{"id":"https://openalex.org/W2976686511","doi":"https://doi.org/10.1109/tcyb.2019.2939424","title":"Adaptive Neural Network-Based Finite-Time Online Optimal Tracking Control of the Nonlinear System With Dead Zone","display_name":"Adaptive Neural Network-Based Finite-Time Online Optimal Tracking Control of the Nonlinear System With Dead Zone","publication_year":2019,"publication_date":"2019-09-27","ids":{"openalex":"https://openalex.org/W2976686511","doi":"https://doi.org/10.1109/tcyb.2019.2939424","mag":"2976686511","pmid":"https://pubmed.ncbi.nlm.nih.gov/31567108"},"language":"en","primary_location":{"id":"doi:10.1109/tcyb.2019.2939424","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcyb.2019.2939424","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/A5012020883","display_name":"Liang Ding","orcid":"https://orcid.org/0000-0002-8351-5178"},"institutions":[{"id":"https://openalex.org/I204983213","display_name":"Harbin Institute of Technology","ror":"https://ror.org/01yqg2h08","country_code":"CN","type":"education","lineage":["https://openalex.org/I204983213"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Liang Ding","raw_affiliation_strings":["State Key Laboratory of Robotics and System, Harbin Institute of Technology, Harbin, China"],"raw_orcid":"https://orcid.org/0000-0002-8351-5178","affiliations":[{"raw_affiliation_string":"State Key Laboratory of Robotics and System, Harbin Institute of Technology, Harbin, China","institution_ids":["https://openalex.org/I204983213"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100627709","display_name":"Shu Li","orcid":"https://orcid.org/0000-0002-5828-3010"},"institutions":[{"id":"https://openalex.org/I204983213","display_name":"Harbin Institute of Technology","ror":"https://ror.org/01yqg2h08","country_code":"CN","type":"education","lineage":["https://openalex.org/I204983213"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Shu Li","raw_affiliation_strings":["State Key Laboratory of Robotics and System, Harbin Institute of Technology, Harbin, China"],"raw_orcid":"https://orcid.org/0000-0002-5828-3010","affiliations":[{"raw_affiliation_string":"State Key Laboratory of Robotics and System, Harbin Institute of Technology, Harbin, China","institution_ids":["https://openalex.org/I204983213"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5033616367","display_name":"Haibo Gao","orcid":"https://orcid.org/0000-0002-6501-656X"},"institutions":[{"id":"https://openalex.org/I204983213","display_name":"Harbin Institute of Technology","ror":"https://ror.org/01yqg2h08","country_code":"CN","type":"education","lineage":["https://openalex.org/I204983213"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Haibo Gao","raw_affiliation_strings":["State Key Laboratory of Robotics and System, Harbin Institute of Technology, Harbin, China"],"raw_orcid":"https://orcid.org/0000-0002-6501-656X","affiliations":[{"raw_affiliation_string":"State Key Laboratory of Robotics and System, Harbin Institute of Technology, Harbin, China","institution_ids":["https://openalex.org/I204983213"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100458928","display_name":"Yan\u2010Jun Liu","orcid":"https://orcid.org/0000-0001-6047-0731"},"institutions":[{"id":"https://openalex.org/I2898894","display_name":"Liaoning University of Technology","ror":"https://ror.org/05ay23762","country_code":"CN","type":"education","lineage":["https://openalex.org/I2898894"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yan-Jun Liu","raw_affiliation_strings":["College of Science, Liaoning University of Technology, Jinzhou, China"],"raw_orcid":"https://orcid.org/0000-0001-6047-0731","affiliations":[{"raw_affiliation_string":"College of Science, Liaoning University of Technology, Jinzhou, China","institution_ids":["https://openalex.org/I2898894"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5103140035","display_name":"Lan Huang","orcid":"https://orcid.org/0000-0001-8640-9162"},"institutions":[{"id":"https://openalex.org/I204983213","display_name":"Harbin Institute of Technology","ror":"https://ror.org/01yqg2h08","country_code":"CN","type":"education","lineage":["https://openalex.org/I204983213"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Lan Huang","raw_affiliation_strings":["State Key Laboratory of Robotics and System, Harbin Institute of Technology, Harbin, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"State Key Laboratory of Robotics and System, Harbin Institute of Technology, Harbin, China","institution_ids":["https://openalex.org/I204983213"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100617483","display_name":"Zongquan Deng","orcid":"https://orcid.org/0000-0003-2432-8329"},"institutions":[{"id":"https://openalex.org/I204983213","display_name":"Harbin Institute of Technology","ror":"https://ror.org/01yqg2h08","country_code":"CN","type":"education","lineage":["https://openalex.org/I204983213"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zongquan