{"id":"https://openalex.org/W4389104903","doi":"https://doi.org/10.1109/tnnls.2023.3335138","title":"Robust Approximate Dynamic Programming for Nonlinear Systems With Both Model Error and External Disturbance","display_name":"Robust Approximate Dynamic Programming for Nonlinear Systems With Both Model Error and External Disturbance","publication_year":2023,"publication_date":"2023-11-28","ids":{"openalex":"https://openalex.org/W4389104903","doi":"https://doi.org/10.1109/tnnls.2023.3335138","pmid":"https://pubmed.ncbi.nlm.nih.gov/38015685"},"language":"en","primary_location":{"id":"doi:10.1109/tnnls.2023.3335138","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tnnls.2023.3335138","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/A5100696317","display_name":"Jie Li","orcid":"https://orcid.org/0000-0002-3718-5593"},"institutions":[{"id":"https://openalex.org/I99065089","display_name":"Tsinghua University","ror":"https://ror.org/03cve4549","country_code":"CN","type":"education","lineage":["https://openalex.org/I99065089"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Jie Li","raw_affiliation_strings":["School of Vehicle and Mobility, Tsinghua University, Beijing, China"],"affiliations":[{"raw_affiliation_string":"School of Vehicle and Mobility, Tsinghua University, Beijing, China","institution_ids":["https://openalex.org/I99065089"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5076961688","display_name":"Ryozo Nagamune","orcid":"https://orcid.org/0000-0002-9416-5564"},"institutions":[{"id":"https://openalex.org/I141945490","display_name":"University of British Columbia","ror":"https://ror.org/03rmrcq20","country_code":"CA","type":"education","lineage":["https://openalex.org/I141945490"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Ryozo Nagamune","raw_affiliation_strings":["Department of Mechanical Engineering, The University of British Columbia, Vancouver, BC, Canada","Department of Mechanical Engineering, The University of British Columbia, Vancouver, Canada"],"affiliations":[{"raw_affiliation_string":"Department of Mechanical Engineering, The University of British Columbia, Vancouver, BC, Canada","institution_ids":["https://openalex.org/I141945490"]},{"raw_affiliation_string":"Department of Mechanical Engineering, The University of British Columbia, Vancouver, Canada","institution_ids":["https://openalex.org/I141945490"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5028357638","display_name":"Yuhang Zhang","orcid":"https://orcid.org/0009-0006-4272-5730"},"institutions":[{"id":"https://openalex.org/I99065089","display_name":"Tsinghua University","ror":"https://ror.org/03cve4549","country_code":"CN","type":"education","lineage":["https://openalex.org/I99065089"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yuhang Zhang","raw_affiliation_strings":["School of Vehicle and Mobility, Tsinghua University, Beijing, China"],"affiliations":[{"raw_affiliation_string":"School of Vehicle and Mobility, Tsinghua University, Beijing, China","institution_ids":["https://openalex.org/I99065089"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100747108","display_name":"Shengbo Eben Li","orcid":"https://orcid.org/0000-0003-4923-3633"},"institutions":[{"id":"https://openalex.org/I99065089","display_name":"Tsinghua University","ror":"https://ror.org/03cve4549","country_code":"CN","type":"education","lineage":["https://openalex.org/I99065089"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Shengbo Eben Li","raw_affiliation_strings":["School of Vehicle and Mobility, Tsinghua University, Beijing, China"],"affiliations":[{"raw_affiliation_string":"School of Vehicle and Mobility, Tsinghua University, Beijing, China","institution_ids":["https://openalex.org/I99065089"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5100696317"],"corresponding_institution_ids":["https://openalex.org/I99065089"],"apc_list":null,"apc_paid":null,"fwci":1.8133,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.87869616,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"36","issue":"1","first_page":"896","last_page":"910"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12794","display_name":"Adaptive Dynamic Programming Control","score":0.991100013256073,"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":0.991100013256073,"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":0.9552000164985657,"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/T14011","display_name":"Elevator Systems and Control","score":0.9380999803543091,"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/lyapunov-function","display_name":"Lyapunov function","score":0.647040605545044},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5838226079940796},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.512794554233551},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5038322806358337},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.47671833634376526},{"id":"https://openalex.org/keywords/notation","display_name":"Notation","score":0.46758389472961426},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.45817041397094727},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3456329107284546},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3230257034301758},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.12770918011665344}],"concepts":[{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.647040605545044},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5838226079940796},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.512794554233551},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5038322806358337},