329763","created_date":"2025-12-26T00:00:00"}