Deng","raw_affiliation_strings":["State Key Laboratory of Robotics and System, Harbin Institute of Technology, Harbin, China"],"raw_orcid":"https://orcid.org/0000-0003-2432-8329","affiliations":[{"raw_affiliation_string":"State Key Laboratory of Robotics and System, Harbin Institute of Technology, Harbin, China","institution_ids":["https://openalex.org/I204983213"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":9.9518,"has_fulltext":false,"cited_by_count":112,"citation_normalized_percentile":{"value":0.98566059,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":97,"max":100},"biblio":{"volume":"51","issue":"1","first_page":"382","last_page":"392"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12794","display_name":"Adaptive Dynamic Programming Control","score":1.0,"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":1.0,"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/T10040","display_name":"Adaptive Control of Nonlinear Systems","score":0.994700014591217,"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"}},{"id":"https://openalex.org/T12277","display_name":"Frequency Control in Power Systems","score":0.9868999719619751,"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":0.7547856569290161},{"id":"https://openalex.org/keywords/lipschitz-continuity","display_name":"Lipschitz continuity","score":0.7098119854927063},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.6130945086479187},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.5964301228523254},{"id":"https://openalex.org/keywords/tracking-error","display_name":"Tracking error","score":0.5856284499168396},{"id":"https://openalex.org/keywords/gradient-descent","display_name":"Gradient descent","score":0.5587836503982544},{"id":"https://openalex.org/keywords/error-function","display_name":"Error function","score":0.5173810720443726},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5142692923545837},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4627959728240967},{"id":"https://openalex.org/keywords/bellman-equation","display_name":"Bellman equation","score":0.44069936871528625},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.4347565770149231},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.43189677596092224},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.42395544052124023},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3658090829849243},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.17427384853363037},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.1020345389842987},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.10059896111488342}],"concepts":[{"id":"https://openalex.org/C196978813","wikidata":"https://www.wikidata.org/wiki/Q3302775","display_name":"Hamilton\u2013Jacobi\u2013Bellman equation","level":3,"score":0.7547856569290161},{"id":"https://openalex.org/C22324862","wikidata":"https://www.wikidata.org/wiki/Q652707","display_name":"Lipschitz continuity","level":2,"score":0.7098119854927063},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.6130945086479187},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.5964301228523254},{"id":"https://openalex.org/C183356978","wikidata":"https://www.wikidata.org/wiki/Q1779213","display_name":"Tracking error","level":3,"score":0.5856284499168396},{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.5587836503982544},{"id":"https://openalex.org/C202286095","wikidata":"https://www.wikidata.org/wiki/Q579262","display_name":"Error function","level":2,"score":0.5173810720443726},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5142692923545837},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4627959728240967},{"id":"https://openalex.org/C14646407","wikidata":"https://www.wikidata.org/wiki/Q1430750","display_name":"Bellman equation","level":2,"score":0.44069936871528625},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.4347565770149231},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.43189677596092224},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.42395544052124023},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3658090829849243},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.17427384853363037},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.1020345389842987},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.10059896111488342},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"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/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.2019.2939424","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcyb.2019.2939424","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:31567108","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/31567108","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":[],"awards":[{"id":"https://openalex.org/G3663909988","display_name":null,"funder_award_id":"51,822,502","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G387971928","display_name":null,"funder_award_id":"B07018","funder_id":"https://openalex.org/F4320327912","funder_display_name":"Higher