{"id":"https://openalex.org/W4417308588","doi":"https://doi.org/10.1109/cdc57313.2025.11312822","title":"Bridging Continuous-time LQR and Reinforcement Learning via Gradient Flow of the Bellman Error","display_name":"Bridging Continuous-time LQR and Reinforcement Learning via Gradient Flow of the Bellman Error","publication_year":2025,"publication_date":"2025-12-09","ids":{"openalex":"https://openalex.org/W4417308588","doi":"https://doi.org/10.1109/cdc57313.2025.11312822"},"language":"en","primary_location":{"id":"doi:10.1109/cdc57313.2025.11312822","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc57313.2025.11312822","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2025 IEEE 64th Conference on Decision and Control (CDC)","raw_type":"proceedings-article"},"type":"conference-paper","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2506.09685","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5018080565","display_name":"Armin Gie\u00dfler","orcid":null},"institutions":[{"id":"https://openalex.org/I102335020","display_name":"Karlsruhe Institute of Technology","ror":"https://ror.org/04t3en479","country_code":"DE","type":"education","lineage":["https://openalex.org/I102335020","https://openalex.org/I1305996414"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Armin Gie\u00dfler","raw_affiliation_strings":["Karlsruhe Institute of Technology (KIT),Institute of Control Systems,Karlsruhe,Germany,76131"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Karlsruhe Institute of Technology (KIT),Institute of Control Systems,Karlsruhe,Germany,76131","institution_ids":["https://openalex.org/I102335020"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5071053356","display_name":"Albertus Johannes Malan","orcid":"https://orcid.org/0000-0002-6564-008X"},"institutions":[{"id":"https://openalex.org/I102335020","display_name":"Karlsruhe Institute of Technology","ror":"https://ror.org/04t3en479","country_code":"DE","type":"education","lineage":["https://openalex.org/I102335020","https://openalex.org/I1305996414"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Albertus Johannes Malan","raw_affiliation_strings":["Karlsruhe Institute of Technology (KIT),Institute of Control Systems,Karlsruhe,Germany,76131"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Karlsruhe Institute of Technology (KIT),Institute of Control Systems,Karlsruhe,Germany,76131","institution_ids":["https://openalex.org/I102335020"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5040502908","display_name":"S\u00f6ren Hohmann","orcid":"https://orcid.org/0000-0002-4170-1431"},"institutions":[{"id":"https://openalex.org/I102335020","display_name":"Karlsruhe Institute of Technology","ror":"https://ror.org/04t3en479","country_code":"DE","type":"education","lineage":["https://openalex.org/I102335020","https://openalex.org/I1305996414"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"S\u00f6ren Hohmann","raw_affiliation_strings":["Karlsruhe Institute of Technology (KIT),Institute of Control Systems,Karlsruhe,Germany,76131"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Karlsruhe Institute of Technology (KIT),Institute of Control Systems,Karlsruhe,Germany,76131","institution_ids":["https://openalex.org/I102335020"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I102335020"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.47443763,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"3761","last_page":"3768"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12794","display_name":"Adaptive Dynamic Programming Control","score":0.772599995136261,"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":0.772599995136261,"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/T11206","display_name":"Model Reduction and Neural Networks","score":0.08640000224113464,"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"}},{"id":"https://openalex.org/T10462","display_name":"Reinforcement Learning in Robotics","score":0.06650000065565109,"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/linear-quadratic-regulator","display_name":"Linear-quadratic regulator","score":0.7057999968528748},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.6703000068664551},{"id":"https://openalex.org/keywords/riccati-equation","display_name":"Riccati equation","score":0.5791000127792358},{"id":"https://openalex.org/keywords/algebraic-riccati-equation","display_name":"Algebraic Riccati equation","score":0.5722000002861023},{"id":"https://openalex.org/keywords/reinforcement-learning","display_name":"Reinforcement learning","score":0.559499979019165},{"id":"https://openalex.org/keywords/trajectory","display_name":"Trajectory","score":0.48410001397132874},{"id":"https://openalex.org/keywords/bellman-equation","display_name":"Bellman equation","score":0.48240000009536743},{"id":"https://openalex.org/keywords/lyapunov-function","display_name":"Lyapunov function","score":0.4675999879837036},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.4413999915122986},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.42419999837875366}],"concepts":[{"id":"https://openalex.org/C98779006","wikidata":"https://www.wikidata.org/wiki/Q2520550","display_name":"Linear-quadratic regulator","level":3,"score":0.7057999968528748},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.6703000068664551},{"id":"https://openalex.org/C45473103","wikidata":"https://www.wikidata.org/wiki/Q851503","display_name":"Riccati equation","level":3,"score":0.5791000127792358},{"id":"https://openalex.org/C13847129","wikidata":"https://www.wikidata.org/wiki/Q4723989","display_name":"Algebraic Riccati equation","level":4,"score":0.5722000002861023},{"id":"https://openalex.org/C97541855","wikidata":"https://www.wikidata.org/wiki/Q830687","display_name":"Reinforcement learning","level":2,"score":0.559499979019165},{"id":"https://openalex.org/C13662910","wikidata":"https://www.wikidata.org/wiki/Q193139","display_name":"Trajectory","level":2,"score":0.48410001397132874},{"id":"https://openalex.org/C14646407","wikidata":"https://www.wikidata.org/wiki/Q1430750","display_name":"Bellman