{"id":"https://openalex.org/W2011310556","doi":"https://doi.org/10.1109/tcyb.2014.2354377","title":"Finite-Approximation-Error-Based Discrete-Time Iterative Adaptive Dynamic Programming","display_name":"Finite-Approximation-Error-Based Discrete-Time Iterative Adaptive Dynamic Programming","publication_year":2014,"publication_date":"2014-09-26","ids":{"openalex":"https://openalex.org/W2011310556","doi":"https://doi.org/10.1109/tcyb.2014.2354377","mag":"2011310556","pmid":"https://pubmed.ncbi.nlm.nih.gov/25265640"},"language":"en","primary_location":{"id":"doi:10.1109/tcyb.2014.2354377","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcyb.2014.2354377","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/A5087825639","display_name":"Qinglai Wei","orcid":"https://orcid.org/0000-0001-7002-9800"},"institutions":[{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"government","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I4210094879","display_name":"Shandong Institute of Automation","ror":"https://ror.org/00qdtba35","country_code":"CN","type":"facility","lineage":["https://openalex.org/I4210094879","https://openalex.org/I4210142748"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Qinglai Wei","raw_affiliation_strings":["State Key Laboratory of Management and Control for Complex Systems, Institute of Automation, Chinese Academy of Sciences, Beijing, China","State Key laboratory of Management and Control for Complex Systems, Institute of Automation, Chinese Academy of Sciences, Beijing, China#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"State Key Laboratory of Management and Control for Complex Systems, Institute of Automation, Chinese Academy of Sciences, Beijing, China","institution_ids":["https://openalex.org/I19820366","https://openalex.org/I4210094879"]},{"raw_affiliation_string":"State Key laboratory of Management and Control for Complex Systems, Institute of Automation, Chinese Academy of Sciences, Beijing, China#TAB#","institution_ids":["https://openalex.org/I19820366"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5113600509","display_name":"Fei\u2013Yue Wang","orcid":"https://orcid.org/0000-0001-9185-3989"},"institutions":[{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"government","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I4210094879","display_name":"Shandong Institute of Automation","ror":"https://ror.org/00qdtba35","country_code":"CN","type":"facility","lineage":["https://openalex.org/I4210094879","https://openalex.org/I4210142748"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Fei-Yue Wang","raw_affiliation_strings":["State Key Laboratory of Management and Control for Complex Systems, Institute of Automation, Chinese Academy of Sciences, Beijing, China","State Key laboratory of Management and Control for Complex Systems, Institute of Automation, Chinese Academy of Sciences, Beijing, China#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"State Key Laboratory of Management and Control for Complex Systems, Institute of Automation, Chinese Academy of Sciences, Beijing, China","institution_ids":["https://openalex.org/I19820366","https://openalex.org/I4210094879"]},{"raw_affiliation_string":"State Key laboratory of Management and Control for Complex Systems, Institute of Automation, Chinese Academy of Sciences, Beijing, China#TAB#","institution_ids":["https://openalex.org/I19820366"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5004057129","display_name":"Derong Liu","orcid":"https://orcid.org/0000-0003-3715-4778"},"institutions":[{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"government","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I4210094879","display_name":"Shandong Institute of Automation","ror":"https://ror.org/00qdtba35","country_code":"CN","type":"facility","lineage":["https://openalex.org/I4210094879","https://openalex.org/I4210142748"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Derong Liu","raw_affiliation_strings":["State Key Laboratory of Management and Control for Complex Systems, Institute of Automation, Chinese Academy of Sciences, Beijing, China","State Key laboratory of Management and Control for Complex Systems, Institute of Automation, Chinese Academy of Sciences, Beijing, China#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"State Key Laboratory of Management and Control for Complex Systems, Institute of Automation, Chinese Academy of Sciences, Beijing, China","institution_ids":["https://openalex.org/I19820366","https://openalex.org/I4210094879"]},{"raw_affiliation_string":"State Key laboratory of Management and Control for Complex Systems, Institute of Automation, Chinese Academy of Sciences, Beijing, China#TAB#","institution_ids":["https://openalex.org/I19820366"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5085440585","display_name":"Xiong Yang","orcid":"https://orcid.org/0000-0002-0128-3036"},"institutions":[{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"government","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I4210094879","display_name":"Shandong Institute of