{"id":"https://openalex.org/W2605659698","doi":"https://doi.org/10.1109/tnnls.2017.2690663","title":"A Discrete-Time Recurrent Neural Network for Solving Rank-Deficient Matrix Equations With an Application to Output Regulation of Linear Systems","display_name":"A Discrete-Time Recurrent Neural Network for Solving Rank-Deficient Matrix Equations With an Application to Output Regulation of Linear Systems","publication_year":2017,"publication_date":"2017-04-17","ids":{"openalex":"https://openalex.org/W2605659698","doi":"https://doi.org/10.1109/tnnls.2017.2690663","mag":"2605659698","pmid":"https://pubmed.ncbi.nlm.nih.gov/28436900"},"language":"en","primary_location":{"id":"doi:10.1109/tnnls.2017.2690663","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tnnls.2017.2690663","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/A5100722456","display_name":"Tao Liu","orcid":"https://orcid.org/0000-0001-8068-8025"},"institutions":[{"id":"https://openalex.org/I177725633","display_name":"Chinese University of Hong Kong","ror":"https://ror.org/00t33hh48","country_code":"HK","type":"education","lineage":["https://openalex.org/I177725633"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"Tao Liu","raw_affiliation_strings":["Department of Mechanical and Automation Engineering, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong"],"raw_orcid":"https://orcid.org/0000-0001-8068-8025","affiliations":[{"raw_affiliation_string":"Department of Mechanical and Automation Engineering, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong","institution_ids":["https://openalex.org/I177725633"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100665863","display_name":"Jie Huang","orcid":"https://orcid.org/0000-0002-6753-8679"},"institutions":[{"id":"https://openalex.org/I177725633","display_name":"Chinese University of Hong Kong","ror":"https://ror.org/00t33hh48","country_code":"HK","type":"education","lineage":["https://openalex.org/I177725633"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"Jie Huang","raw_affiliation_strings":["Department of Mechanical and Automation Engineering, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mechanical and Automation Engineering, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong","institution_ids":["https://openalex.org/I177725633"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I177725633"],"apc_list":{"value":2645,"currency":"USD","value_usd":2645},"apc_paid":null,"fwci":2.0532,"has_fulltext":false,"cited_by_count":25,"citation_normalized_percentile":{"value":0.89573955,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"29","issue":"6","first_page":"2271","last_page":"2277"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10320","display_name":"Neural Networks and Applications","score":0.9987999796867371,"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"}},"topics":[{"id":"https://openalex.org/T10320","display_name":"Neural Networks and Applications","score":0.9987999796867371,"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/T11206","display_name":"Model Reduction and Neural Networks","score":0.9950000047683716,"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/T11236","display_name":"Control Systems and Identification","score":0.9901000261306763,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.665963888168335},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.6640543341636658},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.64662104845047},{"id":"https://openalex.org/keywords/augmented-matrix","display_name":"Augmented matrix","score":0.6128761768341064},{"id":"https://openalex.org/keywords/system-of-linear-equations","display_name":"System of linear equations","score":0.5807152390480042},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.5581327080726624},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.5563564896583557},{"id":"https://openalex.org/keywords/coefficient-matrix","display_name":"Coefficient matrix","score":0.5235999822616577},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5138823986053467},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4841638207435608},{"id":"https://openalex.org/keywords/linear-equation","display_name":"Linear equation","score":0.46780019998550415},{"id":"https://openalex.org/keywords/discrete-time-and-continuous-time","display_name":"Discrete time and continuous time","score":0.44019874930381775},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.433829665184021},{"id":"https://openalex.org/keywords/state-transition-matrix","display_name":"State-transition matrix","score":0.388435423374176},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3678123354911804},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.36360496282577515},{"id":"https://openalex.org/keywords/symmetric-matrix","display_name":"Symmetric matrix","score":0.1858431100845337},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.16801023483276367},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.10097154974937439},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.08211970329284668}],"concepts":[{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.665963888168335},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.6640543341636658},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.64662104845047},{"id":"https://openalex.org/C105129939","wikidata":"https://www.wikidata.org/wiki/Q2750301","display_name":"Augmented