{"id":"https://openalex.org/W3196755144","doi":"https://doi.org/10.1109/tcyb.2021.3108034","title":"Hamiltonian-Driven Adaptive Dynamic Programming With Approximation Errors","display_name":"Hamiltonian-Driven Adaptive Dynamic Programming With Approximation Errors","publication_year":2021,"publication_date":"2021-09-08","ids":{"openalex":"https://openalex.org/W3196755144","doi":"https://doi.org/10.1109/tcyb.2021.3108034","mag":"3196755144","pmid":"https://pubmed.ncbi.nlm.nih.gov/34495864"},"language":"en","primary_location":{"id":"doi:10.1109/tcyb.2021.3108034","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcyb.2021.3108034","pdf_url":null,"source":{"id":"https://openalex.org/S4210191041","display_name":"IEEE Transactions on Cybernetics","issn_l":"2168-2267","issn":["2168-2267","2168-2275"],"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 Cybernetics","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/A5053342436","display_name":"Yongliang Yang","orcid":"https://orcid.org/0000-0002-3144-8604"},"institutions":[{"id":"https://openalex.org/I92403157","display_name":"University of Science and Technology Beijing","ror":"https://ror.org/02egmk993","country_code":"CN","type":"education","lineage":["https://openalex.org/I92403157"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Yongliang Yang","raw_affiliation_strings":["School of Automation and Electrical Engineering and the Institute of Artificial Intelligence, University of Science and Technology Beijing, Beijing, China"],"affiliations":[{"raw_affiliation_string":"School of Automation and Electrical Engineering and the Institute of Artificial Intelligence, University of Science and Technology Beijing, Beijing, China","institution_ids":["https://openalex.org/I92403157"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5063118155","display_name":"Hamidreza Modares","orcid":"https://orcid.org/0000-0003-0800-5140"},"institutions":[{"id":"https://openalex.org/I87216513","display_name":"Michigan State University","ror":"https://ror.org/05hs6h993","country_code":"US","type":"education","lineage":["https://openalex.org/I87216513"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Hamidreza Modares","raw_affiliation_strings":["Mechanical Engineering Department, Michigan State University, East Lansing, MI, USA"],"affiliations":[{"raw_affiliation_string":"Mechanical Engineering Department, Michigan State University, East Lansing, MI, USA","institution_ids":["https://openalex.org/I87216513"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5040301558","display_name":"Kyriakos G. Vamvoudakis","orcid":"https://orcid.org/0000-0003-1978-4848"},"institutions":[{"id":"https://openalex.org/I130701444","display_name":"Georgia Institute of Technology","ror":"https://ror.org/01zkghx44","country_code":"US","type":"education","lineage":["https://openalex.org/I130701444"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Kyriakos G. Vamvoudakis","raw_affiliation_strings":["Daniel Guggenheim School of Aerospace Engineering, Georgia Tech, Atlanta, GA, USA"],"affiliations":[{"raw_affiliation_string":"Daniel Guggenheim School of Aerospace Engineering, Georgia Tech, Atlanta, GA, USA","institution_ids":["https://openalex.org/I130701444"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5022113595","display_name":"Wei He","orcid":"https://orcid.org/0000-0002-8944-9861"},"institutions":[{"id":"https://openalex.org/I92403157","display_name":"University of Science and Technology Beijing","ror":"https://ror.org/02egmk993","country_code":"CN","type":"education","lineage":["https://openalex.org/I92403157"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Wei He","raw_affiliation_strings":["School of Automation and Electrical Engineering and the Institute of Artificial Intelligence, University of Science and Technology Beijing, Beijing, China"],"affiliations":[{"raw_affiliation_string":"School of Automation and Electrical Engineering and the Institute of Artificial Intelligence, University of Science and Technology Beijing, Beijing, China","institution_ids":["https://openalex.org/I92403157"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5012773300","display_name":"Chengzhong Xu","orcid":"https://orcid.org/0000-0001-9480-0356"},"institutions":[{"id":"https://openalex.org/I6469544","display_name":"City University of Macau","ror":"https://ror.org/04gpd4q15","country_code":"MO","type":"education","lineage":["https://openalex.org/I6469544"]},{"id":"https://openalex.org/I204512498","display_name":"University of Macau","ror":"https://ror.org/01r4q9n85","country_code":"MO","type":"education","lineage":["https://openalex.org/I204512498"]}],"countries":["MO"],"is_corresponding":false,"raw_author_name":"Cheng-Zhong Xu","raw_affiliation_strings":["State Key Laboratory of Internet of Things for Smart City, Faculty of Science and Technology, University of Macau, Macau"],"affiliations":[{"raw_affiliation_string":"State Key Laboratory of Internet of Things for Smart City, Faculty of Science and Technology, University of Macau, Macau","institution_ids":["https://openalex.org/I6469544","https://openalex.org/I204512498"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5038037619","display_name":"Donald C. Wunsch","orcid":"https://orcid.org/0000-0002-9726-9051"},"institutions":[{"id":"https://openalex.org/I20382870","display_name":"Missouri University of Science and Technology","ror":"https://ror.org/00scwqd12","country_code":"US","type":"education","lineage":["https://openalex.org/I20382870"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Donald