{"id":"https://openalex.org/W3018832276","doi":"https://doi.org/10.1109/tnnls.2020.2986275","title":"Design and Analysis of Two Prescribed-Time and Robust ZNN Models With Application to Time-Variant Stein Matrix Equation","display_name":"Design and Analysis of Two Prescribed-Time and Robust ZNN Models With Application to Time-Variant Stein Matrix Equation","publication_year":2020,"publication_date":"2020-04-27","ids":{"openalex":"https://openalex.org/W3018832276","doi":"https://doi.org/10.1109/tnnls.2020.2986275","mag":"3018832276","pmid":"https://pubmed.ncbi.nlm.nih.gov/32340965"},"language":"en","primary_location":{"id":"doi:10.1109/tnnls.2020.2986275","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tnnls.2020.2986275","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/A5070031719","display_name":"Jianhua Dai","orcid":"https://orcid.org/0000-0003-1459-0833"},"institutions":[{"id":"https://openalex.org/I173759888","display_name":"Hunan Normal University","ror":"https://ror.org/053w1zy07","country_code":"CN","type":"education","lineage":["https://openalex.org/I173759888"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Jianhua Dai","raw_affiliation_strings":["Hunan Provincial Key Laboratory of Intelligent Computing and Language Information Processing, Hunan Normal University, Changsha, China"],"affiliations":[{"raw_affiliation_string":"Hunan Provincial Key Laboratory of Intelligent Computing and Language Information Processing, Hunan Normal University, Changsha, China","institution_ids":["https://openalex.org/I173759888"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5022255906","display_name":"Lei Jia","orcid":"https://orcid.org/0000-0002-4405-7274"},"institutions":[{"id":"https://openalex.org/I173759888","display_name":"Hunan Normal University","ror":"https://ror.org/053w1zy07","country_code":"CN","type":"education","lineage":["https://openalex.org/I173759888"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Lei Jia","raw_affiliation_strings":["Hunan Provincial Key Laboratory of Intelligent Computing and Language Information Processing, Hunan Normal University, Changsha, China"],"affiliations":[{"raw_affiliation_string":"Hunan Provincial Key Laboratory of Intelligent Computing and Language Information Processing, Hunan Normal University, Changsha, China","institution_ids":["https://openalex.org/I173759888"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5005130812","display_name":"Lin Xiao","orcid":"https://orcid.org/0000-0003-3172-3490"},"institutions":[{"id":"https://openalex.org/I173759888","display_name":"Hunan Normal University","ror":"https://ror.org/053w1zy07","country_code":"CN","type":"education","lineage":["https://openalex.org/I173759888"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Lin Xiao","raw_affiliation_strings":["Hunan Provincial Key Laboratory of Intelligent Computing and Language Information Processing, Hunan Normal University, Changsha, China"],"affiliations":[{"raw_affiliation_string":"Hunan Provincial Key Laboratory of Intelligent Computing and Language Information Processing, Hunan Normal University, Changsha, China","institution_ids":["https://openalex.org/I173759888"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5070031719"],"corresponding_institution_ids":["https://openalex.org/I173759888"],"apc_list":null,"apc_paid":null,"fwci":3.0814,"has_fulltext":false,"cited_by_count":50,"citation_normalized_percentile":{"value":0.91690759,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":93,"max":100},"biblio":{"volume":"32","issue":"4","first_page":"1668","last_page":"1677"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9991999864578247,"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"}},"topics":[{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9991999864578247,"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"}},{"id":"https://openalex.org/T10571","display_name":"Robotic Mechanisms and Dynamics","score":0.9936000108718872,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9916999936103821,"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/convergence","display_name":"Convergence (economics)","score":0.7162414789199829},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6484618186950684},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5505589842796326},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.545943021774292},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.522443950176239},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5170141458511353},{"id":"https://openalex.org/keywords/residual","display_name":"Residual","score":0.5112500190734863},{"id":"https://openalex.org/keywords/recurrent-neural-network","display_name":"Recurrent neural network","score":0.4794168174266815},{"id":"https://openalex.org/keywords/state","display_name":"State (computer science)","score":0.4396263659000397},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.426923930644989},{"id":"https://openalex.org/keywords/noise","display_name":"Noise (video)","score":0.4164934754371643},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.3951474130153656},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.36552900075912476},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3370192050933838},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.1840202808380127},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1746726930141449},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.08469632267951965},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.08113887906074524}],"concepts":[{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.7162414789199829},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6484618186950684},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5505589842796326},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.545943021774292},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.522443950176239},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5170141458511353},{"id":"https://openalex.org/C155512373","wikidata":"https://www.wikidata.org/wiki/Q287450","display_name":"Residual","level":2,"score":0.5112500190734863},{"id":"https://openalex.org/C147168706","wikidata":"https://www.wikidata.org/wiki/Q1457734","display_name":"Recurrent neural