{"id":"https://openalex.org/W2018042408","doi":"https://doi.org/10.1109/tac.2015.2423912","title":"Asymmetric Volterra Models Based on Ladder-Structured Generalized Orthonormal Basis Functions","display_name":"Asymmetric Volterra Models Based on Ladder-Structured Generalized Orthonormal Basis Functions","publication_year":2015,"publication_date":"2015-04-17","ids":{"openalex":"https://openalex.org/W2018042408","doi":"https://doi.org/10.1109/tac.2015.2423912","mag":"2018042408"},"language":"en","primary_location":{"id":"doi:10.1109/tac.2015.2423912","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2015.2423912","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"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 Automatic Control","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"http://dx.doi.org/10.1109/TAC.2015.2423912","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5047947883","display_name":"Jeremias Barbosa Machado","orcid":"https://orcid.org/0009-0001-6986-8751"},"institutions":[{"id":"https://openalex.org/I8165072","display_name":"Universidade Federal de Itajub\u00e1","ror":"https://ror.org/00235nr42","country_code":"BR","type":"education","lineage":["https://openalex.org/I8165072"]}],"countries":["BR"],"is_corresponding":true,"raw_author_name":"Jeremias B. Machado","raw_affiliation_strings":["Institute of System Engineering and Technology of Information, Federal University of Itajuba (UNIFEI), Itajub\u00e1-MG, Brazil","Inst. of Syst. Eng. & Technol. of Inf., Fed. Univ. of Itajuba (UNIFEI), Itajuba, Brazil"],"affiliations":[{"raw_affiliation_string":"Institute of System Engineering and Technology of Information, Federal University of Itajuba (UNIFEI), Itajub\u00e1-MG, Brazil","institution_ids":["https://openalex.org/I8165072"]},{"raw_affiliation_string":"Inst. of Syst. Eng. & Technol. of Inf., Fed. Univ. of Itajuba (UNIFEI), Itajuba, Brazil","institution_ids":["https://openalex.org/I8165072"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5111530335","display_name":"Ricardo J.G.B. Campello","orcid":null},"institutions":[{"id":"https://openalex.org/I17974374","display_name":"Universidade de S\u00e3o Paulo","ror":"https://ror.org/036rp1748","country_code":"BR","type":"education","lineage":["https://openalex.org/I17974374"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Ricardo J. G. B. Campello","raw_affiliation_strings":["Institute of Mathematics and Computer Sciences, University of S\u00e3o Paulo (USP), S\u00e3o Carlos-SP, Brazil","Inst. of Math. & Comput. Sci., Univ. of Sao Paulo (USP), Sao Carlos, Brazil"],"affiliations":[{"raw_affiliation_string":"Institute of Mathematics and Computer Sciences, University of S\u00e3o Paulo (USP), S\u00e3o Carlos-SP, Brazil","institution_ids":["https://openalex.org/I17974374"]},{"raw_affiliation_string":"Inst. of Math. & Comput. Sci., Univ. of Sao Paulo (USP), Sao Carlos, Brazil","institution_ids":["https://openalex.org/I17974374"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5112428259","display_name":"W.C. Amaral","orcid":null},"institutions":[{"id":"https://openalex.org/I181391015","display_name":"Universidade Estadual de Campinas (UNICAMP)","ror":"https://ror.org/04wffgt70","country_code":"BR","type":"education","lineage":["https://openalex.org/I181391015"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Wagner C. Amaral","raw_affiliation_strings":["School of Electrical and Computer Engineering, University of Campinas (UNICAMP), Campinas-SP, Brazil","Sch. of Electr. & Comput. Eng., Univ. of Campinas UNICAMP, Campinas, Brazil"],"affiliations":[{"raw_affiliation_string":"School of Electrical and Computer Engineering, University of Campinas (UNICAMP), Campinas-SP, Brazil","institution_ids":["https://openalex.org/I181391015"]},{"raw_affiliation_string":"Sch. of Electr. & Comput. Eng., Univ. of Campinas UNICAMP, Campinas, Brazil","institution_ids":["https://openalex.org/I181391015"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5047947883"],"corresponding_institution_ids":["https://openalex.org/I8165072"],"apc_list":null,"apc_paid":null,"fwci":0.3403,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.6466024,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"60","issue":"11","first_page":"2879","last_page":"2891"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11236","display_name":"Control Systems and Identification","score":0.9998000264167786,"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/T11236","display_name":"Control Systems and Identification","score":0.9998000264167786,"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/T10534","display_name":"Structural Health Monitoring Techniques","score":0.995199978351593,"subfield":{"id":"https://openalex.org/subfields/2205","display_name":"Civil and Structural 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/T11372","display_name":"Hydraulic and Pneumatic Systems","score":0.9904000163078308,"subfield":{"id":"https://openalex.org/subfields/2210","display_name":"Mechanical 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/orthonormal-basis","display_name":"Orthonormal