{"id":"https://openalex.org/W3112743320","doi":"https://doi.org/10.1109/tnnls.2020.3041350","title":"Optimal Synchronization of Unidirectionally Coupled FO Chaotic Electromechanical Devices With the Hierarchical Neural Network","display_name":"Optimal Synchronization of Unidirectionally Coupled FO Chaotic Electromechanical Devices With the Hierarchical Neural Network","publication_year":2020,"publication_date":"2020-12-10","ids":{"openalex":"https://openalex.org/W3112743320","doi":"https://doi.org/10.1109/tnnls.2020.3041350","mag":"3112743320","pmid":"https://pubmed.ncbi.nlm.nih.gov/33296315"},"language":"en","primary_location":{"id":"doi:10.1109/tnnls.2020.3041350","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tnnls.2020.3041350","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/A5046554461","display_name":"Shaohua Luo","orcid":"https://orcid.org/0000-0002-3949-1914"},"institutions":[{"id":"https://openalex.org/I178232147","display_name":"Guizhou University","ror":"https://ror.org/02wmsc916","country_code":"CN","type":"education","lineage":["https://openalex.org/I178232147"]},{"id":"https://openalex.org/I189196454","display_name":"The University of Texas at Arlington","ror":"https://ror.org/019kgqr73","country_code":"US","type":"education","lineage":["https://openalex.org/I189196454"]}],"countries":["CN","US"],"is_corresponding":false,"raw_author_name":"Shaohua Luo","raw_affiliation_strings":["Key Laboratory of Advanced Manufacturing Technology, Ministry of Education, Guizhou University, Guiyang, China","UTA Research Institute, The University of Texas at Arlington, Fort Worth, TX, USA"],"raw_orcid":"https://orcid.org/0000-0002-3949-1914","affiliations":[{"raw_affiliation_string":"Key Laboratory of Advanced Manufacturing Technology, Ministry of Education, Guizhou University, Guiyang, China","institution_ids":["https://openalex.org/I178232147"]},{"raw_affiliation_string":"UTA Research Institute, The University of Texas at Arlington, Fort Worth, TX, USA","institution_ids":["https://openalex.org/I189196454"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5016137188","display_name":"Frank L. Lewis","orcid":"https://orcid.org/0000-0003-4074-1615"},"institutions":[{"id":"https://openalex.org/I189196454","display_name":"The University of Texas at Arlington","ror":"https://ror.org/019kgqr73","country_code":"US","type":"education","lineage":["https://openalex.org/I189196454"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Frank L. Lewis","raw_affiliation_strings":["UTA Research Institute, The University of Texas at Arlington, Fort Worth, TX, USA"],"raw_orcid":"https://orcid.org/0000-0003-4074-1615","affiliations":[{"raw_affiliation_string":"UTA Research Institute, The University of Texas at Arlington, Fort Worth, TX, USA","institution_ids":["https://openalex.org/I189196454"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5035337020","display_name":"Yongduan Song","orcid":"https://orcid.org/0000-0002-2167-1861"},"institutions":[{"id":"https://openalex.org/I158842170","display_name":"Chongqing University","ror":"https://ror.org/023rhb549","country_code":"CN","type":"education","lineage":["https://openalex.org/I158842170"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yongduan Song","raw_affiliation_strings":["Chongqing Key Laboratory of Intelligent Unmanned Systems, Chongqing University, Chongqing, China","School of Automation, Chongqing University, Chongqing, China","State Key Laboratory of Power Transmission Equipment and System Security and New Technology, Chongqing University, Chongqing, China"],"raw_orcid":"https://orcid.org/0000-0002-2167-1861","affiliations":[{"raw_affiliation_string":"Chongqing Key Laboratory of Intelligent Unmanned Systems, Chongqing University, Chongqing, China","institution_ids":["https://openalex.org/I158842170"]},{"raw_affiliation_string":"School of Automation, Chongqing University, Chongqing, China","institution_ids":["https://openalex.org/I158842170"]},{"raw_affiliation_string":"State Key Laboratory of Power Transmission Equipment and System Security and New Technology, Chongqing University, Chongqing, China","institution_ids":["https://openalex.org/I158842170"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5020335235","display_name":"Hassen M. Ouakad","orcid":"https://orcid.org/0000-0001-7262-2130"},"institutions":[{"id":"https://openalex.org/I47818738","display_name":"Sultan Qaboos University","ror":"https://ror.org/04wq8zb47","country_code":"OM","type":"education","lineage":["https://openalex.org/I47818738"]}],"countries":["OM"],"is_corresponding":false,"raw_author_name":"Hassen M. Ouakad","raw_affiliation_strings":["Department of Mechanical and Industrial Engineering, Sultan Qaboos University, Muscat, Oman"],"raw_orcid":"https://orcid.org/0000-0001-7262-2130","affiliations":[{"raw_affiliation_string":"Department of Mechanical and Industrial Engineering, Sultan Qaboos University, Muscat, Oman","institution_ids":["https://openalex.org/I47818738"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.79,"has_fulltext":false,"cited_by_count":36,"citation_normalized_percentile":{"value":0.92356293,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"33","issue":"3","first_page":"1192","last_page":"1202"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12794","display_name":"Adaptive Dynamic Programming Control","score":0.9994000196456909,"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":0.9994000196456909,"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/T11347","display_name":"Neural