{"id":"https://openalex.org/W2247166775","doi":"https://doi.org/10.1109/tnnls.2015.2442437","title":"Recurrent-Neural-Network-Based Multivariable Adaptive Control for a Class of Nonlinear Dynamic Systems With Time-Varying Delay","display_name":"Recurrent-Neural-Network-Based Multivariable Adaptive Control for a Class of Nonlinear Dynamic Systems With Time-Varying Delay","publication_year":2015,"publication_date":"2015-07-22","ids":{"openalex":"https://openalex.org/W2247166775","doi":"https://doi.org/10.1109/tnnls.2015.2442437","mag":"2247166775","pmid":"https://pubmed.ncbi.nlm.nih.gov/26126287"},"language":"en","primary_location":{"id":"doi:10.1109/tnnls.2015.2442437","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tnnls.2015.2442437","pdf_url":null,"source":{"id":"https://openalex.org/S4210175523","display_name":"IEEE Transactions on Neural Networks and Learning Systems","issn_l":"2162-237X","issn":["2162-237X","2162-2388"],"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 Neural Networks and Learning Systems","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/A5040229352","display_name":"Chih\u2010Lyang Hwang","orcid":"https://orcid.org/0000-0003-0200-8674"},"institutions":[{"id":"https://openalex.org/I154864474","display_name":"National Taiwan University of Science and Technology","ror":"https://ror.org/00q09pe49","country_code":"TW","type":"education","lineage":["https://openalex.org/I154864474"]}],"countries":["TW"],"is_corresponding":true,"raw_author_name":"Chih-Lyang Hwang","raw_affiliation_strings":["Department of Electrical Engineering, National Taiwan University of Science and Technology, Taipei, Taiwan"],"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, National Taiwan University of Science and Technology, Taipei, Taiwan","institution_ids":["https://openalex.org/I154864474"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5063196356","display_name":"Chau Jan","orcid":null},"institutions":[{"id":"https://openalex.org/I4210127362","display_name":"Nan Jeon University of Science and Technology","ror":"https://ror.org/02m77cm13","country_code":"TW","type":"education","lineage":["https://openalex.org/I4210127362"]}],"countries":["TW"],"is_corresponding":false,"raw_author_name":"Chau Jan","raw_affiliation_strings":["Department of Mechanical Engineering, Nan Jeon University of Science and Technology, Tainan, Taiwan"],"affiliations":[{"raw_affiliation_string":"Department of Mechanical Engineering, Nan Jeon University of Science and Technology, Tainan, Taiwan","institution_ids":["https://openalex.org/I4210127362"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5040229352"],"corresponding_institution_ids":["https://openalex.org/I154864474"],"apc_list":null,"apc_paid":null,"fwci":2.3824,"has_fulltext":false,"cited_by_count":35,"citation_normalized_percentile":{"value":0.89883315,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"27","issue":"2","first_page":"388","last_page":"401"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10040","display_name":"Adaptive Control of Nonlinear Systems","score":0.9995999932289124,"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"}},"topics":[{"id":"https://openalex.org/T10040","display_name":"Adaptive Control of Nonlinear Systems","score":0.9995999932289124,"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/T11749","display_name":"Iterative Learning Control Systems","score":0.9976000189781189,"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/T12794","display_name":"Adaptive Dynamic Programming Control","score":0.9965000152587891,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.7627049684524536},{"id":"https://openalex.org/keywords/multivariable-calculus","display_name":"Multivariable calculus","score":0.6958639025688171},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6411968469619751},{"id":"https://openalex.org/keywords/robustness","display_name":"Robustness (evolution)","score":0.6398138403892517},{"id":"https://openalex.org/keywords/recurrent-neural-network","display_name":"Recurrent neural network","score":0.5587027668952942},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.550987720489502},{"id":"https://openalex.org/keywords/tracking-error","display_name":"Tracking error","score":0.5335032939910889},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5334795713424683},{"id":"https://openalex.org/keywords/autoregressive-model","display_name":"Autoregressive model","score":0.4678870737552643},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.45267486572265625},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.40962111949920654},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.2444780170917511},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.13836002349853516},{"id":"https://openalex.org/keywords/control-engineering","display_name":"Control engineering","score":0.13674074411392212},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.11889955401420593},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.07269540429115295}],"concepts":[{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.7627049684524536},{"id":"https://openalex.org/C117312493","wikidata":"https://www.wikidata.org/wiki/Q2035437","display_name":"Multivariable calculus","level":2,"score":0.6958639025688171},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6411968469619751},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.6398138403892517},{"id":"https://openalex.org/C147168706","wikidata":"https://www.wikidata.org/wiki/Q1457734","display_name":"Recurrent neural network","level":3,"score":0.5587027668952942},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.550987720489502},{"id":"https://openalex.org/C183356978","wikidata":"https://www.wikidata.org/wiki/Q1779213","display_name":"Tracking