{"id":"https://openalex.org/W2127935069","doi":"https://doi.org/10.1109/cacsd.2011.6044542","title":"Universal approximation with error bounds for dynamic artificial neural network models: A tutorial and some new results","display_name":"Universal approximation with error bounds for dynamic artificial neural network models: A tutorial and some new results","publication_year":2011,"publication_date":"2011-09-01","ids":{"openalex":"https://openalex.org/W2127935069","doi":"https://doi.org/10.1109/cacsd.2011.6044542","mag":"2127935069"},"language":"en","primary_location":{"id":"doi:10.1109/cacsd.2011.6044542","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cacsd.2011.6044542","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2011 IEEE International Symposium on Computer-Aided Control System Design (CACSD)","raw_type":"proceedings-article"},"type":"conference-paper","indexed_in":["crossref"],"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/A5030563746","display_name":"Kwang Ki Kevin Kim","orcid":null},"institutions":[{"id":"https://openalex.org/I157725225","display_name":"University of Illinois Urbana-Champaign","ror":"https://ror.org/047426m28","country_code":"US","type":"education","lineage":["https://openalex.org/I157725225"]},{"id":"https://openalex.org/I63966007","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44","country_code":"US","type":"education","lineage":["https://openalex.org/I63966007"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Kwang Ki Kevin Kim","raw_affiliation_strings":["Massachusetts Institute of Technology, Cambridge, MA, USA","University of Illinois, Urbana-Champaign, Urbana, IL, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Massachusetts Institute of Technology, Cambridge, MA, USA","institution_ids":["https://openalex.org/I63966007"]},{"raw_affiliation_string":"University of Illinois, Urbana-Champaign, Urbana, IL, USA","institution_ids":["https://openalex.org/I157725225"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5047960946","display_name":"Ernesto R\u00edos Patr\u00f3n","orcid":null},"institutions":[{"id":"https://openalex.org/I52957644","display_name":"Mexican Institute of Petroleum","ror":"https://ror.org/02dfpb916","country_code":"MX","type":"government","lineage":["https://openalex.org/I52957644"]}],"countries":["MX"],"is_corresponding":false,"raw_author_name":"Ernesto Rios Patron","raw_affiliation_strings":["Petr\u00f3leos Mexicanos and Facultad de Quimica, UNAM, Mexico"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Petr\u00f3leos Mexicanos and Facultad de Quimica, UNAM, Mexico","institution_ids":["https://openalex.org/I52957644"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5083684552","display_name":"Richard D. Braatz","orcid":"https://orcid.org/0000-0003-4304-3484"},"institutions":[{"id":"https://openalex.org/I63966007","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44","country_code":"US","type":"education","lineage":["https://openalex.org/I63966007"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Richard D. Braatz","raw_affiliation_strings":["Massachusetts Institute of Technology, Cambridge, MA, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Massachusetts Institute of Technology, Cambridge, MA, USA","institution_ids":["https://openalex.org/I63966007"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.8093,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.71922741,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"40","issue":null,"first_page":"834","last_page":"839"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10320","display_name":"Neural Networks and Applications","score":0.9991000294685364,"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":0.9991000294685364,"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/T11236","display_name":"Control Systems and Identification","score":0.9987000226974487,"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/T10876","display_name":"Fault Detection and Control Systems","score":0.9975000023841858,"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/artificial-neural-network","display_name":"Artificial neural network","score":0.7353928685188293},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6498141288757324},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5958728790283203},{"id":"https://openalex.org/keywords/recurrent-neural-network","display_name":"Recurrent neural network","score":0.5307274460792542},{"id":"https://openalex.org/keywords/block-diagram","display_name":"Block diagram","score":0.5043188333511353},{"id":"https://openalex.org/keywords/identification","display_name":"Identification (biology)","score":0.4899875223636627},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.47236520051956177},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.46235379576683044},{"id":"https://openalex.org/keywords/system-identification","display_name":"System identification","score":0.4603533446788788},{"id":"https://openalex.org/keywords/state-space","display_name":"State space","score":0.45566242933273315},{"id":"https://openalex.org/keywords/nonlinear-system-identification","display_name":"Nonlinear system identification","score":0.4518541395664215},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.41291895508766174},{"id":"https://openalex.org/keywords/block","display_name":"Block (permutation group theory)","score":0.41020727157592773},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.2781642973423004},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.2719373404979706},{"id":"https://openalex.org/keywords/data-modeling","display_name":"Data