{"id":"https://openalex.org/W2129059971","doi":"https://doi.org/10.1109/adprl.2013.6614983","title":"Adaptive optimal control for nonlinear discrete-time systems","display_name":"Adaptive optimal control for nonlinear discrete-time systems","publication_year":2013,"publication_date":"2013-04-01","ids":{"openalex":"https://openalex.org/W2129059971","doi":"https://doi.org/10.1109/adprl.2013.6614983","mag":"2129059971"},"language":"en","primary_location":{"id":"doi:10.1109/adprl.2013.6614983","is_oa":false,"landing_page_url":"https://doi.org/10.1109/adprl.2013.6614983","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2013 IEEE Symposium on Adaptive Dynamic Programming and Reinforcement Learning (ADPRL)","raw_type":"proceedings-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/A5069540002","display_name":"Chunbin Qin","orcid":"https://orcid.org/0000-0002-8238-5922"},"institutions":[{"id":"https://openalex.org/I9224756","display_name":"Northeastern University","ror":"https://ror.org/03awzbc87","country_code":"CN","type":"education","lineage":["https://openalex.org/I9224756"]},{"id":"https://openalex.org/I173899330","display_name":"Henan University","ror":"https://ror.org/003xyzq10","country_code":"CN","type":"education","lineage":["https://openalex.org/I173899330"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Chunbin Qin","raw_affiliation_strings":["Basic Experiment Teaching Center, Henan University, Kaifeng, China","School of Information Science and Engineering, Northeastern University, Shenyang, China"],"affiliations":[{"raw_affiliation_string":"Basic Experiment Teaching Center, Henan University, Kaifeng, China","institution_ids":["https://openalex.org/I173899330"]},{"raw_affiliation_string":"School of Information Science and Engineering, Northeastern University, Shenyang, China","institution_ids":["https://openalex.org/I9224756"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100625792","display_name":"Huaguang Zhang","orcid":"https://orcid.org/0000-0002-2375-9824"},"institutions":[{"id":"https://openalex.org/I9224756","display_name":"Northeastern University","ror":"https://ror.org/03awzbc87","country_code":"CN","type":"education","lineage":["https://openalex.org/I9224756"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Huaguang Zhang","raw_affiliation_strings":["School of Information Science and Engineering, Northeastern University, Shenyang, China"],"affiliations":[{"raw_affiliation_string":"School of Information Science and Engineering, Northeastern University, Shenyang, China","institution_ids":["https://openalex.org/I9224756"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5064721860","display_name":"Yanhong Luo","orcid":"https://orcid.org/0000-0001-6898-7903"},"institutions":[{"id":"https://openalex.org/I9224756","display_name":"Northeastern University","ror":"https://ror.org/03awzbc87","country_code":"CN","type":"education","lineage":["https://openalex.org/I9224756"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yanhong Luo","raw_affiliation_strings":["School of Information Science and Engineering, Northeastern University, Shenyang, China"],"affiliations":[{"raw_affiliation_string":"School of Information Science and Engineering, Northeastern University, Shenyang, China","institution_ids":["https://openalex.org/I9224756"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5069540002"],"corresponding_institution_ids":["https://openalex.org/I173899330","https://openalex.org/I9224756"],"apc_list":null,"apc_paid":null,"fwci":0.3625,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.66434283,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":95},"biblio":{"volume":null,"issue":null,"first_page":"13","last_page":"18"},"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/T10305","display_name":"Power System Optimization and Stability","score":0.9675999879837036,"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"}},{"id":"https://openalex.org/T12277","display_name":"Frequency Control in Power Systems","score":0.9672999978065491,"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":0.8721593618392944},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.7483881711959839},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.6820806860923767},{"id":"https://openalex.org/keywords/bellman-equation","display_name":"Bellman equation","score":0.5841439962387085},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5700501799583435},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.5515196919441223},{"id":"https://openalex.org/keywords/adaptive-control","display_name":"Adaptive control","score":0.5480941534042358},{"id":"https://openalex.org/keywords/function-approximation","display_name":"Function approximation","score":0.5350723266601562},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5340093374252319},{"id":"https://openalex.org/keywords/lyapunov-function","display_name":"Lyapunov