C. Wunsch","raw_affiliation_strings":["Department of Electrical and Computer Engineering, Missouri University of Science and Technology, Rolla, MO, USA"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, Missouri University of Science and Technology, Rolla, MO, USA","institution_ids":["https://openalex.org/I20382870"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":6,"corresponding_author_ids":["https://openalex.org/A5053342436"],"corresponding_institution_ids":["https://openalex.org/I92403157"],"apc_list":null,"apc_paid":null,"fwci":12.5087,"has_fulltext":false,"cited_by_count":92,"citation_normalized_percentile":{"value":0.98960739,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":100},"biblio":{"volume":"52","issue":"12","first_page":"13762","last_page":"13773"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12794","display_name":"Adaptive Dynamic Programming Control","score":0.9994999766349792,"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":0.9994999766349792,"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":0.963699996471405,"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/T12277","display_name":"Frequency Control in Power Systems","score":0.9043999910354614,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic 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/hamilton\u2013jacobi\u2013bellman-equation","display_name":"Hamilton\u2013Jacobi\u2013Bellman equation","score":0.7794142961502075},{"id":"https://openalex.org/keywords/hamiltonian","display_name":"Hamiltonian (control theory)","score":0.6749838590621948},{"id":"https://openalex.org/keywords/dynamic-programming","display_name":"Dynamic programming","score":0.6637015342712402},{"id":"https://openalex.org/keywords/bellman-equation","display_name":"Bellman equation","score":0.6239422559738159},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5815978646278381},{"id":"https://openalex.org/keywords/reinforcement-learning","display_name":"Reinforcement learning","score":0.5046302080154419},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5006537437438965},{"id":"https://openalex.org/keywords/hamiltonian-system","display_name":"Hamiltonian system","score":0.4913729727268219},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4878864288330078},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.4541451930999756},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3252856731414795},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.22169983386993408},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.08251902461051941}],"concepts":[{"id":"https://openalex.org/C196978813","wikidata":"https://www.wikidata.org/wiki/Q3302775","display_name":"Hamilton\u2013Jacobi\u2013Bellman equation","level":3,"score":0.7794142961502075},{"id":"https://openalex.org/C130787639","wikidata":"https://www.wikidata.org/wiki/Q5645293","display_name":"Hamiltonian (control theory)","level":2,"score":0.6749838590621948},{"id":"https://openalex.org/C37404715","wikidata":"https://www.wikidata.org/wiki/Q380679","display_name":"Dynamic programming","level":2,"score":0.6637015342712402},{"id":"https://openalex.org/C14646407","wikidata":"https://www.wikidata.org/wiki/Q1430750","display_name":"Bellman equation","level":2,"score":0.6239422559738159},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5815978646278381},{"id":"https://openalex.org/C97541855","wikidata":"https://www.wikidata.org/wiki/Q830687","display_name":"Reinforcement learning","level":2,"score":0.5046302080154419},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5006537437438965},{"id":"https://openalex.org/C121770821","wikidata":"https://www.wikidata.org/wiki/Q2072471","display_name":"Hamiltonian system","level":2,"score":0.4913729727268219},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4878864288330078},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.4541451930999756},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3252856731414795},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.22169983386993408},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08251902461051941},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","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/tcyb.2021.3108034","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcyb.2021.3108034","pdf_url":null,"source":{"id":"https://openalex.org/S4210191041","display_name":"IEEE Transactions on Cybernetics","issn_l":"2168-2267","issn":["2168-2267","2168-2275"],"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 Cybernetics","raw_type":"journal-article"},{"id":"pmid:34495864","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/34495864","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 cybernetics","raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16","score":0.5600000023841858}],"awards":[{"id":"https://openalex.org/G1131598070","display_name":null,"funder_award_id":"2019YFB2102100","funder_id":"https://openalex.org/F4320335777","funder_display_name":"National Key Research and Development Program of China"},{"id":"https://openalex.org/G1566696561","display_name":null,"funder_award_id":"61903028","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3094653860","display_name":null,"funder_award_id":"W911NF-18-2-0260","funder_id":"https://openalex.org/F4320338295","funder_display_name":"Army Research