{"id":"https://openalex.org/W4312682829","doi":"https://doi.org/10.1109/tnnls.2022.3225636","title":"Nonlinear Decoupling Control With PI<i> <sup>\u03bb</sup> </i> D<i> <sup>\u03bc</sup> </i> Neural Network for MIMO Systems","display_name":"Nonlinear Decoupling Control With PI<i> <sup>\u03bb</sup> </i> D<i> <sup>\u03bc</sup> </i> Neural Network for MIMO Systems","publication_year":2022,"publication_date":"2022-12-07","ids":{"openalex":"https://openalex.org/W4312682829","doi":"https://doi.org/10.1109/tnnls.2022.3225636","pmid":"https://pubmed.ncbi.nlm.nih.gov/37015583"},"language":"en","primary_location":{"id":"doi:10.1109/tnnls.2022.3225636","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tnnls.2022.3225636","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/A5015758351","display_name":"Jie Ding","orcid":"https://orcid.org/0000-0002-9910-6280"},"institutions":[{"id":"https://openalex.org/I41198531","display_name":"Nanjing University of Posts and Telecommunications","ror":"https://ror.org/043bpky34","country_code":"CN","type":"education","lineage":["https://openalex.org/I41198531"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Jie Ding","raw_affiliation_strings":["School of Automation and Artificial Intelligence, Nanjing University of Posts and Telecommunications, Nanjing, Jiangsu, China"],"raw_orcid":"https://orcid.org/0000-0002-9910-6280","affiliations":[{"raw_affiliation_string":"School of Automation and Artificial Intelligence, Nanjing University of Posts and Telecommunications, Nanjing, Jiangsu, China","institution_ids":["https://openalex.org/I41198531"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101924896","display_name":"Min Wu","orcid":"https://orcid.org/0000-0001-5496-8066"},"institutions":[{"id":"https://openalex.org/I41198531","display_name":"Nanjing University of Posts and Telecommunications","ror":"https://ror.org/043bpky34","country_code":"CN","type":"education","lineage":["https://openalex.org/I41198531"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Min Wu","raw_affiliation_strings":["School of Automation and Artificial Intelligence, Nanjing University of Posts and Telecommunications, Nanjing, Jiangsu, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Automation and Artificial Intelligence, Nanjing University of Posts and Telecommunications, Nanjing, Jiangsu, China","institution_ids":["https://openalex.org/I41198531"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5054421000","display_name":"Min Xiao","orcid":"https://orcid.org/0000-0002-8992-153X"},"institutions":[{"id":"https://openalex.org/I41198531","display_name":"Nanjing University of Posts and Telecommunications","ror":"https://ror.org/043bpky34","country_code":"CN","type":"education","lineage":["https://openalex.org/I41198531"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Min Xiao","raw_affiliation_strings":["School of Automation and Artificial Intelligence, Nanjing University of Posts and Telecommunications, Nanjing, Jiangsu, China"],"raw_orcid":"https://orcid.org/0000-0002-8992-153X","affiliations":[{"raw_affiliation_string":"School of Automation and Artificial Intelligence, Nanjing University of Posts and Telecommunications, Nanjing, Jiangsu, China","institution_ids":["https://openalex.org/I41198531"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5015758351"],"corresponding_institution_ids":["https://openalex.org/I41198531"],"apc_list":null,"apc_paid":null,"fwci":1.7011,"has_fulltext":false,"cited_by_count":15,"citation_normalized_percentile":{"value":0.83844487,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":96,"max":98},"biblio":{"volume":"35","issue":"6","first_page":"8715","last_page":"8722"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11081","display_name":"Advanced Control Systems Design","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"}},"topics":[{"id":"https://openalex.org/T11081","display_name":"Advanced Control Systems Design","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/T10320","display_name":"Neural Networks and Applications","score":0.9937999844551086,"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/T12676","display_name":"Machine Learning and ELM","score":0.9812999963760376,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/pid-controller","display_name":"PID controller","score":0.4969053566455841},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.49174764752388},{"id":"https://openalex.org/keywords/decoupling","display_name":"Decoupling (probability)","score":0.4916148781776428},{"id":"https://openalex.org/keywords/notation","display_name":"Notation","score":0.4202273190021515},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4187985956668854},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.40146663784980774},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.33443742990493774},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3287425935268402},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3206353783607483},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.30784815549850464},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.29911738634109497},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.19213637709617615},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.09766554832458496},{"id":"https://openalex.org/keywords/temperature-control","display_name":"Temperature control","score":0.09338578581809998},{"id":"https://openalex.org/keywords/control-engineering","display_name":"Control engineering","score":0.09297239780426025}],"concepts":[{"id":"https://openalex.org/C47116090","wikidata":"https://www.wikidata.org/wiki/Q716829","display_name":"PID controller","level":3,"score":0.4969053566455841},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.49174764752388},{"id":"https://openalex.org/C205606062","wikidata":"https://www.wikidata.org/wiki/Q5249645","display_name":"Decoupling (probability)","level":2,"score":0.4916148781776428},{"id":"https://openalex.org/C45357846","wikidata":"https://www.wikidata.org/wiki/Q2001982","display_name":"Notation","level":2,"score":0.4202273190021515},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4187985956668854},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.40146663784980774},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.33443742990493774},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3287425935268402},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3206353783607483},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.30784815549850464},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.29911738634109497},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.19213637709617615},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.09766554832458496},{"id":"https://openalex.org/C536315585","wikidata":"https://www.wikidata.org/wiki/Q7698332","display_name":"Temperature control","level":2,"score":0.09338578581809998},{"id":"https://openalex.org/C133731056","wikidata":"https://www.wikidata.org/wiki/Q4917288","display_name":"Control engineering","level":1,"score":0.09297239780426025}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tnnls.2022.3225636","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tnnls.2022.3225636","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:37015583","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/37015583","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/G1800890972","display_name":null,"funder_award_id":"BK20211275","funder_id":"https://openalex.org/F4320322769","funder_display_name":"Natural Science Foundation of Jiangsu Province"},{"id":"https://openalex.org/G1810446312","display_name":null,"funder_award_id":"62073172","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/F4320322769","display_name":"Natural Science Foundation of Jiangsu Province","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":43,"referenced_works":["https://openalex.org/W1748133846","https://openalex.org/W1969313263","https://openalex.org/W2000910171","https://openalex.org/W2009619312","https://openalex.org/W2017845303","https://openalex.org/W2024485096","https://openalex.org/W2027897561","https://openalex.org/W2037568427","https://openalex.org/W2096166399","https://openalex.org/W2117680746","https://openalex.org/W2153171506","https://openalex.org/W2165299997","https://openalex.org/W2169007966","https://openalex.org/W2269307768","https://openalex.org/W2313578468","https://openalex.org/W2330892803","https://openalex.org/W2337508653","https://openalex.org/W2339417300","https://openalex.org/W2508852782","https://openalex.org/W2587804202","https://openalex.org/W2592509915","https://openalex.org/W2604400835","https://openalex.org/W2609139220","https://openalex.org/W2751201224","https://openalex.org/W2763080905","https://openalex.org/W2766188596","https://openalex.org/W2766291207","https://openalex.org/W2802292836","https://openalex.org/W2900212435","https://openalex.org/W2941441890","https://openalex.org/W3004243204","https://openalex.org/W3033819782","https://openalex.org/W3042596271","https://openalex.org/W3138086157","https://openalex.org/W3147416837","https://openalex.org/W3147468438","https://openalex.org/W3171595030","https://openalex.org/W3174355718","https://openalex.org/W3193598292","https://openalex.org/W4205713248","https://openalex.org/W4206163104","https://openalex.org/W4206659854","https://openalex.org/W4241960520"],"related_works":["https://openalex.org/W2002388147","https://openalex.org/W3098928304","https://openalex.org/W2394883510","https://openalex.org/W2150958483","https://openalex.org/W2165013373","https://openalex.org/W2121097709","https://openalex.org/W2922503265","https://openalex.org/W2023324176","https://openalex.org/W2576987672","https://openalex.org/W3212795132"],"abstract_inverted_index":{"In":[0],"this":[1,133],"brief,":[2],"a":[3,67],"fractional":[4,34,55,109,140],"order":[5,35,56,110,141],"proportional-integral-differential":[6],"neural":[7,47,150],"network":[8],"(PIDNN)":[9],"controller":[10,82,112],"based":[11],"on":[12,70],"the":[13,33,41,46,54,60,71,78,81,84,88,96,115,129,135,139,156,161],"beetle":[14],"swarm":[15],"optimization":[16],"algorithm":[17,98],"(BSO-PI":[18],"[Formula:":[19,90,143],"see":[20,91,144],"text]NN)":[21],"is":[22,38,74,93,134],"proposed":[23,108,162],"for":[24],"multi-input":[25],"multi-output":[26],"(MIMO)":[27],"systems":[28],"with":[29],"strong":[30],"coupling.":[31],"First,":[32],"PID":[36],"operator":[37],"introduced":[39],"to":[40,76,99],"hidden":[42],"layer":[43],"neurons":[44,57,146],"of":[45,53,80,160],"network,":[48],"where":[49],"long":[50],"memory":[51],"characteristics":[52],"can":[58,113],"improve":[59],"control":[61,122],"accuracy":[62],"and":[63,119,158],"convergence":[64],"speed.":[65],"Second,":[66],"sufficient":[68],"condition":[69],"learning":[72],"rate":[73],"established":[75],"ensure":[77],"stability":[79],"by":[83,95],"Lyapunov":[85],"theory.":[86],"Third,":[87],"PI":[89,142],"text]NN":[92],"initialized":[94],"BSO":[97],"prevent":[100],"weights":[101],"from":[102],"falling":[103],"into":[104],"local":[105],"optima.":[106],"The":[107],"PIDNN":[111],"eliminate":[114],"coupling":[116],"between":[117],"variables":[118],"achieve":[120],"desirable":[121],"performance":[123],"without":[124],"specific":[125],"system":[126],"models.":[127],"To":[128],"authors'":[130],"best":[131],"knowledge,":[132],"first":[136],"work":[137],"that":[138],"text]":[145],"are":[147],"employed":[148],"in":[149],"network.":[151],"Two":[152],"simulation":[153],"examples":[154],"verify":[155],"effectiveness":[157],"superiority":[159],"controller.":[163]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":5}],"updated_date":"2026-03-27T05:58:40.876381","created_date":"2023-01-05T00:00:00"}