Automation","ror":"https://ror.org/00qdtba35","country_code":"CN","type":"facility","lineage":["https://openalex.org/I4210094879","https://openalex.org/I4210142748"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiong Yang","raw_affiliation_strings":["State Key Laboratory of Management and Control for Complex Systems, Institute of Automation, Chinese Academy of Sciences, Beijing, China","State Key laboratory of Management and Control for Complex Systems, Institute of Automation, Chinese Academy of Sciences, Beijing, China#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"State Key Laboratory of Management and Control for Complex Systems, Institute of Automation, Chinese Academy of Sciences, Beijing, China","institution_ids":["https://openalex.org/I19820366","https://openalex.org/I4210094879"]},{"raw_affiliation_string":"State Key laboratory of Management and Control for Complex Systems, Institute of Automation, Chinese Academy of Sciences, Beijing, China#TAB#","institution_ids":["https://openalex.org/I19820366"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":2645,"currency":"USD","value_usd":2645},"apc_paid":null,"fwci":36.0466,"has_fulltext":false,"cited_by_count":188,"citation_normalized_percentile":{"value":0.99899067,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":100},"biblio":{"volume":"44","issue":"12","first_page":"2820","last_page":"2833"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12794","display_name":"Adaptive Dynamic Programming Control","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9761999845504761,"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":0.9474999904632568,"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/mathematical-optimization","display_name":"Mathematical optimization","score":0.6022685766220093},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.5907063484191895},{"id":"https://openalex.org/keywords/bellman-equation","display_name":"Bellman equation","score":0.5693840980529785},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5327764749526978},{"id":"https://openalex.org/keywords/dynamic-programming","display_name":"Dynamic programming","score":0.4807867407798767},{"id":"https://openalex.org/keywords/approximation-error","display_name":"Approximation error","score":0.46364083886146545},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4567829370498657},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.45566031336784363},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4369674026966095},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.42746347188949585}],"concepts":[{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.6022685766220093},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.5907063484191895},{"id":"https://openalex.org/C14646407","wikidata":"https://www.wikidata.org/wiki/Q1430750","display_name":"Bellman equation","level":2,"score":0.5693840980529785},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5327764749526978},{"id":"https://openalex.org/C37404715","wikidata":"https://www.wikidata.org/wiki/Q380679","display_name":"Dynamic programming","level":2,"score":0.4807867407798767},{"id":"https://openalex.org/C122383733","wikidata":"https://www.wikidata.org/wiki/Q865920","display_name":"Approximation error","level":2,"score":0.46364083886146545},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4567829370498657},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.45566031336784363},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4369674026966095},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.42746347188949585},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","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/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/tcyb.2014.2354377","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcyb.2014.2354377","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:25265640","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/25265640","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":"Journal Article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.7699999809265137,"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions"}],"awards":[{"id":"https://openalex.org/G2139553994","display_name":"\u590d\u6742\u975e\u7ebf\u6027\u7cfb\u7edf\u6570\u636e\u9a71\u52a8\u81ea\u5b66\u4e60\u6700\u4f18\u63a7\u5236\u7406\u8bba\u4e0e\u65b9\u6cd5\u7814\u7a76","funder_award_id":"61374105","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2801732935","display_name":null,"funder_award_id":"61 273140","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2966638085","display_name":null,"funder_award_id":"4132078","funder_id":"https://openalex.org/F4320322919","funder_display_name":"Natural Science Foundation of Beijing