Networks Stability and Synchronization","score":0.9991999864578247,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/T10244","display_name":"Chaos control and synchronization","score":0.991100013256073,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"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":0.7231796383857727},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.6427798271179199},{"id":"https://openalex.org/keywords/feed-forward","display_name":"Feed forward","score":0.6150000095367432},{"id":"https://openalex.org/keywords/synchronization","display_name":"Synchronization (alternating current)","score":0.5878562331199646},{"id":"https://openalex.org/keywords/controller","display_name":"Controller (irrigation)","score":0.5705418586730957},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5675743222236633},{"id":"https://openalex.org/keywords/feedforward-neural-network","display_name":"Feedforward neural network","score":0.5066257119178772},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.4565436840057373},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.2749049663543701},{"id":"https://openalex.org/keywords/control-engineering","display_name":"Control engineering","score":0.27014392614364624},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.2049441635608673},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.1574421226978302},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.11806690692901611},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.09997466206550598}],"concepts":[{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.7231796383857727},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.6427798271179199},{"id":"https://openalex.org/C38858127","wikidata":"https://www.wikidata.org/wiki/Q5441228","display_name":"Feed forward","level":2,"score":0.6150000095367432},{"id":"https://openalex.org/C2778562939","wikidata":"https://www.wikidata.org/wiki/Q1298791","display_name":"Synchronization (alternating current)","level":3,"score":0.5878562331199646},{"id":"https://openalex.org/C203479927","wikidata":"https://www.wikidata.org/wiki/Q5165939","display_name":"Controller (irrigation)","level":2,"score":0.5705418586730957},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5675743222236633},{"id":"https://openalex.org/C47702885","wikidata":"https://www.wikidata.org/wiki/Q5441227","display_name":"Feedforward neural network","level":3,"score":0.5066257119178772},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.4565436840057373},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2749049663543701},{"id":"https://openalex.org/C133731056","wikidata":"https://www.wikidata.org/wiki/Q4917288","display_name":"Control engineering","level":1,"score":0.27014392614364624},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.2049441635608673},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.1574421226978302},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.11806690692901611},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.09997466206550598},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.0},{"id":"https://openalex.org/C6557445","wikidata":"https://www.wikidata.org/wiki/Q173113","display_name":"Agronomy","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/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.0}],"mesh":[{"descriptor_ui":"D000465","descriptor_name":"Algorithms","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D000465","descriptor_name":"Algorithms","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D000465","descriptor_name":"Algorithms","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D003198","descriptor_name":"Computer Simulation","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D003198","descriptor_name":"Computer Simulation","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D003198","descriptor_name":"Computer Simulation","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D005246","descriptor_name":"Feedback","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D005246","descriptor_name":"Feedback","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D005246","descriptor_name":"Feedback","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D016571","descriptor_name":"Neural Networks, Computer","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D016571","descriptor_name":"Neural Networks, Computer","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D016571","descriptor_name":"Neural Networks, Computer","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D017711","descriptor_name":"Nonlinear Dynamics","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D017711","descriptor_name":"Nonlinear Dynamics","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D017711","descriptor_name":"Nonlinear Dynamics","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true}],"locations_count":2,"locations":[{"id":"doi:10.1109/tnnls.2020.3041350","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tnnls.2020.3041350","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:33296315","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/33296315","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":[{"id":"https://openalex.org/G4623930966","display_name":"MEMS\u9640\u87ba\u4eea\u7684\u975e\u7ebf\u6027\u52a8\u529b\u5b66\u5206\u6790\u4e0e\u81ea\u9002\u5e94\u63a7\u5236\u7814\u7a76","funder_award_id":"52065008","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5756972503","display_name":null,"funder_award_id":"KYzhi[2019]041","funder_id":"https://openalex.org/F4320326674","funder_display_name":"Department