matrix","level":5,"score":0.6128761768341064},{"id":"https://openalex.org/C94523830","wikidata":"https://www.wikidata.org/wiki/Q11203","display_name":"System of linear equations","level":2,"score":0.5807152390480042},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.5581327080726624},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.5563564896583557},{"id":"https://openalex.org/C60866291","wikidata":"https://www.wikidata.org/wiki/Q5140577","display_name":"Coefficient matrix","level":3,"score":0.5235999822616577},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5138823986053467},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4841638207435608},{"id":"https://openalex.org/C77346573","wikidata":"https://www.wikidata.org/wiki/Q484637","display_name":"Linear equation","level":2,"score":0.46780019998550415},{"id":"https://openalex.org/C55689738","wikidata":"https://www.wikidata.org/wiki/Q15963867","display_name":"Discrete time and continuous time","level":2,"score":0.44019874930381775},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.433829665184021},{"id":"https://openalex.org/C22629506","wikidata":"https://www.wikidata.org/wiki/Q7602993","display_name":"State-transition matrix","level":4,"score":0.388435423374176},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3678123354911804},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.36360496282577515},{"id":"https://openalex.org/C54848796","wikidata":"https://www.wikidata.org/wiki/Q339011","display_name":"Symmetric matrix","level":3,"score":0.1858431100845337},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.16801023483276367},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.10097154974937439},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.08211970329284668},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","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},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tnnls.2017.2690663","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tnnls.2017.2690663","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:28436900","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/28436900","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":"Journal Article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1547273885","display_name":"Leader following with connectivity preservation of multi-agent systems by distributed observer based approach","funder_award_id":"14202914","funder_id":"https://openalex.org/F4320321592","funder_display_name":"Research Grants Council, University Grants Committee"}],"funders":[{"id":"https://openalex.org/F4320321592","display_name":"Research Grants Council, University Grants Committee","ror":"https://ror.org/00djwmt25"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W114979488","https://openalex.org/W2010411578","https://openalex.org/W2038137192","https://openalex.org/W2072281876","https://openalex.org/W2074678431","https://openalex.org/W2075767141","https://openalex.org/W2091339772","https://openalex.org/W2093627685","https://openalex.org/W2118589723","https://openalex.org/W2133702739","https://openalex.org/W2138844572","https://openalex.org/W2149087996","https://openalex.org/W2162406405","https://openalex.org/W2164060839","https://openalex.org/W2220083659","https://openalex.org/W2416581454","https://openalex.org/W2481799503","https://openalex.org/W2552003518","https://openalex.org/W2563073222","https://openalex.org/W2581282721","https://openalex.org/W4213367573"],"related_works":["https://openalex.org/W3097421206","https://openalex.org/W2048286546","https://openalex.org/W2365527693","https://openalex.org/W2037819582","https://openalex.org/W2980165407","https://openalex.org/W2370263758","https://openalex.org/W2506892714","https://openalex.org/W2355478383","https://openalex.org/W2349379571","https://openalex.org/W2015081464"],"abstract_inverted_index":{"This":[0],"paper":[1],"presents":[2],"a":[3,27,39],"discrete-time":[4],"recurrent":[5],"neural":[6],"network":[7],"approach":[8],"to":[9,45,74,78],"solving":[10,58],"systems":[11],"of":[12,21,41,69],"linear":[13,22,64,84],"equations":[14,23],"with":[15],"two":[16],"features.":[17],"First,":[18],"the":[19,31,46,59,79],"system":[20,32,48],"may":[24],"not":[25,35],"have":[26],"unique":[28],"solution.":[29],"Second,":[30],"matrix":[33,49],"is":[34,51,55],"known":[36],"precisely,":[37],"but":[38],"sequence":[40],"matrices":[42],"that":[43],"converges":[44],"unknown":[47],"exponentially":[50],"known.":[52],"The":[53],"problem":[54,62,82],"motivated":[56],"from":[57],"output":[60,80],"regulation":[61,81],"for":[63,83],"systems.":[65,85],"Thus,":[66],"an":[67,75],"application":[68],"our":[70],"main":[71],"result":[72],"leads":[73],"online":[76],"solution":[77]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":1}],"updated_date":"2026-08-21T09:56:20.448147","created_date":"2025-10-10T00:00:00"}