{"id":"https://openalex.org/W2912259603","doi":"https://doi.org/10.1109/tii.2019.2894282","title":"Optimized Adaptive Nonlinear Tracking Control Using Actor\u2013Critic Reinforcement Learning Strategy","display_name":"Optimized Adaptive Nonlinear Tracking Control Using Actor\u2013Critic Reinforcement Learning Strategy","publication_year":2019,"publication_date":"2019-01-22","ids":{"openalex":"https://openalex.org/W2912259603","doi":"https://doi.org/10.1109/tii.2019.2894282","mag":"2912259603"},"language":"en","primary_location":{"id":"doi:10.1109/tii.2019.2894282","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tii.2019.2894282","pdf_url":null,"source":{"id":"https://openalex.org/S184777250","display_name":"IEEE Transactions on Industrial Informatics","issn_l":"1551-3203","issn":["1551-3203","1941-0050"],"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 Industrial Informatics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"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/A5063205336","display_name":"Guoxing Wen","orcid":"https://orcid.org/0000-0002-6392-5989"},"institutions":[{"id":"https://openalex.org/I151013683","display_name":"Shandong University of Aeronautics","ror":"https://ror.org/05frpfj73","country_code":"CN","type":"education","lineage":["https://openalex.org/I151013683"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Guoxing Wen","raw_affiliation_strings":["College of Science and the Institute of Aeronautical Engineering and Technology (IAET), Binzhou University, Binzhou, China"],"raw_orcid":"https://orcid.org/0000-0002-6392-5989","affiliations":[{"raw_affiliation_string":"College of Science and the Institute of Aeronautical Engineering and Technology (IAET), Binzhou University, Binzhou, China","institution_ids":["https://openalex.org/I151013683"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100643265","display_name":"C. L. Philip Chen","orcid":"https://orcid.org/0000-0001-5451-7230"},"institutions":[{"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":"C. L. Philip Chen","raw_affiliation_strings":["Department of Computer and Information Science, University of Macau, Macau, China"],"raw_orcid":"https://orcid.org/0000-0001-5451-7230","affiliations":[{"raw_affiliation_string":"Department of Computer and Information Science, University of Macau, Macau, China","institution_ids":["https://openalex.org/I204512498"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5008501506","display_name":"Shuzhi Sam Ge","orcid":"https://orcid.org/0000-0001-5549-312X"},"institutions":[{"id":"https://openalex.org/I108688024","display_name":"Qingdao University","ror":"https://ror.org/021cj6z65","country_code":"CN","type":"education","lineage":["https://openalex.org/I108688024"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Shuzhi Sam Ge","raw_affiliation_strings":["Institute for Future, Qingdao University, Qingdao, China"],"raw_orcid":"https://orcid.org/0000-0001-5549-312X","affiliations":[{"raw_affiliation_string":"Institute for Future, Qingdao University, Qingdao, China","institution_ids":["https://openalex.org/I108688024"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5102884345","display_name":"Hongli Yang","orcid":"https://orcid.org/0000-0002-8259-5241"},"institutions":[{"id":"https://openalex.org/I80143920","display_name":"Shandong University of Science and Technology","ror":"https://ror.org/04gtjhw98","country_code":"CN","type":"education","lineage":["https://openalex.org/I80143920"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Hongli Yang","raw_affiliation_strings":["Mathematics and Systems Science College, Shandong University of Science and Technology, Qingdao, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematics and Systems Science College, Shandong University of Science and Technology, Qingdao, China","institution_ids":["https://openalex.org/I80143920"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100390112","display_name":"Xiaoguang Liu","orcid":"https://orcid.org/0000-0002-0176-3101"},"institutions":[{"id":"https://openalex.org/I2799449666","display_name":"State Ethnic Affairs Commission","ror":"https://ror.org/01p9g6b97","country_code":"CN","type":"government","lineage":["https://openalex.org/I2799449666"]},{"id":"https://openalex.org/I6645349","display_name":"Southwest Minzu University","ror":"https://ror.org/04gaexw88","country_code":"CN","type":"education","lineage":["https://openalex.org/I6645349"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiaoguang Liu","raw_affiliation_strings":["Key Laboratory for Computer Systems of State Ethnic Affairs Commission, and the School of Computer Science and Technology, Southwest Minzu University, Chengdu, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Key Laboratory for Computer Systems of State Ethnic Affairs Commission, and the School of Computer Science and Technology, Southwest