{"id":"https://openalex.org/W4206519638","doi":"https://doi.org/10.1109/tac.2021.3138701","title":"Tracking Control for Nonlinear Nonparametric Systems Based on the Stochastic Approximation Algorithm","display_name":"Tracking Control for Nonlinear Nonparametric Systems Based on the Stochastic Approximation Algorithm","publication_year":2021,"publication_date":"2021-12-28","ids":{"openalex":"https://openalex.org/W4206519638","doi":"https://doi.org/10.1109/tac.2021.3138701"},"language":"en","primary_location":{"id":"doi:10.1109/tac.2021.3138701","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2021.3138701","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":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5103122662","display_name":"Wenhui Feng","orcid":"https://orcid.org/0000-0002-0839-7861"},"institutions":[{"id":"https://openalex.org/I90090648","display_name":"Shijiazhuang Tiedao University","ror":"https://ror.org/022e9e065","country_code":"CN","type":"education","lineage":["https://openalex.org/I90090648"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Wenhui Feng","raw_affiliation_strings":["Department of Mathematics and Physics, Shijiazhuang Tiedao University, Shijiazhuang, China"],"raw_orcid":"https://orcid.org/0000-0002-0839-7861","affiliations":[{"raw_affiliation_string":"Department of Mathematics and Physics, Shijiazhuang Tiedao University, Shijiazhuang, China","institution_ids":["https://openalex.org/I90090648"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5102007532","display_name":"Shixin Zhao","orcid":"https://orcid.org/0000-0001-8889-4771"},"institutions":[{"id":"https://openalex.org/I90090648","display_name":"Shijiazhuang Tiedao University","ror":"https://ror.org/022e9e065","country_code":"CN","type":"education","lineage":["https://openalex.org/I90090648"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Shixin Zhao","raw_affiliation_strings":["Department of Mathematics and Physics, Shijiazhuang Tiedao University, Shijiazhuang, China"],"raw_orcid":"https://orcid.org/0000-0001-8889-4771","affiliations":[{"raw_affiliation_string":"Department of Mathematics and Physics, Shijiazhuang Tiedao University, Shijiazhuang, China","institution_ids":["https://openalex.org/I90090648"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I90090648"],"apc_list":null,"apc_paid":null,"fwci":0.2707,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.56676563,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"68","issue":"1","first_page":"230","last_page":"241"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10791","display_name":"Advanced Control Systems Optimization","score":0.9968000054359436,"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/T10791","display_name":"Advanced Control Systems Optimization","score":0.9968000054359436,"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/T10067","display_name":"Stochastic processes and financial applications","score":0.9857000112533569,"subfield":{"id":"https://openalex.org/subfields/2003","display_name":"Finance"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T11236","display_name":"Control Systems and Identification","score":0.984499990940094,"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/truncation","display_name":"Truncation (statistics)","score":0.6437786221504211},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6333185434341431},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5716893076896667},{"id":"https://openalex.org/keywords/nonparametric-statistics","display_name":"Nonparametric statistics","score":0.5494248270988464},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.5093156099319458},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.5029005408287048},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.49901795387268066},{"id":"https://openalex.org/keywords/tracking","display_name":"Tracking (education)","score":0.45046350359916687},{"id":"https://openalex.org/keywords/stochastic-approximation","display_name":"Stochastic approximation","score":0.43517613410949707},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.42530637979507446},{"id":"https://openalex.org/keywords/noise","display_name":"Noise (video)","score":0.41642627120018005},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.41293489933013916},{"id":"https://openalex.org/keywords/stochastic-process","display_name":"Stochastic process","score":0.4108502268791199},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4030468165874481},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4028772711753845},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2975819706916809},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.17563676834106445},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.10220244526863098},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.06713956594467163},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.06380927562713623}],"concepts":[{"id":"https://openalex.org/C106195933","wikidata":"https://www.wikidata.org/wiki/Q7847935","display_name":"Truncation (statistics)","level":2,"score":0.6437786221504211},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6333185434341431},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5716893076896667},{"id":"https://openalex.org/C102366305","wikidata":"https://www.wikidata.org/wiki/Q1097688","display_name":"Nonparametric