basis","score":0.899715006351471},{"id":"https://openalex.org/keywords/parameterized-complexity","display_name":"Parameterized complexity","score":0.6682299971580505},{"id":"https://openalex.org/keywords/basis-function","display_name":"Basis function","score":0.6371029019355774},{"id":"https://openalex.org/keywords/basis","display_name":"Basis (linear algebra)","score":0.6295181512832642},{"id":"https://openalex.org/keywords/kernel","display_name":"Kernel (algebra)","score":0.6278036832809448},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.5903353095054626},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5857133865356445},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5501081943511963},{"id":"https://openalex.org/keywords/orthogonal-functions","display_name":"Orthogonal functions","score":0.545368492603302},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5393147468566895},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.448309987783432},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4325462579727173},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.35622620582580566},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3196471333503723},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.17609941959381104},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.12484085559844971},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.1034063994884491}],"concepts":[{"id":"https://openalex.org/C5806529","wikidata":"https://www.wikidata.org/wiki/Q2365325","display_name":"Orthonormal basis","level":2,"score":0.899715006351471},{"id":"https://openalex.org/C165464430","wikidata":"https://www.wikidata.org/wiki/Q1570441","display_name":"Parameterized complexity","level":2,"score":0.6682299971580505},{"id":"https://openalex.org/C5917680","wikidata":"https://www.wikidata.org/wiki/Q2621825","display_name":"Basis function","level":2,"score":0.6371029019355774},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.6295181512832642},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.6278036832809448},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.5903353095054626},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5857133865356445},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5501081943511963},{"id":"https://openalex.org/C135925592","wikidata":"https://www.wikidata.org/wiki/Q2637908","display_name":"Orthogonal functions","level":2,"score":0.545368492603302},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5393147468566895},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.448309987783432},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4325462579727173},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.35622620582580566},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3196471333503723},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.17609941959381104},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.12484085559844971},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.1034063994884491},{"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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","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},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1109/tac.2015.2423912","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2015.2423912","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"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 Automatic Control","raw_type":"journal-article"},{"id":"pmh:oai:www.producao.usp.br:BDPI/50763","is_oa":false,"landing_page_url":"http://www.producao.usp.br/handle/BDPI/50763","pdf_url":null,"source":{"id":"https://openalex.org/S4306401373","display_name":"Scientific Electronic Library Online (S\u00e3o Paulo Research Foundation, Latin American and Caribbean Center on Health Sciences Information, Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2982035970","host_organization_name":"Costa Rican Department of Social Security","host_organization_lineage":["https://openalex.org/I2982035970"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"","raw_type":"article"},{"id":"pmh:002699469","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1109/TAC.2015.2423912","pdf_url":null,"source":{"id":"https://openalex.org/S4306402641","display_name":"LA Referencia (Red Federada de Repositorios Institucionales de Publicaciones Cient\u00edficas)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4383465926","host_organization_name":"LA Referencia","host_organization_lineage":["https://openalex.org/I4383465926"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"reponame:Reposit\u00f3rio Institucional da USP (Biblioteca Digital da Produ\u00e7\u00e3o Intelectual)","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:www.producao.usp.br:BDPI/49829","is_oa":false,"landing_page_url":"http://www.producao.usp.br/handle/BDPI/49829","pdf_url":null,"source":{"id":"https://openalex.org/S4306401373","display_name":"Scientific Electronic Library Online (S\u00e3o Paulo Research Foundation, Latin American and Caribbean Center on Health Sciences Information, Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2982035970","host_organization_name":"Costa Rican Department of Social