{"id":"https://openalex.org/W4394698481","doi":"https://doi.org/10.1109/tnnls.2024.3383030","title":"Adaptive Neural Consensus Observer Networks Design for a Class of Semilinear Parabolic PDE Systems","display_name":"Adaptive Neural Consensus Observer Networks Design for a Class of Semilinear Parabolic PDE Systems","publication_year":2024,"publication_date":"2024-04-10","ids":{"openalex":"https://openalex.org/W4394698481","doi":"https://doi.org/10.1109/tnnls.2024.3383030","pmid":"https://pubmed.ncbi.nlm.nih.gov/38598392"},"language":"en","primary_location":{"id":"doi:10.1109/tnnls.2024.3383030","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tnnls.2024.3383030","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/A5000824720","display_name":"Mingxing Cai","orcid":"https://orcid.org/0009-0002-7465-7737"},"institutions":[{"id":"https://openalex.org/I139660479","display_name":"Central South University","ror":"https://ror.org/00f1zfq44","country_code":"CN","type":"education","lineage":["https://openalex.org/I139660479"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Mingxing Cai","raw_affiliation_strings":["School of Automation, Central South University, Changsha, China"],"raw_orcid":"https://orcid.org/0009-0002-7465-7737","affiliations":[{"raw_affiliation_string":"School of Automation, Central South University, Changsha, China","institution_ids":["https://openalex.org/I139660479"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100334753","display_name":"Yuan Yuan","orcid":"https://orcid.org/0000-0002-2640-0809"},"institutions":[{"id":"https://openalex.org/I56934997","display_name":"Changsha University of Science and Technology","ror":"https://ror.org/03yph8055","country_code":"CN","type":"education","lineage":["https://openalex.org/I56934997"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yuan Yuan","raw_affiliation_strings":["School of Electrical and Information Engineering, Changsha University of Science and Technology, Changsha, China"],"raw_orcid":"https://orcid.org/0000-0002-2640-0809","affiliations":[{"raw_affiliation_string":"School of Electrical and Information Engineering, Changsha University of Science and Technology, Changsha, China","institution_ids":["https://openalex.org/I56934997"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5012004938","display_name":"Biao Luo","orcid":"https://orcid.org/0000-0002-3353-2586"},"institutions":[{"id":"https://openalex.org/I139660479","display_name":"Central South University","ror":"https://ror.org/00f1zfq44","country_code":"CN","type":"education","lineage":["https://openalex.org/I139660479"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Biao Luo","raw_affiliation_strings":["School of Automation, Central South University, Changsha, China"],"raw_orcid":"https://orcid.org/0000-0002-3353-2586","affiliations":[{"raw_affiliation_string":"School of Automation, Central South University, Changsha, China","institution_ids":["https://openalex.org/I139660479"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5035583615","display_name":"Fanbiao Li","orcid":"https://orcid.org/0000-0002-4237-855X"},"institutions":[{"id":"https://openalex.org/I139660479","display_name":"Central South University","ror":"https://ror.org/00f1zfq44","country_code":"CN","type":"education","lineage":["https://openalex.org/I139660479"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Fanbiao Li","raw_affiliation_strings":["School of Automation, Central South University, Changsha, China"],"raw_orcid":"https://orcid.org/0000-0002-4237-855X","affiliations":[{"raw_affiliation_string":"School of Automation, Central South University, Changsha, China","institution_ids":["https://openalex.org/I139660479"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5018027570","display_name":"Xiaodong Xu","orcid":"https://orcid.org/0000-0003-4795-9967"},"institutions":[{"id":"https://openalex.org/I139660479","display_name":"Central South University","ror":"https://ror.org/00f1zfq44","country_code":"CN","type":"education","lineage":["https://openalex.org/I139660479"]},{"id":"https://openalex.org/I154425047","display_name":"University of Alberta","ror":"https://ror.org/0160cpw27","country_code":"CA","type":"education","lineage":["https://openalex.org/I154425047"]}],"countries":["CA","CN"],"is_corresponding":false,"raw_author_name":"Xiaodong Xu","raw_affiliation_strings":["School of Automation, Central South University, Changsha, China","Department of Chemical and Materials Engineering, University of