function","score":0.5148317217826843},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.49579963088035583},{"id":"https://openalex.org/keywords/discrete-time-and-continuous-time","display_name":"Discrete time and continuous time","score":0.49058809876441956},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.441635400056839},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.42109447717666626},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3968753218650818},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.24518421292304993},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.10148665308952332}],"concepts":[{"id":"https://openalex.org/C196978813","wikidata":"https://www.wikidata.org/wiki/Q3302775","display_name":"Hamilton\u2013Jacobi\u2013Bellman equation","level":3,"score":0.8721593618392944},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.7483881711959839},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.6820806860923767},{"id":"https://openalex.org/C14646407","wikidata":"https://www.wikidata.org/wiki/Q1430750","display_name":"Bellman equation","level":2,"score":0.5841439962387085},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5700501799583435},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.5515196919441223},{"id":"https://openalex.org/C107464732","wikidata":"https://www.wikidata.org/wiki/Q235781","display_name":"Adaptive control","level":3,"score":0.5480941534042358},{"id":"https://openalex.org/C91873725","wikidata":"https://www.wikidata.org/wiki/Q3445816","display_name":"Function approximation","level":3,"score":0.5350723266601562},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5340093374252319},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.5148317217826843},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.49579963088035583},{"id":"https://openalex.org/C55689738","wikidata":"https://www.wikidata.org/wiki/Q15963867","display_name":"Discrete time and continuous time","level":2,"score":0.49058809876441956},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.441635400056839},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.42109447717666626},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3968753218650818},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.24518421292304993},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.10148665308952332},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/adprl.2013.6614983","is_oa":false,"landing_page_url":"https://doi.org/10.1109/adprl.2013.6614983","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2013 IEEE Symposium on Adaptive Dynamic Programming and Reinforcement Learning (ADPRL)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":12,"referenced_works":["https://openalex.org/W648594167","https://openalex.org/W2013419313","https://openalex.org/W2017570421","https://openalex.org/W2093831009","https://openalex.org/W2098035803","https://openalex.org/W2116545640","https://openalex.org/W2132858840","https://openalex.org/W2136064843","https://openalex.org/W2137092694","https://openalex.org/W2150841368","https://openalex.org/W2159543578","https://openalex.org/W2165501837"],"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/W3168988147","https://openalex.org/W4239477580","https://openalex.org/W4292330635"],"abstract_inverted_index":{"This":[0],"paper":[1],"proposes":[2],"an":[3],"on-line":[4,21,76],"near-optimal":[5],"control":[6,25,43,60],"scheme":[7],"based":[8],"on":[9],"capabilities":[10],"of":[11,23,98,118],"neural":[12,46],"networks":[13,47],"(NNs),":[14],"in":[15,40],"function":[16,54],"approximation,":[17],"to":[18,32,50,56,66,114],"attain":[19],"the":[20,34,41,52,58,67,72,75,81,95,99,116,119],"solution":[22],"optimal":[24,42,59],"problem":[26],"for":[27,80],"nonlinear":[28],"discrete-time":[29],"systems.":[30],"First,":[31],"solve":[33],"Hamilton-Jacobi-Bellman":[35],"(HJB)":[36],"equation":[37],"forward-in-time":[38],"appearing":[39],"problem,":[44],"two":[45],"are":[48,87],"used":[49],"approximate":[51],"cost":[53],"and":[55,71,84],"compute":[57],"policy,":[61],"respectively.":[62,89],"And":[63],"then,":[64],"according":[65],"Bellman's":[68],"optimality":[69],"principle":[70],"adaptive":[73],"technology,":[74],"weight":[77],"updating":[78],"laws":[79],"critic":[82],"network":[83,86],"action":[85],"derived,":[88],"Further,":[90],"considering":[91],"NNs":[92],"approximative":[93],"errors,":[94],"stability":[96],"analysis":[97],"closed-loop":[100],"system":[101],"is":[102,112],"demonstrated":[103],"by":[104],"Lyapunov":[105],"theory.":[106],"At":[107],"last,":[108],"a":[109],"numerical":[110],"example":[111],"provided":[113],"demonstrate":[115],"effectiveness":[117],"proposed":[120],"method.":[121]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2016,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}