{"id":"https://openalex.org/W1601719319","doi":"https://doi.org/10.1109/acc.2015.7170899","title":"State following (StaF) kernel functions for function approximation Part I: Theory and motivation","display_name":"State following (StaF) kernel functions for function approximation Part I: Theory and motivation","publication_year":2015,"publication_date":"2015-07-01","ids":{"openalex":"https://openalex.org/W1601719319","doi":"https://doi.org/10.1109/acc.2015.7170899","mag":"1601719319"},"language":"en","primary_location":{"id":"doi:10.1109/acc.2015.7170899","is_oa":false,"landing_page_url":"https://doi.org/10.1109/acc.2015.7170899","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2015 American Control Conference (ACC)","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/A5058488295","display_name":"Joel A. Rosenfeld","orcid":"https://orcid.org/0000-0003-3219-448X"},"institutions":[{"id":"https://openalex.org/I33213144","display_name":"University of Florida","ror":"https://ror.org/02y3ad647","country_code":"US","type":"education","lineage":["https://openalex.org/I33213144"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Joel A. Rosenfeld","raw_affiliation_strings":["Department of Mechanical and Aerospace Engineering, University of Florida, Gainesville, FL, USA","Department of Mechanical & Aerospace Engineering, University of Florida, Gainesville, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mechanical and Aerospace Engineering, University of Florida, Gainesville, FL, USA","institution_ids":["https://openalex.org/I33213144"]},{"raw_affiliation_string":"Department of Mechanical & Aerospace Engineering, University of Florida, Gainesville, USA","institution_ids":["https://openalex.org/I33213144"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5071224574","display_name":"Rushikesh Kamalapurkar","orcid":"https://orcid.org/0000-0001-9963-5361"},"institutions":[{"id":"https://openalex.org/I33213144","display_name":"University of Florida","ror":"https://ror.org/02y3ad647","country_code":"US","type":"education","lineage":["https://openalex.org/I33213144"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Rushikesh Kamalapurkar","raw_affiliation_strings":["Department of Mechanical and Aerospace Engineering, University of Florida, Gainesville, FL, USA","Department of Mechanical & Aerospace Engineering, University of Florida, Gainesville, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mechanical and Aerospace Engineering, University of Florida, Gainesville, FL, USA","institution_ids":["https://openalex.org/I33213144"]},{"raw_affiliation_string":"Department of Mechanical & Aerospace Engineering, University of Florida, Gainesville, USA","institution_ids":["https://openalex.org/I33213144"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5032651215","display_name":"Warren E. Dixon","orcid":"https://orcid.org/0000-0002-5091-181X"},"institutions":[{"id":"https://openalex.org/I33213144","display_name":"University of Florida","ror":"https://ror.org/02y3ad647","country_code":"US","type":"education","lineage":["https://openalex.org/I33213144"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Warren E. Dixon","raw_affiliation_strings":["Department of Mechanical and Aerospace Engineering, University of Florida, Gainesville, FL, USA","Department of Mechanical & Aerospace Engineering, University of Florida, Gainesville, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mechanical and Aerospace Engineering, University of Florida, Gainesville, FL, USA","institution_ids":["https://openalex.org/I33213144"]},{"raw_affiliation_string":"Department of Mechanical & Aerospace Engineering, University of Florida, Gainesville, USA","institution_ids":["https://openalex.org/I33213144"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I33213144"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":12,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"1217","last_page":"1222"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12794","display_name":"Adaptive Dynamic Programming Control","score":0.9997000098228455,"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"}},"topics":[{"id":"https://openalex.org/T12794","display_name":"Adaptive Dynamic Programming Control","score":0.9997000098228455,"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"}},{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9940000176429749,"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":0.9911999702453613,"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/reproducing-kernel-hilbert-space","display_name":"Reproducing