modeling","score":0.21935239434242249},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.08836141228675842}],"concepts":[{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.7353928685188293},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6498141288757324},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5958728790283203},{"id":"https://openalex.org/C147168706","wikidata":"https://www.wikidata.org/wiki/Q1457734","display_name":"Recurrent neural network","level":3,"score":0.5307274460792542},{"id":"https://openalex.org/C149227320","wikidata":"https://www.wikidata.org/wiki/Q884718","display_name":"Block diagram","level":2,"score":0.5043188333511353},{"id":"https://openalex.org/C116834253","wikidata":"https://www.wikidata.org/wiki/Q2039217","display_name":"Identification (biology)","level":2,"score":0.4899875223636627},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.47236520051956177},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.46235379576683044},{"id":"https://openalex.org/C119247159","wikidata":"https://www.wikidata.org/wiki/Q1366192","display_name":"System identification","level":3,"score":0.4603533446788788},{"id":"https://openalex.org/C72434380","wikidata":"https://www.wikidata.org/wiki/Q230930","display_name":"State space","level":2,"score":0.45566242933273315},{"id":"https://openalex.org/C22157029","wikidata":"https://www.wikidata.org/wiki/Q17080460","display_name":"Nonlinear system identification","level":4,"score":0.4518541395664215},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.41291895508766174},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.41020727157592773},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.2781642973423004},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2719373404979706},{"id":"https://openalex.org/C67186912","wikidata":"https://www.wikidata.org/wiki/Q367664","display_name":"Data modeling","level":2,"score":0.21935239434242249},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.08836141228675842},{"id":"https://openalex.org/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C59822182","wikidata":"https://www.wikidata.org/wiki/Q441","display_name":"Botany","level":1,"score":0.0},{"id":"https://openalex.org/C119599485","wikidata":"https://www.wikidata.org/wiki/Q43035","display_name":"Electrical engineering","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":1,"locations":[{"id":"doi:10.1109/cacsd.2011.6044542","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cacsd.2011.6044542","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2011 IEEE International Symposium on Computer-Aided Control System Design (CACSD)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":38,"referenced_works":["https://openalex.org/W1494912895","https://openalex.org/W1971735090","https://openalex.org/W1976068816","https://openalex.org/W1984481057","https://openalex.org/W1985921845","https://openalex.org/W1994921381","https://openalex.org/W2000647458","https://openalex.org/W2001389674","https://openalex.org/W2004175622","https://openalex.org/W2015156326","https://openalex.org/W2029686441","https://openalex.org/W2043260411","https://openalex.org/W2047161049","https://openalex.org/W2071125069","https://openalex.org/W2072627349","https://openalex.org/W2082512543","https://openalex.org/W2095941969","https://openalex.org/W2103496339","https://openalex.org/W2113442785","https://openalex.org/W2116930657","https://openalex.org/W2118553088","https://openalex.org/W2120115609","https://openalex.org/W2128084896","https://openalex.org/W2133869087","https://openalex.org/W2136492299","https://openalex.org/W2137983211","https://openalex.org/W2138484437","https://openalex.org/W2147347068","https://openalex.org/W2166116275","https://openalex.org/W2522160417","https://openalex.org/W2523938131","https://openalex.org/W3146803896","https://openalex.org/W3210839039","https://openalex.org/W4253271010","https://openalex.org/W6674676103","https://openalex.org/W6677134587","https://openalex.org/W6680242971","https://openalex.org/W6727579130"],"related_works":["https://openalex.org/W2152282424","https://openalex.org/W2091914113","https://openalex.org/W564324191","https://openalex.org/W2021395081","https://openalex.org/W4386033416","https://openalex.org/W2004841036","https://openalex.org/W1595492935","https://openalex.org/W1987213476","https://openalex.org/W176335707","https://openalex.org/W4245871790"],"abstract_inverted_index":{"The":[0,32,67],"three":[1],"main":[2],"classes":[3,68],"of":[4,12,34,47,69,92],"dynamic":[5,27],"artificial":[6],"neural":[7,19,29],"network":[8,30],"models":[9,37,79,112],"for":[10,53,64],"identification":[11],"nonlinear":[13,70],"dynamical":[14,71],"systems":[15,72],"are":[16,40,74,80,95],"reviewed:":[17],"(1)":[18],"state-space":[20],"models,":[21,25],"(2)":[22],"global":[23],"input-output":[24],"(3)":[26],"recurrent":[28],"models.":[31],"presentation":[33],"the":[35,87,93,98,103,129,132],"mathematical":[36],"and":[38,55,58,108,113,121],"architectures":[39],"followed":[41],"by":[42,77],"their":[43,114],"representations":[44],"in":[45,97,128,131],"terms":[46],"a":[48,118],"consistent":[49],"block":[50],"diagram":[51],"convenient":[52],"stability":[54],"performance":[56],"analyses":[57],"argued":[59],"to":[60,105,116,126],"potentially":[61],"have":[62],"benefits":[63],"process":[65],"identification.":[66],"that":[73],"universally":[75],"approximated":[76],"such":[78],"characterized,":[81],"with":[82],"rigorous":[83],"upper":[84],"bounds":[85],"on":[86],"approximation":[88],"errors.":[89],"While":[90],"many":[91],"results":[94,125],"available":[96],"literature,":[99],"this":[100],"paper":[101],"is":[102],"first":[104],"fully":[106],"develop":[107],"clearly":[109],"explain":[110],"these":[111],"interrelationships":[115],"provide":[117],"broader":[119],"perspective,":[120],"presents":[122],"some":[123],"new":[124],"fill":[127],"gaps":[130],"literature.":[133]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-07-29T14:22:42.915294","created_date":"2025-10-10T00:00:00"}