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.47671833634376526},{"id":"https://openalex.org/C45357846","wikidata":"https://www.wikidata.org/wiki/Q2001982","display_name":"Notation","level":2,"score":0.46758389472961426},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.45817041397094727},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3456329107284546},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3230257034301758},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.12770918011665344},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"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/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tnnls.2023.3335138","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tnnls.2023.3335138","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:38015685","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/38015685","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":[],"awards":[{"id":"https://openalex.org/G1095835165","display_name":null,"funder_award_id":"52221005","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G1500936459","display_name":null,"funder_award_id":"2022YFB2502901","funder_id":"https://openalex.org/F4320335777","funder_display_name":"National Key Research and Development Program of China"},{"id":"https://openalex.org/G166390454","display_name":null,"funder_award_id":"U20A20334","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6259678243","display_name":null,"funder_award_id":"52072213","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/F4320335777","display_name":"National Key Research and Development Program of China","ror":null}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":36,"referenced_works":["https://openalex.org/W1461376240","https://openalex.org/W1524505501","https://openalex.org/W1558831267","https://openalex.org/W1614417283","https://openalex.org/W1650553268","https://openalex.org/W1680219837","https://openalex.org/W1989855774","https://openalex.org/W1997603681","https://openalex.org/W1998361253","https://openalex.org/W1999213690","https://openalex.org/W2019478222","https://openalex.org/W2030615861","https://openalex.org/W2073591687","https://openalex.org/W2085194340","https://openalex.org/W2109640889","https://openalex.org/W2116479681","https://openalex.org/W2117717397","https://openalex.org/W2120581895","https://openalex.org/W2142976549","https://openalex.org/W2157577161","https://openalex.org/W2173261491","https://openalex.org/W2293777325","https://openalex.org/W2484646121","https://openalex.org/W2498694880","https://openalex.org/W2583050531","https://openalex.org/W2618268502","https://openalex.org/W2727279496","https://openalex.org/W2758863483","https://openalex.org/W2797189006","https://openalex.org/W2809391642","https://openalex.org/W3005837809","https://openalex.org/W3011286351","https://openalex.org/W3094638344","https://openalex.org/W4323897042","https://openalex.org/W4362650413","https://openalex.org/W4364856217"],"related_works":["https://openalex.org/W2504004674","https://openalex.org/W2498744856","https://openalex.org/W1595229445","https://openalex.org/W4390482104","https://openalex.org/W322408318","https://openalex.org/W149041114","https://openalex.org/W2963177394","https://openalex.org/W1965815883","https://openalex.org/W4313359513","https://openalex.org/W763418848"],"abstract_inverted_index":{"Model":[0],"error":[1,61],"and":[2,27,62,92,106,113,138,143,168],"external":[3,63],"disturbance":[4,64],"have":[5],"been":[6],"separately":[7],"addressed":[8],"by":[9,147],"optimizing":[10],"the":[11,20,30,48,59,72,85,88,121,124,135,148,162,178,181],"definite":[12],"performance":[13,68],"in":[14,47,65,75],"standard":[15],"linear":[16],"control":[17,78],"problems.":[18,39,69],"However,":[19],"concurrent":[21],"handling":[22],"of":[23,53,123,151,165,180],"both":[24,141],"introduces":[25,42],"uncertainty":[26,94],"nonconvexity":[28],"into":[29],"performance,":[31],"posing":[32],"a":[33,130],"huge":[34],"challenge":[35],"for":[36],"solving":[37],"nonlinear":[38,66,76],"This":[40],"article":[41],"an":[43],"additional":[44,89],"cost":[45,90],"function":[46,91],"augmented":[49,125],"Hamilton-Jacobi-Isaacs":[50],"(HJI)":[51],"equation":[52],"zero-sum":[54],"games":[55],"to":[56,109,119,176],"simultaneously":[57],"manage":[58],"model":[60,83,93],"robust":[67,77],"For":[70],"satisfying":[71],"Hamilton-Jacobi":[73],"inequality":[74],"theory":[79],"under":[80],"all":[81],"considered":[82],"errors,":[84],"relationship":[86],"between":[87],"is":[95,117],"revealed.":[96],"A":[97],"critic":[98,136,169],"online":[99],"learning":[100],"algorithm,":[101],"applying":[102],"Lyapunov":[103,132],"stabilizing":[104],"terms":[105],"historical":[107,159],"states":[108],"reinforce":[110],"training":[111],"stability":[112,142],"achieve":[114],"persistent":[115],"learning,":[116],"proposed":[118,182],"approximate":[120],"solution":[122],"HJI":[126],"equation.":[127],"By":[128],"constructing":[129],"joint":[131],"candidate":[133],"about":[134],"weight":[137],"system":[139,166],"state,":[140],"convergence":[144],"are":[145,174],"proved":[146],"second":[149],"method":[150],"Lyapunov.":[152],"Theoretical":[153],"results":[154],"also":[155],"show":[156],"that":[157],"introducing":[158],"data":[160],"reduces":[161],"ultimate":[163],"bounds":[164],"state":[167],"error.":[170],"Three":[171],"numerical":[172],"examples":[173],"conducted":[175],"demonstrate":[177],"effectiveness":[179],"method.":[183]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":2}],"updated_date":"2026-03-15T09:29:46.208133","created_date":"2025-10-10T00:00:00"}