Alberta, Edmonton, Canada"],"raw_orcid":"https://orcid.org/0000-0003-4795-9967","affiliations":[{"raw_affiliation_string":"School of Automation, Central South University, Changsha, China","institution_ids":["https://openalex.org/I139660479"]},{"raw_affiliation_string":"Department of Chemical and Materials Engineering, University of Alberta, Edmonton, Canada","institution_ids":["https://openalex.org/I154425047"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101971818","display_name":"Chunhua Yang","orcid":"https://orcid.org/0000-0002-3770-9887"},"institutions":[{"id":"https://openalex.org/I139660479","display_name":"Central South University","ror":"https://ror.org/00f1zfq44","country_code":"CN","type":"education","lineage":["https://openalex.org/I139660479"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Chunhua Yang","raw_affiliation_strings":["School of Automation, Central South University, Changsha, China"],"raw_orcid":"https://orcid.org/0000-0002-3770-9887","affiliations":[{"raw_affiliation_string":"School of Automation, Central South University, Changsha, China","institution_ids":["https://openalex.org/I139660479"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100711522","display_name":"Weihua Gui","orcid":"https://orcid.org/0000-0003-0312-436X"},"institutions":[{"id":"https://openalex.org/I139660479","display_name":"Central South University","ror":"https://ror.org/00f1zfq44","country_code":"CN","type":"education","lineage":["https://openalex.org/I139660479"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Weihua Gui","raw_affiliation_strings":["School of Automation, Central South University, Changsha, China"],"raw_orcid":"https://orcid.org/0000-0003-0312-436X","affiliations":[{"raw_affiliation_string":"School of Automation, Central South University, Changsha, China","institution_ids":["https://openalex.org/I139660479"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.0862,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.75924205,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"36","issue":"3","first_page":"5734","last_page":"5746"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11110","display_name":"Stability and Controllability of Differential Equations","score":1.0,"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/T11110","display_name":"Stability and Controllability of Differential Equations","score":1.0,"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/T11347","display_name":"Neural Networks Stability and Synchronization","score":0.9835000038146973,"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9785000085830688,"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/observer","display_name":"Observer (physics)","score":0.6874455809593201},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.6224077939987183},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.5688750147819519},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.5213750004768372},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4738346040248871},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.41546130180358887},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.2021161913871765},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.14302632212638855}],"concepts":[{"id":"https://openalex.org/C2780704645","wikidata":"https://www.wikidata.org/wiki/Q9251458","display_name":"Observer (physics)","level":2,"score":0.6874455809593201},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.6224077939987183},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.5688750147819519},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.5213750004768372},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4738346040248871},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.41546130180358887},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.2021161913871765},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.14302632212638855},{"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/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tnnls.2024.3383030","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tnnls.2024.3383030","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:38598392","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/38598392","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":[{"display_name":"Peace, Justice and strong institutions","score":0.7200000286102295,"id":"https://metadata.un.org/sdg/16"}],"awards":[{"id":"https://openalex.org/G1765971304","display_name":null,"funder_award_id":"2022YFB3304700","funder_id":"https://openalex.org/F4320335777","funder_display_name":"National