equation","level":2,"score":0.48240000009536743},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4754999876022339},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.4675999879837036},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.4413999915122986},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.43389999866485596},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.42419999837875366},{"id":"https://openalex.org/C167964875","wikidata":"https://www.wikidata.org/wiki/Q17011487","display_name":"Exponential stability","level":3,"score":0.4171999990940094},{"id":"https://openalex.org/C174348530","wikidata":"https://www.wikidata.org/wiki/Q188635","display_name":"Bridging (networking)","level":2,"score":0.40059998631477356},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.35510000586509705},{"id":"https://openalex.org/C167879884","wikidata":"https://www.wikidata.org/wiki/Q727568","display_name":"Balanced flow","level":2,"score":0.35109999775886536},{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.3508000075817108},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.34779998660087585},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.3456999957561493},{"id":"https://openalex.org/C115680565","wikidata":"https://www.wikidata.org/wiki/Q5977448","display_name":"Gradient method","level":2,"score":0.3391999900341034},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.33230000734329224},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.3285999894142151},{"id":"https://openalex.org/C196978813","wikidata":"https://www.wikidata.org/wiki/Q3302775","display_name":"Hamilton\u2013Jacobi\u2013Bellman equation","level":3,"score":0.31130000948905945},{"id":"https://openalex.org/C61445026","wikidata":"https://www.wikidata.org/wiki/Q217608","display_name":"Fixed point","level":2,"score":0.30880001187324524},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.29660001397132874},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.28610000014305115},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.2851000130176544},{"id":"https://openalex.org/C3018623182","wikidata":"https://www.wikidata.org/wiki/Q154021","display_name":"Output feedback","level":3,"score":0.2732999920845032},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.2728999853134155},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.2689000070095062},{"id":"https://openalex.org/C189237950","wikidata":"https://www.wikidata.org/wiki/Q2500758","display_name":"Stationary point","level":2,"score":0.26600000262260437},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.265500009059906},{"id":"https://openalex.org/C3018651601","wikidata":"https://www.wikidata.org/wiki/Q183635","display_name":"Feedback control","level":2,"score":0.2574000060558319},{"id":"https://openalex.org/C6929976","wikidata":"https://www.wikidata.org/wiki/Q3771881","display_name":"Regulator","level":3,"score":0.25540000200271606},{"id":"https://openalex.org/C2776829284","wikidata":"https://www.wikidata.org/wiki/Q1341651","display_name":"Lyapunov stability","level":3,"score":0.25110000371932983}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1109/cdc57313.2025.11312822","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc57313.2025.11312822","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2025 IEEE 64th Conference on Decision and Control (CDC)","raw_type":"proceedings-article"},{"id":"pmh:oai:arXiv.org:2506.09685","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2506.09685","pdf_url":"https://arxiv.org/pdf/2506.09685","source":{"id":"https://openalex.org/S4393918464","display_name":"ArXiv.org","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:arXiv.org:2506.09685","is_oa":true,"landing_page_url":"https://arxiv.org/abs/2506.09685","pdf_url":"https://arxiv.org/pdf/2506.09685","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2506.09685","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2506.09685","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2506.09685","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2506.09685","pdf_url":"https://arxiv.org/pdf/2506.09685","source":{"id":"https://openalex.org/S4393918464","display_name":"ArXiv.org","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"In":[0],"this":[1,114],"paper,":[2],"we":[3,81],"present":[4],"a":[5,29,72,83,93,104,136,140,157],"novel":[6,30],"method":[7,155],"for":[8],"computing":[9],"the":[10,15,36,42,53,69,77,88,99,130,149,163,166],"optimal":[11,100],"feedback":[12,54,101,111],"gain":[13],"of":[14,44,52,71,87,129,165],"infinite-horizon":[16,150],"Linear":[17],"Quadratic":[18],"Regulator":[19],"(LQR)":[20],"problem":[21],"via":[22],"an":[23],"ordinary":[24],"differential":[25],"equation.":[26],"We":[27,56,152],"introduce":[28],"continuous-time":[31],"Bellman":[32,89,137],"error,":[33,138],"derived":[34],"from":[35],"Hamilton-Jacobi-Bellman":[37],"(HJB)":[38],"equation,":[39],"which":[40],"quantifies":[41],"suboptimality":[43,128],"stabilizing":[45,110],"policies":[46],"and":[47,65,67,102,122,143,159],"is":[48],"parametrized":[49],"in":[50,156],"terms":[51],"gain.":[55],"analyze":[57],"its":[58,61],"properties,":[59],"including":[60],"effective":[62],"domain,":[63],"smoothness,":[64],"coerciveness,":[66],"show":[68],"existence":[70],"unique":[73,105],"stationary":[74],"point":[75],"within":[76],"stability":[78],"region.":[79],"Furthermore,":[80],"derive":[82],"closed-form":[84],"gradient":[85,94],"expression":[86],"error":[90],"that":[91,107],"induces":[92],"flow.":[95],"This":[96],"converges":[97],"to":[98,147,162],"generates":[103],"trajectory":[106],"exclusively":[108],"comprises":[109],"policies.":[112],"Additionally,":[113],"work":[115],"advances":[116],"interesting":[117],"connections":[118],"between":[119],"LQR":[120],"theory":[121],"Reinforcement":[123],"Learning":[124],"(RL)":[125],"by":[126],"redefining":[127],"Algebraic":[131],"Riccati":[132],"Equation":[133],"(ARE)":[134],"as":[135],"adapting":[139],"state-independent":[141],"formulation,":[142],"leveraging":[144],"Lyapunov":[145],"equations":[146],"overcome":[148],"challenge.":[151],"validate":[153],"our":[154],"simulation":[158],"compare":[160],"it":[161],"state":[164],"art.":[167]},"counts_by_year":[],"updated_date":"2026-07-29T14:22:42.915294","created_date":"2025-10-10T00:00:00"}