Education Discipline Innovation Project"},{"id":"https://openalex.org/G5383534787","display_name":null,"funder_award_id":"51521003","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5945508851","display_name":null,"funder_award_id":"61622303","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G852853916","display_name":null,"funder_award_id":"HIT.BRETIV.201903","funder_id":"https://openalex.org/F4320335787","funder_display_name":"Fundamental Research Funds for the Central Universities"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320327912","display_name":"Higher Education Discipline Innovation Project","ror":null},{"id":"https://openalex.org/F4320335787","display_name":"Fundamental Research Funds for the Central Universities","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":54,"referenced_works":["https://openalex.org/W560518094","https://openalex.org/W1565170927","https://openalex.org/W1891098503","https://openalex.org/W1968908471","https://openalex.org/W1977458621","https://openalex.org/W1983523797","https://openalex.org/W1986864433","https://openalex.org/W1994951210","https://openalex.org/W1997603681","https://openalex.org/W2000201135","https://openalex.org/W2006025321","https://openalex.org/W2009594301","https://openalex.org/W2018160758","https://openalex.org/W2032704188","https://openalex.org/W2041109651","https://openalex.org/W2041866840","https://openalex.org/W2044375425","https://openalex.org/W2048687352","https://openalex.org/W2103700523","https://openalex.org/W2106071123","https://openalex.org/W2108286682","https://openalex.org/W2116490015","https://openalex.org/W2122995702","https://openalex.org/W2130180074","https://openalex.org/W2132858840","https://openalex.org/W2137320068","https://openalex.org/W2140742596","https://openalex.org/W2146342888","https://openalex.org/W2151966330","https://openalex.org/W2156629001","https://openalex.org/W2159543578","https://openalex.org/W2203022174","https://openalex.org/W2343036750","https://openalex.org/W2388591084","https://openalex.org/W2512613132","https://openalex.org/W2520851130","https://openalex.org/W2529405793","https://openalex.org/W2603406422","https://openalex.org/W2650555469","https://openalex.org/W2695358573","https://openalex.org/W2729263647","https://openalex.org/W2753313310","https://openalex.org/W2770878849","https://openalex.org/W2780033408","https://openalex.org/W2782127155","https://openalex.org/W2792294435","https://openalex.org/W2800384809","https://openalex.org/W2809883483","https://openalex.org/W2883469527","https://openalex.org/W2892281448","https://openalex.org/W2895199821","https://openalex.org/W2896967075","https://openalex.org/W2897039614","https://openalex.org/W6740022615"],"related_works":["https://openalex.org/W2032834442","https://openalex.org/W3153900688","https://openalex.org/W2115544975","https://openalex.org/W2902017027","https://openalex.org/W1654696814","https://openalex.org/W4291598237","https://openalex.org/W2766998270","https://openalex.org/W4292330635","https://openalex.org/W3168988147","https://openalex.org/W4239477580"],"abstract_inverted_index":{"Considering":[0],"the":[1,24,28,35,55,60,68,74,81,89,93,96,105,110,123],"uncertain":[2],"nonstrict":[3],"nonlinear":[4],"system":[5,41],"with":[6,54],"dead-zone":[7,75],"input,":[8],"an":[9,39],"adaptive":[10],"neural":[11],"network":[12],"(NN)-based":[13],"finite-time":[14,69,117],"online":[15],"optimal":[16],"tracking":[17,25,32,124],"control":[18],"algorithm":[19],"is":[20,42,50,65,77,120],"proposed.":[21],"By":[22],"using":[23,104],"errors":[26,125],"and":[27,98,122],"Lipschitz":[29],"linearized":[30],"desired":[31],"function":[33,49,84],"as":[34,67],"new":[36],"state":[37],"vector,":[38],"extended":[40],"present.":[43],"Then,":[44,92],"a":[45,128,134],"novel":[46],"Hamilton-Jacobi-Bellman":[47],"(HJB)":[48],"defined":[51],"to":[52,127],"associate":[53],"nonquadratic":[56],"performance":[57],"function.":[58,91,113],"Further,":[59],"upper":[61],"limit":[62],"of":[63,95],"integration":[64],"selected":[66],"convergence":[70,126],"time,":[71],"in":[72,133],"which":[73],"input":[76],"considered.":[78],"In":[79],"addition,":[80],"Bellman":[82,111],"error":[83,112],"can":[85],"be":[86],"obtained":[87],"from":[88],"Hamiltonian":[90],"adaptations":[94],"critic":[97],"action":[99],"NN":[100],"are":[101],"updated":[102],"by":[103,131],"gradient":[106],"descent":[107],"method":[108],"on":[109],"The":[114],"semiglobal":[115],"practical":[116],"stability":[118],"(SGPFS)":[119],"guaranteed,":[121],"compact":[129],"set":[130],"zero":[132],"finite":[135],"time.":[136]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":19},{"year":2024,"cited_by_count":19},{"year":2023,"cited_by_count":16},{"year":2022,"cited_by_count":17},{"year":2021,"cited_by_count":32},{"year":2020,"cited_by_count":7}],"updated_date":"2026-08-01T09:00:35.917206","created_date":"2025-10-10T00:00:00"}