kernel Hilbert space","score":0.7465064525604248},{"id":"https://openalex.org/keywords/kernel","display_name":"Kernel (algebra)","score":0.6833881139755249},{"id":"https://openalex.org/keywords/function-approximation","display_name":"Function approximation","score":0.6541209816932678},{"id":"https://openalex.org/keywords/hilbert-space","display_name":"Hilbert space","score":0.60329270362854},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.5646698474884033},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5571891665458679},{"id":"https://openalex.org/keywords/approximation-theory","display_name":"Approximation theory","score":0.5545613765716553},{"id":"https://openalex.org/keywords/euclidean-geometry","display_name":"Euclidean geometry","score":0.5388900637626648},{"id":"https://openalex.org/keywords/compact-space","display_name":"Compact space","score":0.5282905101776123},{"id":"https://openalex.org/keywords/state","display_name":"State (computer science)","score":0.5219606757164001},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.48867562413215637},{"id":"https://openalex.org/keywords/representer-theorem","display_name":"Representer theorem","score":0.4724994897842407},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.46822282671928406},{"id":"https://openalex.org/keywords/approximation-algorithm","display_name":"Approximation algorithm","score":0.43455949425697327},{"id":"https://openalex.org/keywords/euclidean-space","display_name":"Euclidean space","score":0.42976051568984985},{"id":"https://openalex.org/keywords/stochastic-gradient-descent","display_name":"Stochastic gradient descent","score":0.4121052026748657},{"id":"https://openalex.org/keywords/minimax-approximation-algorithm","display_name":"Minimax approximation algorithm","score":0.4119693338871002},{"id":"https://openalex.org/keywords/kernel-method","display_name":"Kernel method","score":0.3823027014732361},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.37877750396728516},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.30522024631500244},{"id":"https://openalex.org/keywords/kernel-embedding-of-distributions","display_name":"Kernel embedding of distributions","score":0.27647700905799866},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2672901153564453},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.2573777437210083},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.17010954022407532},{"id":"https://openalex.org/keywords/support-vector-machine","display_name":"Support vector machine","score":0.1442764401435852},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.06616249680519104},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.06122145056724548}],"concepts":[{"id":"https://openalex.org/C80884492","wikidata":"https://www.wikidata.org/wiki/Q3345678","display_name":"Reproducing kernel Hilbert space","level":3,"score":0.7465064525604248},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.6833881139755249},{"id":"https://openalex.org/C91873725","wikidata":"https://www.wikidata.org/wiki/Q3445816","display_name":"Function approximation","level":3,"score":0.6541209816932678},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.60329270362854},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5646698474884033},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5571891665458679},{"id":"https://openalex.org/C145242015","wikidata":"https://www.wikidata.org/wiki/Q774123","display_name":"Approximation theory","level":2,"score":0.5545613765716553},{"id":"https://openalex.org/C129782007","wikidata":"https://www.wikidata.org/wiki/Q162886","display_name":"Euclidean geometry","level":2,"score":0.5388900637626648},{"id":"https://openalex.org/C18648836","wikidata":"https://www.wikidata.org/wiki/Q381892","display_name":"Compact space","level":2,"score":0.5282905101776123},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.5219606757164001},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.48867562413215637},{"id":"https://openalex.org/C172623408","wikidata":"https://www.wikidata.org/wiki/Q7314263","display_name":"Representer theorem","level":5,"score":0.4724994897842407},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.46822282671928406},{"id":"https://openalex.org/C148764684","wikidata":"https://www.wikidata.org/wiki/Q621751","display_name":"Approximation algorithm","level":2,"score":0.43455949425697327},{"id":"https://openalex.org/C186450821","wikidata":"https://www.wikidata.org/wiki/Q17295","display_name":"Euclidean