{"id":"https://openalex.org/W2734952783","doi":"https://doi.org/10.23919/acc.2017.7963839","title":"Adaptive estimation in reproducing kernel Hilbert spaces","display_name":"Adaptive estimation in reproducing kernel Hilbert spaces","publication_year":2017,"publication_date":"2017-05-01","ids":{"openalex":"https://openalex.org/W2734952783","doi":"https://doi.org/10.23919/acc.2017.7963839","mag":"2734952783"},"language":"en","primary_location":{"id":"doi:10.23919/acc.2017.7963839","is_oa":false,"landing_page_url":"https://doi.org/10.23919/acc.2017.7963839","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2017 American Control Conference (ACC)","raw_type":"proceedings-article"},"type":"article","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/A5027359912","display_name":"Parag Bobade","orcid":"https://orcid.org/0000-0001-5544-7676"},"institutions":[{"id":"https://openalex.org/I4210089311","display_name":"Yanan University Affiliated Hospital","ror":"https://ror.org/006992e45","country_code":"CN","type":"healthcare","lineage":["https://openalex.org/I4210089311"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Parag Bobade","raw_affiliation_strings":["School of Physics and Electronic Information, Yanan University, Yan'an, China","[School of Physics and Electronic Information, Yanan University, Yan'an, China]"],"affiliations":[{"raw_affiliation_string":"School of Physics and Electronic Information, Yanan University, Yan'an, China","institution_ids":["https://openalex.org/I4210089311"]},{"raw_affiliation_string":"[School of Physics and Electronic Information, Yanan University, Yan'an, China]","institution_ids":["https://openalex.org/I4210089311"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5045863884","display_name":"Suprotim Majumdar","orcid":null},"institutions":[{"id":"https://openalex.org/I4210089311","display_name":"Yanan University Affiliated Hospital","ror":"https://ror.org/006992e45","country_code":"CN","type":"healthcare","lineage":["https://openalex.org/I4210089311"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Suprotim Majumdar","raw_affiliation_strings":["School of Physics and Electronic Information, Yanan University, Yan'an, China","[School of Physics and Electronic Information, Yanan University, Yan'an, China]"],"affiliations":[{"raw_affiliation_string":"School of Physics and Electronic Information, Yanan University, Yan'an, China","institution_ids":["https://openalex.org/I4210089311"]},{"raw_affiliation_string":"[School of Physics and Electronic Information, Yanan University, Yan'an, China]","institution_ids":["https://openalex.org/I4210089311"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5001099386","display_name":"Savio Pereira","orcid":null},"institutions":[{"id":"https://openalex.org/I4210089311","display_name":"Yanan University Affiliated Hospital","ror":"https://ror.org/006992e45","country_code":"CN","type":"healthcare","lineage":["https://openalex.org/I4210089311"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Savio Pereira","raw_affiliation_strings":["School of Physics and Electronic Information, Yanan University, Yan'an, China","[School of Physics and Electronic Information, Yanan University, Yan'an, China]"],"affiliations":[{"raw_affiliation_string":"School of Physics and Electronic Information, Yanan University, Yan'an, China","institution_ids":["https://openalex.org/I4210089311"]},{"raw_affiliation_string":"[School of Physics and Electronic Information, Yanan University, Yan'an, China]","institution_ids":["https://openalex.org/I4210089311"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5023864855","display_name":"Andrew J. Kurdila","orcid":"https://orcid.org/0000-0002-9042-5146"},"institutions":[{"id":"https://openalex.org/I4210089311","display_name":"Yanan University Affiliated Hospital","ror":"https://ror.org/006992e45","country_code":"CN","type":"healthcare","lineage":["https://openalex.org/I4210089311"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Andrew J. Kurdila","raw_affiliation_strings":["School of Physics and Electronic Information, Yanan University, Yan'an, China","[School of Physics and Electronic Information, Yanan University, Yan'an, China]"],"affiliations":[{"raw_affiliation_string":"School of Physics and Electronic Information, Yanan University, Yan'an, China","institution_ids":["https://openalex.org/I4210089311"]},{"raw_affiliation_string":"[School of Physics and Electronic Information, Yanan University, Yan'an, China]","institution_ids":["https://openalex.org/I4210089311"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5021100760","display_name":"John B. Ferris","orcid":"https://orcid.org/0000-0001-7283-8214"},"institutions":[{"id":"https://openalex.org/I4210089311","display_name":"Yanan University Affiliated Hospital","ror":"https://ror.org/006992e45","country_code":"CN","type":"healthcare","lineage":["https://openalex.org/I4210089311"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"John B. Ferris","raw_affiliation_strings":["School of Physics and Electronic Information, Yanan University, Yan'an, China","[School of Physics and Electronic Information, Yanan University, Yan'an, China]"],"affiliations":[{"raw_affiliation_string":"School of Physics and Electronic Information, Yanan University, Yan'an, China","institution_ids":["https://openalex.org/I4210089311"]},{"raw_affiliation_string":"[School of Physics and Electronic Information, Yanan University, Yan'an, China]","institution_ids":["https://openalex.org/I4210089311"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5027359912"],"corresponding_institution_ids":["https://openalex.org/I4210089311"],"apc_list":null,"apc_paid":null,"fwci":1.6093,"has_fulltext":false,"cited_by_count":17,"citation_normalized_percentile":{"value":0.84270994,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":96,"max":98},"biblio":{"volume":null,"issue":null,"first_page":"5678","last_page":"5683"},"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":0.9986000061035156,"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":0.9986000061035156,"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/T11206","display_name":"Model Reduction and Neural Networks","score":0.996399998664856,"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/T11416","display_name":"Numerical methods for differential equations","score":0.9955000281333923,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"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":0.7678415179252625},{"id":"https://openalex.org/keywords/hilbert-space","display_name":"Hilbert