Key Research and Development Program of China"},{"id":"https://openalex.org/G1769911756","display_name":null,"funder_award_id":"2022JJ20082","funder_id":"https://openalex.org/F4320322843","funder_display_name":"Natural Science Foundation of\u00a0Hunan Province"},{"id":"https://openalex.org/G713340247","display_name":null,"funder_award_id":"62222317","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7867171252","display_name":null,"funder_award_id":"62303072","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/F4320322843","display_name":"Natural Science Foundation of\u00a0Hunan Province","ror":null},{"id":"https://openalex.org/F4320335777","display_name":"National Key Research and Development Program of China","ror":null}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":38,"referenced_works":["https://openalex.org/W1606119439","https://openalex.org/W1968421013","https://openalex.org/W1968710032","https://openalex.org/W2001218902","https://openalex.org/W2008850282","https://openalex.org/W2019333520","https://openalex.org/W2025189603","https://openalex.org/W2046733765","https://openalex.org/W2058538513","https://openalex.org/W2067603665","https://openalex.org/W2079309923","https://openalex.org/W2092914488","https://openalex.org/W2116810757","https://openalex.org/W2119967247","https://openalex.org/W2121855948","https://openalex.org/W2132871031","https://openalex.org/W2153344006","https://openalex.org/W2171844855","https://openalex.org/W2187984384","https://openalex.org/W2345049064","https://openalex.org/W2492548893","https://openalex.org/W2499641798","https://openalex.org/W2560381229","https://openalex.org/W2883928315","https://openalex.org/W2889492704","https://openalex.org/W2911123472","https://openalex.org/W3091778540","https://openalex.org/W3126382552","https://openalex.org/W3206395178","https://openalex.org/W4200259043","https://openalex.org/W4229068424","https://openalex.org/W4248038912","https://openalex.org/W4282919728","https://openalex.org/W4295996101","https://openalex.org/W4296558740","https://openalex.org/W4310465421","https://openalex.org/W4312700838","https://openalex.org/W4388812608"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W2142036596","https://openalex.org/W2072657027","https://openalex.org/W2962838298","https://openalex.org/W2600246793"],"abstract_inverted_index":{"This":[0],"article":[1],"concerns":[2],"the":[3,6,10,48,57,66,78,81,86,92,104,112,120,133,143,150,157],"investigation":[4],"on":[5,149],"consensus":[7,159],"problem":[8],"for":[9,47,91,103],"joint":[11,129],"state-uncertainty":[12,130],"estimation":[13,131,141],"of":[14,17,35,50,77,107,123,135,145,156],"a":[15,31,74,164],"class":[16],"parabolic":[18],"partial":[19],"differential":[20],"equation":[21],"(PDE)":[22],"systems":[23],"with":[24,62],"parametric":[25,136],"and":[26,37,138],"nonparametric":[27,93,146],"uncertainties.":[28,51],"We":[29],"propose":[30],"two-layer":[32],"network":[33,58,122],"consisting":[34],"informed":[36],"uninformed":[38],"boundary":[39],"observers":[40,125],"where":[41],"novel":[42],"adaptation":[43,71],"laws":[44,72],"are":[45,101,161],"developed":[46],"identification":[49],"Particularly,":[52],"all":[53],"observer":[54,88],"agents":[55],"in":[56,132,142],"transmit":[59],"their":[60],"information":[61],"each":[63],"other":[64,87],"across":[65],"entire":[67],"network.":[68],"The":[69,154],"proposed":[70,121,158],"include":[73],"penalty":[75],"term":[76],"mismatch":[79],"between":[80],"parameter":[82],"estimates":[83],"generated":[84],"by":[85],"agents.":[89],"Moreover,":[90],"uncertainties,":[94],"radial":[95],"basis":[96],"function":[97],"(RBF)":[98],"neural":[99],"networks":[100],"employed":[102],"universal":[105],"approximation":[106],"unknown":[108],"nonlinear":[109],"functions.":[110],"Given":[111],"persistently":[113],"exciting":[114],"condition,":[115],"it":[116],"is":[117],"shown":[118],"that":[119],"adaptive":[124],"can":[126],"achieve":[127],"exponential":[128],"presence":[134,144],"uncertainties":[137,147],"ultimate":[139],"bounded":[140],"based":[148],"Lyapunov":[151],"stability":[152],"theory.":[153],"effects":[155],"method":[160],"demonstrated":[162],"through":[163],"typical":[165],"reaction-diffusion":[166],"system":[167],"example,":[168],"which":[169],"implies":[170],"convincing":[171],"numerical":[172],"findings.":[173]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":1}],"updated_date":"2026-03-27T05:58:40.876381","created_date":"2025-10-10T00:00:00"}