Laboratory"},{"id":"https://openalex.org/G4286541177","display_name":null,"funder_award_id":"CPS1851588","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G4997969063","display_name":null,"funder_award_id":"S&AS1849198","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G76066946","display_name":null,"funder_award_id":"0015/2019/AKP","funder_id":"https://openalex.org/F4320323893","funder_display_name":"Fundo para o Desenvolvimento das Ci\u00eancias e da Tecnologia"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320323893","display_name":"Fundo para o Desenvolvimento das Ci\u00eancias e da Tecnologia","ror":"https://ror.org/05vna4324"},{"id":"https://openalex.org/F4320333675","display_name":"Intelligent Systems Center","ror":null},{"id":"https://openalex.org/F4320335777","display_name":"National Key Research and Development Program of China","ror":null},{"id":"https://openalex.org/F4320338295","display_name":"Army Research Laboratory","ror":"https://ror.org/011hc8f90"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":60,"referenced_works":["https://openalex.org/W1522684141","https://openalex.org/W1559261542","https://openalex.org/W1566309885","https://openalex.org/W1614417283","https://openalex.org/W1972243698","https://openalex.org/W1983089547","https://openalex.org/W1983523797","https://openalex.org/W2010152647","https://openalex.org/W2011310556","https://openalex.org/W2012451615","https://openalex.org/W2017570421","https://openalex.org/W2019478222","https://openalex.org/W2024303516","https://openalex.org/W2037025184","https://openalex.org/W2047090868","https://openalex.org/W2073591687","https://openalex.org/W2073990179","https://openalex.org/W2098432798","https://openalex.org/W2104843094","https://openalex.org/W2108286682","https://openalex.org/W2109640889","https://openalex.org/W2118005002","https://openalex.org/W2120249358","https://openalex.org/W2124829859","https://openalex.org/W2135574445","https://openalex.org/W2136064843","https://openalex.org/W2148439597","https://openalex.org/W2159543578","https://openalex.org/W2165501837","https://openalex.org/W2331243380","https://openalex.org/W2417679505","https://openalex.org/W2484646121","https://openalex.org/W2538000344","https://openalex.org/W2580629550","https://openalex.org/W2585299106","https://openalex.org/W2727279496","https://openalex.org/W2803973384","https://openalex.org/W2919774326","https://openalex.org/W2940942829","https://openalex.org/W2961703895","https://openalex.org/W2962974451","https://openalex.org/W2963393268","https://openalex.org/W2988823422","https://openalex.org/W2995552585","https://openalex.org/W2999863957","https://openalex.org/W3006344226","https://openalex.org/W3009014967","https://openalex.org/W3094615062","https://openalex.org/W3103456419","https://openalex.org/W3111531580","https://openalex.org/W3120441334","https://openalex.org/W3187550742","https://openalex.org/W3213472335","https://openalex.org/W4205326910","https://openalex.org/W4213295258","https://openalex.org/W4296154082","https://openalex.org/W4301747304","https://openalex.org/W6772863106","https://openalex.org/W6788948764","https://openalex.org/W6804409665"],"related_works":["https://openalex.org/W4239477580","https://openalex.org/W4255265352","https://openalex.org/W2921905705","https://openalex.org/W1632524629","https://openalex.org/W4292330635","https://openalex.org/W2902017027","https://openalex.org/W2766998270","https://openalex.org/W2950982235","https://openalex.org/W2052286527","https://openalex.org/W4306892756"],"abstract_inverted_index":{"In":[0],"this":[1],"article,":[2],"we":[3,77],"consider":[4],"an":[5,79,127],"iterative":[6,80,103],"adaptive":[7],"dynamic":[8],"programming":[9],"(ADP)":[10],"algorithm":[11,63,82],"within":[12,72],"the":[13,18,23,43,47,55,59,70,73,87,91,102,111,119,140,143],"Hamiltonian-driven":[14,74],"framework":[15],"to":[16,41,106,118],"solve":[17],"Hamilton-Jacobi-Bellman":[19],"(HJB)":[20],"equation":[21,57],"for":[22,31],"infinite-horizon":[24],"optimal":[25,120],"control":[26],"problem":[27],"in":[28,67],"continuous":[29],"time":[30],"nonlinear":[32],"systems.":[33],"First,":[34],"a":[35,98],"novel":[36],"function,":[37],"\"min-Hamiltonian,\"":[38],"is":[39,51,133],"defined":[40],"capture":[42],"fundamental":[44],"properties":[45],"of":[46,69,110,142],"classical":[48],"Hamiltonian.":[49],"It":[50],"shown":[52],"that":[53,83],"both":[54],"HJB":[56],"and":[58],"policy":[60,92],"iteration":[61],"(PI)":[62],"can":[64],"be":[65],"formulated":[66],"terms":[68],"min-Hamiltonian":[71],"framework.":[75,145],"Moreover,":[76],"develop":[78],"ADP":[81],"takes":[84],"into":[85],"consideration":[86],"approximation":[88],"errors":[89],"during":[90],"evaluation":[93],"step.":[94],"We":[95],"then":[96],"derive":[97],"sufficient":[99],"condition":[100],"on":[101,126],"value":[104],"gradient":[105],"guarantee":[107],"closed-loop":[108],"stability":[109],"equilibrium":[112],"point":[113],"as":[114,116],"well":[115],"convergence":[117],"value.":[121],"A":[122],"model-free":[123],"extension":[124],"based":[125],"off-policy":[128],"reinforcement":[129],"learning":[130],"(RL)":[131],"technique":[132],"also":[134],"provided.":[135],"Finally,":[136],"numerical":[137],"results":[138],"illustrate":[139],"efficacy":[141],"proposed":[144]},"counts_by_year":[{"year":2025,"cited_by_count":9},{"year":2024,"cited_by_count":21},{"year":2023,"cited_by_count":34},{"year":2022,"cited_by_count":27},{"year":2021,"cited_by_count":1}],"updated_date":"2026-03-12T08:34:05.389933","created_date":"2025-10-10T00:00:00"}