statistics","level":2,"score":0.5494248270988464},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5093156099319458},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.5029005408287048},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.49901795387268066},{"id":"https://openalex.org/C2775936607","wikidata":"https://www.wikidata.org/wiki/Q466845","display_name":"Tracking (education)","level":2,"score":0.45046350359916687},{"id":"https://openalex.org/C55479107","wikidata":"https://www.wikidata.org/wiki/Q97663916","display_name":"Stochastic approximation","level":3,"score":0.43517613410949707},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.42530637979507446},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.41642627120018005},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.41293489933013916},{"id":"https://openalex.org/C8272713","wikidata":"https://www.wikidata.org/wiki/Q176737","display_name":"Stochastic process","level":2,"score":0.4108502268791199},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4030468165874481},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4028772711753845},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2975819706916809},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.17563676834106445},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.10220244526863098},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.06713956594467163},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.06380927562713623},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"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/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.0},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","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},{"id":"https://openalex.org/C19417346","wikidata":"https://www.wikidata.org/wiki/Q7922","display_name":"Pedagogy","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/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.0},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","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/tac.2021.3138701","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2021.3138701","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1503720616","display_name":null,"funder_award_id":"QN2021133","funder_id":"https://openalex.org/F4320321949","funder_display_name":"Department of Education of Hebei Province"}],"funders":[{"id":"https://openalex.org/F4320321949","display_name":"Department of Education of Hebei Province","ror":"https://ror.org/01jkyjd96"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":25,"referenced_works":["https://openalex.org/W103934657","https://openalex.org/W584080168","https://openalex.org/W1498711961","https://openalex.org/W1981220283","https://openalex.org/W1994616650","https://openalex.org/W2009797711","https://openalex.org/W2030054607","https://openalex.org/W2065699608","https://openalex.org/W2066406546","https://openalex.org/W2108641449","https://openalex.org/W2127510298","https://openalex.org/W2157395874","https://openalex.org/W2162725061","https://openalex.org/W2165628062","https://openalex.org/W2166667156","https://openalex.org/W2235056388","https://openalex.org/W2897048230","https://openalex.org/W2954033048","https://openalex.org/W2964337808","https://openalex.org/W3084696483","https://openalex.org/W3100387237","https://openalex.org/W4237649808","https://openalex.org/W4243772471","https://openalex.org/W4254127125","https://openalex.org/W4302033506"],"related_works":["https://openalex.org/W4243114048","https://openalex.org/W4237896776","https://openalex.org/W4231665652","https://openalex.org/W2735486534","https://openalex.org/W2949597507","https://openalex.org/W2156326090","https://openalex.org/W2150901859","https://openalex.org/W84146095","https://openalex.org/W2119298659","https://openalex.org/W2963001040"],"abstract_inverted_index":{"In":[0],"this":[1,116],"article,":[2],"we":[3],"study":[4],"the":[5,47,50,67,71,80,90,119],"tracking":[6,92,95],"control":[7,39,42,75],"problem":[8],"for":[9,99],"nonlinear":[10],"nonparametric":[11],"systems,":[12],"and":[13,32,57,77],"additive":[14],"random":[15],"observation":[16],"noise":[17],"is":[18,26,44,59,63,96],"also":[19],"taken":[20],"into":[21],"account.":[22],"The":[23,41],"dynamical":[24,72],"function":[25,73],"allowed":[27],"to":[28,84],"be":[29,85,108],"time":[30],"varying":[31],"possess":[33],"an":[34],"arbitrary":[35],"growth":[36,68],"rate":[37,69],"at":[38,74],"input.":[40],"algorithm":[43,53],"designed":[45],"on":[46],"basis":[48],"of":[49,70,79,102],"stochastic":[51],"approximation":[52],"with":[54],"expanding":[55],"truncations,":[56],"it":[58],"found":[60],"that":[61,78,89],"there":[62],"a":[64,100],"tradeoff":[65],"between":[66],"input":[76],"truncation":[81],"bound":[82],"sequence":[83],"chosen.":[86],"We":[87],"prove":[88],"average":[91],"or":[93],"strong":[94],"asymptotically":[97],"achieved":[98],"class":[101],"reference":[103],"state":[104],"sequences,":[105],"which":[106],"can":[107],"strongly":[109],"averaged.":[110],"Finally,":[111],"numerical":[112],"simulations":[113],"given":[114],"in":[115],"article":[117],"justify":[118],"theoretical":[120],"assertions.":[121]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}