Minzu University, Chengdu, China","institution_ids":["https://openalex.org/I2799449666","https://openalex.org/I6645349"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":6,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":12.0793,"has_fulltext":false,"cited_by_count":208,"citation_normalized_percentile":{"value":0.98951033,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":100},"biblio":{"volume":"15","issue":"9","first_page":"4969","last_page":"4977"},"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/T10462","display_name":"Reinforcement Learning in Robotics","score":0.9832000136375427,"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"}},{"id":"https://openalex.org/T10305","display_name":"Power System Optimization and Stability","score":0.9549000263214111,"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/reinforcement-learning","display_name":"Reinforcement learning","score":0.8337925672531128},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.6964157819747925},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.6678791046142578},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6594604253768921},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.628506064414978},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.593736469745636},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.5782214403152466},{"id":"https://openalex.org/keywords/trajectory","display_name":"Trajectory","score":0.5568505525588989},{"id":"https://openalex.org/keywords/tracking-error","display_name":"Tracking error","score":0.5509971380233765},{"id":"https://openalex.org/keywords/bellman-equation","display_name":"Bellman equation","score":0.47876468300819397},{"id":"https://openalex.org/keywords/function-approximation","display_name":"Function approximation","score":0.4761279225349426},{"id":"https://openalex.org/keywords/tracking","display_name":"Tracking (education)","score":0.45825353264808655},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.38340815901756287},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3672051429748535},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.258923202753067},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.24971535801887512},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.13303717970848083}],"concepts":[{"id":"https://openalex.org/C97541855","wikidata":"https://www.wikidata.org/wiki/Q830687","display_name":"Reinforcement learning","level":2,"score":0.8337925672531128},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.6964157819747925},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.6678791046142578},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6594604253768921},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.628506064414978},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.593736469745636},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5782214403152466},{"id":"https://openalex.org/C13662910","wikidata":"https://www.wikidata.org/wiki/Q193139","display_name":"Trajectory","level":2,"score":0.5568505525588989},{"id":"https://openalex.org/C183356978","wikidata":"https://www.wikidata.org/wiki/Q1779213","display_name":"Tracking error","level":3,"score":0.5509971380233765},{"id":"https://openalex.org/C14646407","wikidata":"https://www.wikidata.org/wiki/Q1430750","display_name":"Bellman equation","level":2,"score":0.47876468300819397},{"id":"https://openalex.org/C91873725","wikidata":"https://www.wikidata.org/wiki/Q3445816","display_name":"Function approximation","level":3,"score":0.4761279225349426},{"id":"https://openalex.org/C2775936607","wikidata":"https://www.wikidata.org/wiki/Q466845","display_name":"Tracking (education)","level":2,"score":0.45825353264808655},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.38340815901756287},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3672051429748535},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.258923202753067},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.24971535801887512},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.13303717970848083},{"id":"https://openalex.org/C1276947","wikidata":"https://www.wikidata.org/wiki/Q333","display_name":"Astronomy","level":1,"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/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.0},{"id":"https://openalex.org/C19417346","wikidata":"https://www.wikidata.org/wiki/Q7922","display_name":"Pedagogy","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":1,"locations":[{"id":"doi:10.1109/tii.2019.2894282","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tii.2019.2894282","pdf_url":null,"source":{"id":"https://openalex.org/S184777250","display_name":"IEEE Transactions on Industrial Informatics","issn_l":"1551-3203","issn":["1551-3203","1941-0050"],"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 Industrial