of Education of Guizhou Province"},{"id":"https://openalex.org/G6248645078","display_name":null,"funder_award_id":"61860206008","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6487918314","display_name":null,"funder_award_id":"61773081","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/F4320326674","display_name":"Department of Education of Guizhou Province","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":48,"referenced_works":["https://openalex.org/W1223467140","https://openalex.org/W1614417283","https://openalex.org/W1968908471","https://openalex.org/W1974145940","https://openalex.org/W1982675115","https://openalex.org/W2015849223","https://openalex.org/W2016107280","https://openalex.org/W2037931656","https://openalex.org/W2041867553","https://openalex.org/W2056992506","https://openalex.org/W2059722814","https://openalex.org/W2070669992","https://openalex.org/W2071565849","https://openalex.org/W2143270297","https://openalex.org/W2158552938","https://openalex.org/W2292844798","https://openalex.org/W2343900735","https://openalex.org/W2346126941","https://openalex.org/W2468785923","https://openalex.org/W2482509550","https://openalex.org/W2488956545","https://openalex.org/W2498331080","https://openalex.org/W2508512712","https://openalex.org/W2556875844","https://openalex.org/W2568770738","https://openalex.org/W2579592432","https://openalex.org/W2594149384","https://openalex.org/W2616301069","https://openalex.org/W2724448021","https://openalex.org/W2781534416","https://openalex.org/W2801959273","https://openalex.org/W2884733963","https://openalex.org/W2907011619","https://openalex.org/W2910182934","https://openalex.org/W2912803089","https://openalex.org/W2915076694","https://openalex.org/W2921790353","https://openalex.org/W2943141190","https://openalex.org/W2946157668","https://openalex.org/W2948800568","https://openalex.org/W2954511463","https://openalex.org/W2955775727","https://openalex.org/W3003537242","https://openalex.org/W3005937281","https://openalex.org/W3008682111","https://openalex.org/W3010249541","https://openalex.org/W3014148024","https://openalex.org/W3039238353"],"related_works":["https://openalex.org/W2286391053","https://openalex.org/W1557629110","https://openalex.org/W2115072676","https://openalex.org/W4311212821","https://openalex.org/W2045727192","https://openalex.org/W2102065768","https://openalex.org/W1529660427","https://openalex.org/W3121106353","https://openalex.org/W2090361488","https://openalex.org/W2158578859"],"abstract_inverted_index":{"This":[0],"article":[1],"solves":[2],"the":[3,40,52,57,74,84,87,115,122,135,139,147,165,171,178,188,227,230],"problem":[4],"of":[5,21,39,65,86,117,130,149,187,203,220,229],"optimal":[6,91,103,172,212],"synchronization,":[7],"which":[8,94,134,177],"is":[9,49,107,112,161,182],"important":[10],"but":[11,214],"challenging":[12],"for":[13],"coupled":[14,205],"fractional-order":[15],"(FO)":[16],"chaotic":[17,207],"electromechanical":[18,42,208],"devices":[19,43,209],"composed":[20],"mechanical":[22],"and":[23,26,46,51,70,101,142,151,210],"electrical":[24],"oscillators":[25],"electromagnetic":[27],"filed":[28],"by":[29],"using":[30],"a":[31,217],"hierarchical":[32,123,143,179],"neural":[33,98,104,124,173,180],"network":[34,125,137,181],"structure.":[35],"The":[36,109,194],"synchronization":[37,92,213],"model":[38],"FO":[41,118,206],"with":[44,121],"capacitive":[45],"resistive":[47],"couplings":[48],"built,":[50],"phase":[53],"diagrams":[54],"reveal":[55],"that":[56],"dynamic":[58,131,157],"properties":[59],"are":[60],"closely":[61],"related":[62],"to":[63,77,83,126,145,163,184],"sets":[64],"physical":[66],"parameters,":[67],"coupling":[68],"coefficients,":[69],"FOs.":[71],"To":[72],"force":[73],"slave":[75],"system":[76,132],"move":[78],"from":[79],"its":[80],"original":[81],"orbits":[82,85],"master":[88],"system,":[89],"an":[90,96,102,155],"policy,":[93,106],"includes":[95],"adaptive":[97,156],"feedforward":[99,110],"policy":[100,160],"feedback":[105,174],"proposed.":[108],"controller":[111,175],"developed":[113],"in":[114,133,170,176],"framework":[116],"backstepping":[119],"integrated":[120],"estimate":[127],"unknown":[128],"functions":[129],"mentioned":[136],"has":[138],"formula":[140],"transformation":[141],"form":[144],"reduce":[146],"numbers":[148],"weights":[150],"membership":[152],"functions.":[153],"Also,":[154],"programming":[158],"(ADP)":[159],"proposed":[162],"address":[164],"zero-sum":[166],"differential":[167],"game":[168],"issue":[169],"designed":[183],"yield":[185],"solutions":[186],"constrained":[189],"Hamilton-Jacobi-Isaacs":[190],"(HJI)":[191],"equation":[192],"online.":[193],"presented":[195,231],"scheme":[196],"not":[197],"only":[198],"ensures":[199],"uniform":[200],"ultimate":[201],"boundedness":[202],"closed-loop":[204],"realizes":[211],"also":[215],"achieves":[216],"minimum":[218],"value":[219],"cost":[221],"function.":[222],"Simulation":[223],"results":[224],"further":[225],"show":[226],"validity":[228],"scheme.":[232]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":10},{"year":2023,"cited_by_count":10},{"year":2022,"cited_by_count":7},{"year":2021,"cited_by_count":5}],"updated_date":"2026-08-01T09:00:35.917206","created_date":"2025-10-10T00:00:00"}