space","score":0.5519895553588867},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5456247925758362},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5403525829315186},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5338842272758484},{"id":"https://openalex.org/keywords/kernel","display_name":"Kernel (algebra)","score":0.5111001133918762},{"id":"https://openalex.org/keywords/uniqueness","display_name":"Uniqueness","score":0.5019598007202148},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4988887310028076},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.4920808672904968},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.48923707008361816},{"id":"https://openalex.org/keywords/estimation-theory","display_name":"Estimation theory","score":0.4184921979904175},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3894615173339844},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.35243138670921326},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2798246741294861},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.2077263593673706},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.19342562556266785},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.18952873349189758}],"concepts":[{"id":"https://openalex.org/C80884492","wikidata":"https://www.wikidata.org/wiki/Q3345678","display_name":"Reproducing kernel Hilbert space","level":3,"score":0.7678415179252625},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.5519895553588867},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5456247925758362},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5403525829315186},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5338842272758484},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.5111001133918762},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.5019598007202148},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4988887310028076},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.4920808672904968},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.48923707008361816},{"id":"https://openalex.org/C167928553","wikidata":"https://www.wikidata.org/wiki/Q1376021","display_name":"Estimation theory","level":2,"score":0.4184921979904175},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3894615173339844},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.35243138670921326},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2798246741294861},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.2077263593673706},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.19342562556266785},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.18952873349189758},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"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/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.23919/acc.2017.7963839","is_oa":false,"landing_page_url":"https://doi.org/10.23919/acc.2017.7963839","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2017 American Control Conference (ACC)","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":24,"referenced_works":["https://openalex.org/W130083205","https://openalex.org/W234738007","https://openalex.org/W1486164486","https://openalex.org/W1527296550","https://openalex.org/W1559107966","https://openalex.org/W1572161815","https://openalex.org/W1978856622","https://openalex.org/W1979384859","https://openalex.org/W1982338022","https://openalex.org/W1986594128","https://openalex.org/W2006483662","https://openalex.org/W2017902642","https://openalex.org/W2045659360","https://openalex.org/W2046806116","https://openalex.org/W2059651107","https://openalex.org/W2063819119","https://openalex.org/W2064154240","https://openalex.org/W2084122929","https://openalex.org/W2117191495","https://openalex.org/W2138484437","https://openalex.org/W2154017413","https://openalex.org/W6628910748","https://openalex.org/W6654997159","https://openalex.org/W6677228271"],"related_works":["https://openalex.org/W2374023116","https://openalex.org/W4299118182","https://openalex.org/W4285290579","https://openalex.org/W1986863144","https://openalex.org/W3134083315","https://openalex.org/W2018264451","https://openalex.org/W2948180181","https://openalex.org/W2964184113","https://openalex.org/W4298112926","https://openalex.org/W2896419989"],"abstract_inverted_index":{"This":[0,135],"paper":[1,136],"introduces":[2],"a":[3,16,58,74,107,119,181],"novel":[4],"framework":[5],"for":[6,15,40,142],"the":[7,42,46,49,55,79,98,115,129,132,139,143,150,155,161,169,172,215,218],"study":[8],"of":[9,19,48,88,97,109,121,147,154,163,186,206,217],"adaptive":[10,67,102,189,204],"or":[11,208],"online":[12],"estimation":[13,68,76,103,157,190,205],"problems":[14,191],"common":[17],"class":[18],"nonlinear":[20,51,66],"systems":[21],"governed":[22],"by":[23],"ordinary":[24],"differential":[25],"equations":[26],"(ODEs)":[27],"on":[28,171,203],"\u211d":[29,82],"<sup":[30,83],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[31,84],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">d</sup>":[32,85],".":[33],"In":[34],"contrast":[35],"to":[36,168,197,213],"most":[37],"conventional":[38],"strategies":[39],"ODEs,":[41],"approach":[43],"here":[44],"embeds":[45],"estimate":[47],"unknown":[50,99,124],"function":[52,125,219],"appearing":[53],"in":[54,57,78,128,222],"plant":[56],"reproducing":[59],"kernel":[60],"Hilbert":[61],"space":[62,81],"(RKHS),":[63],"H.":[64],"The":[65,101,123,177],"problem":[69,77,104],"is":[70,118,131,211],"then":[71],"cast":[72],"as":[73],"time-varying":[75],"product":[80],"\u00d7":[86],"H":[87],"finite":[89,164],"dimensional":[90,95,165,174],"state":[91,156,175],"estimates":[92,96,220],"and":[93,145,152,159,183],"infinite":[94,173],"function.":[100],"thereby":[105],"constitutes":[106],"type":[108],"distributed":[110,133],"parameter":[111],"system,":[112],"even":[113],"though":[114],"original":[116],"system":[117],"collection":[120],"ODEs.":[122],"that":[126,194],"lies":[127],"RKHS":[130],"parameter.":[134],"derives":[137],"(1)":[138],"sufficient":[140],"conditions":[141],"existence":[144],"uniqueness":[146],"solutions,":[148],"(2)":[149],"stability":[151],"convergence":[153,162,216],"error,":[158],"(3)":[160],"approximate":[166],"solutions":[167],"solution":[170],"space.":[176],"new":[178],"formulation":[179],"provides":[180],"succinct":[182],"direct":[184],"way":[185],"rigorously":[187],"posing":[188],"using":[192],"bases":[193],"are":[195],"amenable":[196],"scattered":[198],"approximation.":[199],"A":[200],"numerical":[201],"example":[202],"road":[207],"terrain":[209],"maps":[210],"presented":[212],"illustrate":[214],"derived":[221],"this":[223],"paper.":[224]},"counts_by_year":[{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":5},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}