Informatics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G566332922","display_name":null,"funder_award_id":"2016Y14","funder_id":"https://openalex.org/F4320325296","funder_display_name":"Binzhou University"},{"id":"https://openalex.org/G5971077570","display_name":null,"funder_award_id":"ZR2018MF015","funder_id":"https://openalex.org/F4320324174","funder_display_name":"Natural Science Foundation of Shandong Province"},{"id":"https://openalex.org/G653700208","display_name":null,"funder_award_id":"61751202","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G936074557","display_name":null,"funder_award_id":"61572540","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/F4320322522","display_name":"Shandong University of Science and Technology","ror":"https://ror.org/04gtjhw98"},{"id":"https://openalex.org/F4320324174","display_name":"Natural Science Foundation of Shandong Province","ror":null},{"id":"https://openalex.org/F4320325296","display_name":"Binzhou University","ror":"https://ror.org/05frpfj73"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":36,"referenced_works":["https://openalex.org/W1054396882","https://openalex.org/W1540245649","https://openalex.org/W1662782209","https://openalex.org/W1839500782","https://openalex.org/W1907796993","https://openalex.org/W1941777059","https://openalex.org/W1966118876","https://openalex.org/W1974061378","https://openalex.org/W1977237536","https://openalex.org/W1983523797","https://openalex.org/W2010152647","https://openalex.org/W2027029581","https://openalex.org/W2047090868","https://openalex.org/W2085194340","https://openalex.org/W2121863487","https://openalex.org/W2147914308","https://openalex.org/W2153890087","https://openalex.org/W2167287735","https://openalex.org/W2262108890","https://openalex.org/W2342610385","https://openalex.org/W2375724275","https://openalex.org/W2498440523","https://openalex.org/W2530077971","https://openalex.org/W2591999327","https://openalex.org/W2773301312","https://openalex.org/W2780149228","https://openalex.org/W2780814805","https://openalex.org/W2801873668","https://openalex.org/W2802990478","https://openalex.org/W2887519063","https://openalex.org/W3213472335","https://openalex.org/W4205326910","https://openalex.org/W4214717370","https://openalex.org/W4298300677","https://openalex.org/W6641840359","https://openalex.org/W6804409665"],"related_works":["https://openalex.org/W2386410636","https://openalex.org/W3038962357","https://openalex.org/W2025663273","https://openalex.org/W3099153698","https://openalex.org/W1859185863","https://openalex.org/W2964126589","https://openalex.org/W4285537323","https://openalex.org/W1932159282","https://openalex.org/W4307691181","https://openalex.org/W3016225735"],"abstract_inverted_index":{"This":[0],"paper":[1],"proposes":[2],"an":[3,85],"optimized":[4,73],"tracking":[5,26],"control":[6,37,74,113,121,136],"approach":[7],"using":[8],"neural":[9],"network":[10],"(NN)":[11],"based":[12,66],"reinforcement":[13],"learning":[14],"(RL)":[15],"for":[16,34,76],"a":[17],"class":[18],"of":[19,130],"nonlinear":[20],"dynamic":[21],"systems,":[22],"which":[23],"requires":[24],"both":[25,97],"and":[27,95,99,115,123,145,147],"optimizing":[28],"to":[29,43,48,81,104,111,119,126],"be":[30,44],"performed":[31],"simultaneously.":[32],"Generally,":[33],"obtaining":[35],"optimal":[36,91],"solution,":[38],"Hamilton-Jacobi-Bellman":[39],"equation":[40,52],"is":[41,53,68,88,143],"expected":[42],"solvable,":[45],"but,":[46],"owing":[47],"strong":[49],"nonlinearity,":[50],"the":[51,72,82,134,148],"solved":[54],"difficultly":[55],"or":[56],"even":[57],"impossibly":[58],"by":[59],"analytical":[60],"methods.":[61],"Therefore,":[62],"adaptive":[63],"NN":[64,109,117],"approximation":[65],"RL":[67,106],"usually":[69],"considered.":[70],"In":[71],"design,":[75],"driving":[77],"output":[78],"state":[79],"following":[80],"desired":[83,135,149],"trajectory,":[84],"error":[86],"term":[87],"split":[89],"from":[90],"performance":[92,122],"index":[93],"function,":[94],"then":[96],"actor":[98],"critic":[100,116],"NNs":[101],"are":[102,138,151],"built":[103],"perform":[105],"algorithm.":[107],"Actor":[108],"aims":[110,118],"execute":[112],"behaviors,":[114],"appraise":[120],"make":[124],"feedback":[125],"actor.":[127],"The":[128],"proof":[129],"stability":[131],"concludes":[132],"that":[133],"performances":[137],"obtained.":[139],"A":[140],"numerical":[141],"simulation":[142],"designed":[144],"implemented,":[146],"results":[150],"shown.":[152]},"counts_by_year":[{"year":2026,"cited_by_count":16},{"year":2025,"cited_by_count":43},{"year":2024,"cited_by_count":41},{"year":2023,"cited_by_count":39},{"year":2022,"cited_by_count":23},{"year":2021,"cited_by_count":23},{"year":2020,"cited_by_count":14},{"year":2019,"cited_by_count":8},{"year":2012,"cited_by_count":1}],"updated_date":"2026-08-05T07:39:15.569665","created_date":"2025-10-10T00:00:00"}