Municipality"},{"id":"https://openalex.org/G3864574643","display_name":"ERP3.0:\u4f01\u4e1a\u5e73\u884c\u7ba1\u7406\u7cfb\u7edf\u7406\u8bba\u4e0e\u5173\u952e\u6280\u672f\u7814\u7a76","funder_award_id":"71232006","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5605584058","display_name":"\u57fa\u4e8e\u6570\u636e\u7684\u975e\u7ebf\u6027\u63a7\u5236\u7cfb\u7edf\u5206\u6790\u4e0e\u8bbe\u8ba1","funder_award_id":"61034002","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6391760457","display_name":null,"funder_award_id":"61304086","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8230378891","display_name":"\u590d\u6742\u7cfb\u7edf\u5e73\u884c\u63a7\u5236\u57fa\u7840\u7406\u8bba\u53ca\u5178\u578b\u5e94\u7528","funder_award_id":"61233001","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/F4320322919","display_name":"Natural Science Foundation of Beijing Municipality","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":58,"referenced_works":["https://openalex.org/W92805021","https://openalex.org/W1966334496","https://openalex.org/W1968173975","https://openalex.org/W1972809999","https://openalex.org/W1976527148","https://openalex.org/W1983089547","https://openalex.org/W1983523797","https://openalex.org/W1984533547","https://openalex.org/W1986864433","https://openalex.org/W1988688219","https://openalex.org/W1993194347","https://openalex.org/W1993512950","https://openalex.org/W1997603681","https://openalex.org/W1998344411","https://openalex.org/W1999213690","https://openalex.org/W2002260889","https://openalex.org/W2008809493","https://openalex.org/W2013895638","https://openalex.org/W2020632721","https://openalex.org/W2020688906","https://openalex.org/W2034903360","https://openalex.org/W2036729506","https://openalex.org/W2040228279","https://openalex.org/W2042736720","https://openalex.org/W2044922360","https://openalex.org/W2048687352","https://openalex.org/W2051562408","https://openalex.org/W2052305027","https://openalex.org/W2060605484","https://openalex.org/W2060686658","https://openalex.org/W2072333675","https://openalex.org/W2076522620","https://openalex.org/W2081758070","https://openalex.org/W2083351175","https://openalex.org/W2090582772","https://openalex.org/W2093831009","https://openalex.org/W2098035803","https://openalex.org/W2098432798","https://openalex.org/W2100276679","https://openalex.org/W2108286682","https://openalex.org/W2109320898","https://openalex.org/W2109494272","https://openalex.org/W2110040537","https://openalex.org/W2110422826","https://openalex.org/W2111980775","https://openalex.org/W2116488102","https://openalex.org/W2120249358","https://openalex.org/W2138131694","https://openalex.org/W2149919902","https://openalex.org/W2151966330","https://openalex.org/W2152161277","https://openalex.org/W2160561608","https://openalex.org/W2163209452","https://openalex.org/W2165501837","https://openalex.org/W2165545652","https://openalex.org/W2171754584","https://openalex.org/W2322341491","https://openalex.org/W4205326910"],"related_works":["https://openalex.org/W4255265352","https://openalex.org/W4239477580","https://openalex.org/W2952594763","https://openalex.org/W2090698372","https://openalex.org/W4383890581","https://openalex.org/W2965004901","https://openalex.org/W2921905705","https://openalex.org/W2379312070","https://openalex.org/W1932159282","https://openalex.org/W4285537323"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"a":[3,29,98,132],"new":[4,30,99],"iterative":[5,42,79,83,126,148],"adaptive":[6],"dynamic":[7],"programming":[8],"(ADP)":[9],"algorithm":[10,34,58,112],"is":[11,37,113],"developed":[12,38,163],"to":[13,39,47,65,123,131,145,157],"solve":[14],"optimal":[15,137],"control":[16,80],"problems":[17],"for":[18,94,106],"infinite":[19],"horizon":[20],"discrete-time":[21],"nonlinear":[22],"systems":[23],"with":[24],"finite":[25,133],"approximation":[26,117],"errors.":[27],"First,":[28],"generalized":[31,55,109],"value":[32,56,74,110],"iteration":[33,57,75,89,111],"of":[35,50,72,102,135,161],"ADP":[36,149],"make":[40,124],"the":[41,48,51,70,78,95,103,107,125,136,147,159,162],"performance":[43,84,127,138,160],"index":[44,85,128,139],"function":[45,64,86,129],"converge":[46,130],"solution":[49],"Hamilton-Jacobi-Bellman":[52],"equation.":[53],"The":[54],"permits":[59],"an":[60],"arbitrary":[61],"positive":[62],"semi-definite":[63],"initialize":[66],"it,":[67],"which":[68],"overcomes":[69],"disadvantage":[71],"traditional":[73],"algorithms.":[76],"When":[77],"law":[81],"and":[82],"in":[87],"each":[88],"cannot":[90],"accurately":[91],"be":[92,120],"obtained,":[93],"first":[96],"time":[97],"\"design":[100],"method":[101],"convergence":[104],"criteria\"":[105],"finite-approximation-error-based":[108],"established.":[114],"A":[115],"suitable":[116],"error":[118],"can":[119],"designed":[121],"adaptively":[122],"neighborhood":[134],"function.":[140],"Neural":[141],"networks":[142],"are":[143,155],"used":[144],"implement":[146],"algorithm.":[150],"Finally,":[151],"two":[152],"simulation":[153],"examples":[154],"given":[156],"illustrate":[158],"method.":[164]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":7},{"year":2023,"cited_by_count":16},{"year":2022,"cited_by_count":10},{"year":2021,"cited_by_count":8},{"year":2020,"cited_by_count":9},{"year":2019,"cited_by_count":12},{"year":2018,"cited_by_count":17},{"year":2017,"cited_by_count":33},{"year":2016,"cited_by_count":37},{"year":2015,"cited_by_count":31},{"year":2014,"cited_by_count":1}],"updated_date":"2026-08-21T09:56:20.448147","created_date":"2025-10-10T00:00:00"}