error","level":3,"score":0.5335032939910889},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5334795713424683},{"id":"https://openalex.org/C159877910","wikidata":"https://www.wikidata.org/wiki/Q2202883","display_name":"Autoregressive model","level":2,"score":0.4678870737552643},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.45267486572265625},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.40962111949920654},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.2444780170917511},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.13836002349853516},{"id":"https://openalex.org/C133731056","wikidata":"https://www.wikidata.org/wiki/Q4917288","display_name":"Control engineering","level":1,"score":0.13674074411392212},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.11889955401420593},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.07269540429115295},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tnnls.2015.2442437","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tnnls.2015.2442437","pdf_url":null,"source":{"id":"https://openalex.org/S4210175523","display_name":"IEEE Transactions on Neural Networks and Learning Systems","issn_l":"2162-237X","issn":["2162-237X","2162-2388"],"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 Neural Networks and Learning Systems","raw_type":"journal-article"},{"id":"pmid:26126287","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/26126287","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 neural networks and learning systems","raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320309321","display_name":"Georgia Institute of Technology","ror":"https://ror.org/01zkghx44"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":37,"referenced_works":["https://openalex.org/W1551596967","https://openalex.org/W1972972294","https://openalex.org/W1993920342","https://openalex.org/W2001089302","https://openalex.org/W2026763266","https://openalex.org/W2039617089","https://openalex.org/W2055673018","https://openalex.org/W2058804598","https://openalex.org/W2082294283","https://openalex.org/W2085932691","https://openalex.org/W2089904313","https://openalex.org/W2091339772","https://openalex.org/W2100134099","https://openalex.org/W2101136244","https://openalex.org/W2102432893","https://openalex.org/W2108018708","https://openalex.org/W2110104109","https://openalex.org/W2111986387","https://openalex.org/W2112961899","https://openalex.org/W2114467592","https://openalex.org/W2115394511","https://openalex.org/W2115459565","https://openalex.org/W2126057182","https://openalex.org/W2134668622","https://openalex.org/W2135058870","https://openalex.org/W2136490634","https://openalex.org/W2136492299","https://openalex.org/W2136838997","https://openalex.org/W2140974246","https://openalex.org/W2144712295","https://openalex.org/W2145581742","https://openalex.org/W2150827104","https://openalex.org/W2165206308","https://openalex.org/W2169007966","https://openalex.org/W2489526136","https://openalex.org/W6677001794","https://openalex.org/W6677258281"],"related_works":["https://openalex.org/W1576377477","https://openalex.org/W2224575301","https://openalex.org/W2721687755","https://openalex.org/W2388146630","https://openalex.org/W418212511","https://openalex.org/W2086932047","https://openalex.org/W2099048101","https://openalex.org/W1964208669","https://openalex.org/W2112363989","https://openalex.org/W13811253"],"abstract_inverted_index":{"At":[0],"the":[1,29,35,65,76,80,95,102,106,123,127,131,135,163,169,178,190,195],"beginning,":[2],"an":[3],"approximate":[4],"nonlinear":[5,19],"autoregressive":[6],"moving":[7],"average":[8],"(NARMA)":[9],"model":[10,37,68],"is":[11,26,88,119,151,175],"employed":[12,120],"to":[13,52,75,91,101,121,153,188],"represent":[14],"a":[15,83,116,146],"class":[16],"of":[17,31,79,105,109,126,134,138,171,194],"multivariable":[18,181],"dynamic":[20,77],"systems":[21],"with":[22,60,145,168],"time-varying":[23],"delay.":[24],"It":[25],"known":[27],"that":[28],"disadvantages":[30],"robust":[32],"control":[33,43],"for":[34,45,148],"NARMA":[36,67,81],"are":[38,49,186],"as":[39],"follows:":[40],"1)":[41],"suitable":[42,161],"parameters":[44],"larger":[46,107],"time":[47],"delay":[48],"more":[50],"sensitive":[51],"achieving":[53],"desirable":[54],"performance;":[55],"2)":[56],"it":[57],"only":[58],"deals":[59],"bounded":[61,166],"uncertainty;":[62],"and":[63,192],"3)":[64],"nominal":[66],"must":[69],"be":[70],"learned":[71],"in":[72],"advance.":[73],"Due":[74],"feature":[78],"model,":[82],"recurrent":[84],"neural":[85],"network":[86,118],"(RNN)":[87],"online":[89],"applied":[90,152],"learn":[92],"it.":[93],"However,":[94],"system":[96,110],"performance":[97],"becomes":[98],"deteriorated":[99],"due":[100],"poor":[103],"learning":[104,143],"variation":[108],"vector":[111],"functions.":[112],"In":[113],"this":[114],"situation,":[115],"simple":[117],"compensate":[122],"upper":[124],"bound":[125],"residue":[128],"caused":[129],"by":[130,177],"linear":[132],"parameterization":[133],"approximation":[136],"error":[137],"RNN.":[139],"An":[140],"e":[141],"-modification":[142],"law":[144],"projection":[147],"weight":[149,173],"matrix":[150,174],"guarantee":[154],"its":[155],"boundedness":[156,170],"without":[157],"persistent":[158],"excitation.":[159],"Under":[160],"conditions,":[162],"semiglobally":[164],"ultimately":[165],"tracking":[167],"estimated":[172],"obtained":[176],"proposed":[179,196],"RNN-based":[180],"adaptive":[182],"control.":[183,197],"Finally,":[184],"simulations":[185],"presented":[187],"verify":[189],"effectiveness":[191],"robustness":[193]},"counts_by_year":[{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":1}],"updated_date":"2026-03-27T14:29:43.386196","created_date":"2025-10-10T00:00:00"}