space","level":2,"score":0.42976051568984985},{"id":"https://openalex.org/C206688291","wikidata":"https://www.wikidata.org/wiki/Q7617819","display_name":"Stochastic gradient descent","level":3,"score":0.4121052026748657},{"id":"https://openalex.org/C117148685","wikidata":"https://www.wikidata.org/wiki/Q6865376","display_name":"Minimax approximation algorithm","level":2,"score":0.4119693338871002},{"id":"https://openalex.org/C122280245","wikidata":"https://www.wikidata.org/wiki/Q620622","display_name":"Kernel method","level":3,"score":0.3823027014732361},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.37877750396728516},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.30522024631500244},{"id":"https://openalex.org/C134517425","wikidata":"https://www.wikidata.org/wiki/Q16000131","display_name":"Kernel embedding of distributions","level":4,"score":0.27647700905799866},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2672901153564453},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2573777437210083},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.17010954022407532},{"id":"https://openalex.org/C12267149","wikidata":"https://www.wikidata.org/wiki/Q282453","display_name":"Support vector machine","level":2,"score":0.1442764401435852},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.06616249680519104},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.06122145056724548},{"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/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/acc.2015.7170899","is_oa":false,"landing_page_url":"https://doi.org/10.1109/acc.2015.7170899","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2015 American Control Conference (ACC)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Sustainable cities and communities","id":"https://metadata.un.org/sdg/11","score":0.5}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W90602582","https://openalex.org/W130083205","https://openalex.org/W1486526736","https://openalex.org/W1572161815","https://openalex.org/W1698155719","https://openalex.org/W1749408314","https://openalex.org/W1983523797","https://openalex.org/W1986280275","https://openalex.org/W2067603665","https://openalex.org/W2085194340","https://openalex.org/W2090167557","https://openalex.org/W2098219423","https://openalex.org/W2104843094","https://openalex.org/W2113442785","https://openalex.org/W2113483277","https://openalex.org/W2798766386","https://openalex.org/W2913243980","https://openalex.org/W2963273254","https://openalex.org/W3135109640","https://openalex.org/W4254313632","https://openalex.org/W4256522009","https://openalex.org/W6758804334"],"related_works":["https://openalex.org/W1994655188","https://openalex.org/W2392804273","https://openalex.org/W2087686193","https://openalex.org/W2737349826","https://openalex.org/W2156766998","https://openalex.org/W2272385214","https://openalex.org/W2064547980","https://openalex.org/W2123358778","https://openalex.org/W2167394514","https://openalex.org/W4387422913"],"abstract_inverted_index":{"Unlike":[0],"traditional":[1],"methods":[2],"that":[3,23,36,61,115],"aim":[4],"to":[5,25,84],"approximate":[6,26],"a":[7,10,14,27,30,34,39,89,93,105,109,121],"function":[8,15,28,110],"over":[9,52],"large":[11,94],"compact":[12,40,95],"set,":[13],"approximation":[16,87,107],"method":[17],"is":[18,44,102,118],"developed":[19],"in":[20,29],"this":[21,66],"paper":[22],"aims":[24],"small":[31],"neighborhood":[32],"of":[33,65,77,108],"state":[35,67,90],"travels":[37],"within":[38],"set.":[41,96],"The":[42],"development":[43,64],"based":[45],"on":[46],"universal":[47],"reproducing":[48],"kernel":[49,79],"Hilbert":[50],"spaces":[51],"the":[53,63,116],"n-dimensional":[54],"Euclidean":[55],"space.":[56],"Three":[57],"theorems":[58],"are":[59],"introduced":[60],"support":[62],"following":[68],"(StaF)":[69],"method.":[70],"In":[71],"particular":[72],"an":[73],"explicit":[74],"uniform":[75],"number":[76],"StaF":[78],"functions":[80],"can":[81,111],"be":[82,112],"calculated":[83],"ensure":[85],"good":[86,106],"as":[88],"moves":[91],"through":[92],"An":[97],"algorithm":[98,117],"for":[99],"gradient":[100],"descent":[101],"demonstrated":[103],"where":[104],"achieved":[113],"provided":[114],"applied":[119],"with":[120],"high":[122],"enough":[123],"frequency.":[124]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":4},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1}],"updated_date":"2026-07-14T23:27:15.235271","created_date":"2025-10-10T00:00:00"}