Security","host_organization_lineage":["https://openalex.org/I2982035970"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"article"}],"best_oa_location":{"id":"pmh:002699469","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1109/TAC.2015.2423912","pdf_url":null,"source":{"id":"https://openalex.org/S4306402641","display_name":"LA Referencia (Red Federada de Repositorios Institucionales de Publicaciones Cient\u00edficas)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4383465926","host_organization_name":"LA Referencia","host_organization_lineage":["https://openalex.org/I4383465926"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"reponame:Reposit\u00f3rio Institucional da USP (Biblioteca Digital da Produ\u00e7\u00e3o Intelectual)","raw_type":"info:eu-repo/semantics/publishedVersion"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":42,"referenced_works":["https://openalex.org/W565862821","https://openalex.org/W567972298","https://openalex.org/W616910851","https://openalex.org/W641543390","https://openalex.org/W1490488263","https://openalex.org/W1597839575","https://openalex.org/W1898259317","https://openalex.org/W1971450333","https://openalex.org/W1981116189","https://openalex.org/W1991777572","https://openalex.org/W2002261071","https://openalex.org/W2028702048","https://openalex.org/W2031578473","https://openalex.org/W2037950596","https://openalex.org/W2054106012","https://openalex.org/W2055337535","https://openalex.org/W2065537360","https://openalex.org/W2080138696","https://openalex.org/W2093846413","https://openalex.org/W2095753402","https://openalex.org/W2115844704","https://openalex.org/W2119043701","https://openalex.org/W2124320708","https://openalex.org/W2128526375","https://openalex.org/W2140834769","https://openalex.org/W2146109515","https://openalex.org/W2158290540","https://openalex.org/W2160068178","https://openalex.org/W2163105287","https://openalex.org/W2167043468","https://openalex.org/W2326753286","https://openalex.org/W2501068758","https://openalex.org/W2615406886","https://openalex.org/W2885672338","https://openalex.org/W3020882730","https://openalex.org/W4211171019","https://openalex.org/W4235848843","https://openalex.org/W4242386574","https://openalex.org/W4247834132","https://openalex.org/W6701328621","https://openalex.org/W6738136826","https://openalex.org/W6753944201"],"related_works":["https://openalex.org/W1547339931","https://openalex.org/W1976397437","https://openalex.org/W2619281917","https://openalex.org/W2096954214","https://openalex.org/W2081762384","https://openalex.org/W2163105287","https://openalex.org/W2036563345","https://openalex.org/W3183088836","https://openalex.org/W2158290540","https://openalex.org/W4323644128"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"an":[3,30,95,154,174],"improved":[4],"method":[5,22],"to":[6,133,159,162,187,194],"construct":[7],"and":[8,113,168],"estimate":[9],"Volterra":[10,41],"models":[11,42],"using":[12],"Generalized":[13],"Orthonormal":[14],"Basis":[15],"Functions":[16],"(GOBF)":[17],"is":[18,61,74,92,118,126],"presented.":[19,47],"The":[20,48,150],"proposed":[21,49,200],"extends":[23],"results":[24],"obtained":[25],"in":[26,53,63],"previous":[27],"works,":[28],"where":[29],"exact":[31,151,170],"technique":[32],"for":[33,39,101,173],"optimizing":[34],"the":[35,58,72,103,107,115,139,160,184,196,199],"GOBF":[36,123,140],"parameters":[37,132,145,161],"(poles)":[38],"symmetric":[40],"of":[43,71,79,90,98,106,137,153,198],"any":[44],"order":[45],"was":[46],"extensions":[50],"take":[51],"place":[52],"two":[54],"different":[55],"ways:":[56],"(i)":[57],"new":[59,116],"formulation":[60,117],"derived":[62],"such":[64],"a":[65,77,85,110,121],"way":[66],"that":[67,125,177],"each":[68,89],"multidimensional":[69],"kernel":[70,108],"model":[73],"decomposed":[75],"into":[76],"set":[78,97],"independent":[80],"orthonormal":[81],"bases":[82],"(rather":[83],"than":[84],"single,":[86],"common":[87],"basis),":[88],"which":[91],"parameterized":[93],"by":[94,128,143],"individual":[96],"poles":[99,141],"responsible":[100],"representing":[102],"dominant":[104],"dynamic":[105,185],"along":[109],"particular":[111],"dimension;":[112],"(ii)":[114],"based":[119],"on":[120],"ladder-structured":[122],"architecture":[124],"characterized":[127],"having":[129],"only":[130,179],"real-valued":[131],"be":[134,163,188],"estimated,":[135],"regardless":[136],"whether":[138],"encoded":[142],"these":[144],"are":[146,165,192],"real-":[147],"or":[148],"complex-valued.":[149],"gradients":[152],"error":[155],"functional":[156],"with":[157],"respect":[158],"optimized":[164],"computed":[166],"analytically":[167],"provide":[169],"search":[171],"directions":[172],"optimization":[175],"process":[176],"uses":[178],"input-output":[180],"data":[181],"measured":[182],"from":[183],"system":[186],"modeled.":[189],"Computational":[190],"experiments":[191],"presented":[193],"illustrate":[195],"benefits":[197],"approach":[201],"when":[202],"modeling":[203],"nonlinear":[204],"systems.":[205]},"counts_by_year":[{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":1}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2016-06-24T00:00:00"}