network","level":3,"score":0.4794168174266815},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.4396263659000397},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.426923930644989},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.4164934754371643},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.3951474130153656},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.36552900075912476},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3370192050933838},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.1840202808380127},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1746726930141449},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.08469632267951965},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08113887906074524},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tnnls.2020.2986275","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tnnls.2020.2986275","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:32340965","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/32340965","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/G1991401205","display_name":null,"funder_award_id":"18A289","funder_id":"https://openalex.org/F4320322843","funder_display_name":"Natural Science Foundation of\u00a0Hunan Province"},{"id":"https://openalex.org/G5166635775","display_name":null,"funder_award_id":"61866013","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6367171472","display_name":null,"funder_award_id":"2018RS3065","funder_id":"https://openalex.org/F4320322843","funder_display_name":"Natural Science Foundation of\u00a0Hunan Province"},{"id":"https://openalex.org/G6633472649","display_name":null,"funder_award_id":"2018TP1018","funder_id":"https://openalex.org/F4320322843","funder_display_name":"Natural Science Foundation of\u00a0Hunan Province"},{"id":"https://openalex.org/G6806792462","display_name":null,"funder_award_id":"61473259","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8064630213","display_name":null,"funder_award_id":"61976089","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8303539496","display_name":null,"funder_award_id":"2019JJ50478","funder_id":"https://openalex.org/F4320322843","funder_display_name":"Natural Science Foundation of\u00a0Hunan Province"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320322843","display_name":"Natural Science Foundation of\u00a0Hunan Province","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":42,"referenced_works":["https://openalex.org/W1972380187","https://openalex.org/W1973446088","https://openalex.org/W1997270899","https://openalex.org/W2013549301","https://openalex.org/W2013635942","https://openalex.org/W2023757295","https://openalex.org/W2034877773","https://openalex.org/W2048443683","https://openalex.org/W2053961820","https://openalex.org/W2062551655","https://openalex.org/W2072223610","https://openalex.org/W2076414975","https://openalex.org/W2077633635","https://openalex.org/W2088026800","https://openalex.org/W2094206629","https://openalex.org/W2111470704","https://openalex.org/W2113927241","https://openalex.org/W2125690024","https://openalex.org/W2128171517","https://openalex.org/W2130317597","https://openalex.org/W2133702739","https://openalex.org/W2138244240","https://openalex.org/W2138844572","https://openalex.org/W2165552175","https://openalex.org/W2178354815","https://openalex.org/W2332672415","https://openalex.org/W2344415132","https://openalex.org/W2398606097","https://openalex.org/W2593923441","https://openalex.org/W2732094339","https://openalex.org/W2767834527","https://openalex.org/W2790232939","https://openalex.org/W2794132121","https://openalex.org/W2806365404","https://openalex.org/W2900351265","https://openalex.org/W2906482729","https://openalex.org/W2911281195","https://openalex.org/W2911835134","https://openalex.org/W2922391289","https://openalex.org/W2938800094","https://openalex.org/W2973166946","https://openalex.org/W3005162187"],"related_works":["https://openalex.org/W4225394202","https://openalex.org/W4298287631","https://openalex.org/W2953061907","https://openalex.org/W1847088711","https://openalex.org/W3036642985","https://openalex.org/W3032952384","https://openalex.org/W3017902212","https://openalex.org/W2964335273","https://openalex.org/W2982145560","https://openalex.org/W2790400419"],"abstract_inverted_index":{"The":[0,103],"zeroing":[1],"neural":[2],"network":[3],"(ZNN)":[4],"activated":[5,87],"by":[6,88],"nonlinear":[7,64,90],"activation":[8,65,91],"functions":[9,66,92],"plays":[10],"an":[11],"important":[12],"role":[13],"in":[14,32,53],"many":[15],"fields.":[16],"However,":[17],"conventional":[18],"ZNN":[19,31,84],"can":[20,129],"only":[21],"realize":[22],"finite-time":[23,37],"convergence,":[24],"which":[25],"greatly":[26],"limits":[27],"the":[28,41,47,62,75,98,138,146,153,167,170,173,179],"application":[29],"of":[30,44,77,157,172],"a":[33],"noisy":[34],"environment.":[35],"Generally,":[36],"convergence":[38,115,148,154],"depends":[39],"on":[40,74,120],"original":[42,48,121],"state":[43,49],"ZNN,":[45],"but":[46],"is":[50,142],"often":[51],"unknown":[52],"advance.":[54],"In":[55,71],"addition,":[56],"when":[57],"meeting":[58],"with":[59,152],"different":[60],"noises,":[61],"applied":[63],"cannot":[67],"tolerate":[68,130],"external":[69],"disturbances.":[70],"this":[72,78],"article,":[73],"strength":[76],"idea,":[79],"two":[80,89,105,109,175],"prescribed-time":[81,114,147],"and":[82,123,134,149,169],"robust":[83],"(PTR-ZNN)":[85],"models":[86,107,177],"are":[93],"put":[94],"forward":[95],"to":[96,144],"address":[97],"time-variant":[99,131,180],"Stein":[100,181],"matrix":[101,182],"equation.":[102],"proposed":[104,174],"PTR-ZNN":[106,176],"own":[108],"remarkable":[110],"advantages":[111],"simultaneously:":[112],"1)":[113],"that":[116,128],"does":[117],"not":[118],"rely":[119],"states":[122],"2)":[124],"superior":[125],"noise-tolerance":[126,150],"performance":[127],"bounded":[132],"vanishing":[133],"nonvanishing":[135],"noises.":[136],"Furthermore,":[137],"detailed":[139],"theoretical":[140],"analysis":[141],"provided":[143],"guarantee":[145],"performance,":[151],"upper":[155],"bounds":[156],"steady-state":[158],"residual":[159],"errors":[160],"calculated.":[161],"Finally,":[162],"simulative":[163],"comparison":[164],"results":[165],"indicate":[166],"effectiveness":[168],"superiority":[171],"for":[178],"equation":[183],"solving.":[184]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":13},{"year":2024,"cited_by_count":11},{"year":2023,"cited_by_count":14},{"year":2022,"cited_by_count":7},{"year":2021,"cited_by_count":2}],"updated_date":"2026-03-18T14:38:29.013473","created_date":"2025-10-10T00:00:00"}