{"id":"https://openalex.org/W2014750778","doi":"https://doi.org/10.1109/acc.2010.5530487","title":"Stochastic averaging in continuous time and its applications to extremum seeking","display_name":"Stochastic averaging in continuous time and its applications to extremum seeking","publication_year":2010,"publication_date":"2010-06-01","ids":{"openalex":"https://openalex.org/W2014750778","doi":"https://doi.org/10.1109/acc.2010.5530487","mag":"2014750778"},"language":"en","primary_location":{"id":"doi:10.1109/acc.2010.5530487","is_oa":false,"landing_page_url":"https://doi.org/10.1109/acc.2010.5530487","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2010 American Control Conference","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/A5100726822","display_name":"Shu\u2010Jun Liu","orcid":"https://orcid.org/0000-0002-6004-9733"},"institutions":[{"id":"https://openalex.org/I36258959","display_name":"University of California San Diego","ror":"https://ror.org/0168r3w48","country_code":"US","type":"education","lineage":["https://openalex.org/I36258959"]},{"id":"https://openalex.org/I76569877","display_name":"Southeast University","ror":"https://ror.org/04ct4d772","country_code":"CN","type":"education","lineage":["https://openalex.org/I76569877"]}],"countries":["CN","US"],"is_corresponding":false,"raw_author_name":"Shu-Jun Liu","raw_affiliation_strings":["Department of Mathematics, South-East University, Nanjing, China","University of California, San Diego, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, South-East University, Nanjing, China","institution_ids":["https://openalex.org/I76569877"]},{"raw_affiliation_string":"University of California, San Diego, USA","institution_ids":["https://openalex.org/I36258959"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5018293076","display_name":"Miroslav Krsti\u0107","orcid":"https://orcid.org/0000-0002-5523-941X"},"institutions":[{"id":"https://openalex.org/I36258959","display_name":"University of California San Diego","ror":"https://ror.org/0168r3w48","country_code":"US","type":"education","lineage":["https://openalex.org/I36258959"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"M Krstic","raw_affiliation_strings":["Department of Mechanical and Aerospace Engineering, University of California, San Diego, CA, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mechanical and Aerospace Engineering, University of California, San Diego, CA, USA","institution_ids":["https://openalex.org/I36258959"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.8314,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.83038275,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":null,"issue":null,"first_page":"172","last_page":"177"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T14083","display_name":"Extremum Seeking Control Systems","score":0.9998999834060669,"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/T14083","display_name":"Extremum Seeking Control Systems","score":0.9998999834060669,"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/T10791","display_name":"Advanced Control Systems Optimization","score":0.9336000084877014,"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/T10553","display_name":"Combustion and flame dynamics","score":0.9125999808311462,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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/nonlinear-system","display_name":"Nonlinear system","score":0.6732269525527954},{"id":"https://openalex.org/keywords/stochastic-process","display_name":"Stochastic process","score":0.5886009335517883},{"id":"https://openalex.org/keywords/lipschitz-continuity","display_name":"Lipschitz continuity","score":0.5544405579566956},{"id":"https://openalex.org/keywords/exponential-stability","display_name":"Exponential stability","score":0.5262845158576965},{"id":"https://openalex.org/keywords/perturbation","display_name":"Perturbation (astronomy)","score":0.5192568302154541},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5138747692108154},{"id":"https://openalex.org/keywords/continuous-time-stochastic-process","display_name":"Continuous-time stochastic process","score":0.5005745887756348},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.4744775593280792},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.4525725543498993},{"id":"https://openalex.org/keywords/stochastic-optimization","display_name":"Stochastic optimization","score":0.44597721099853516},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.42458418011665344},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.414081871509552},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3430865406990051},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.12541022896766663},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.06540030241012573}],"concepts":[{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6732269525527954},{"id":"https://openalex.org/C8272713","wikidata":"https://www.wikidata.org/wiki/Q176737","display_name":"Stochastic process","level":2,"score":0.5886009335517883},{"id":"https://openalex.org/C22324862","wikidata":"https://www.wikidata.org/wiki/Q652707","display_name":"Lipschitz continuity","level":2,"score":0.5544405579566956},{"id":"https://openalex.org/C167964875","wikidata":"https://www.wikidata.org/wiki/Q17011487","display_name":"Exponential stability","level":3,"score":0.5262845158576965},{"id":"https://openalex.org/C177918212","wikidata":"https://www.wikidata.org/wiki/Q803623","display_name":"Perturbation (astronomy)","level":2,"score":0.5192568302154541},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5138747692108154},{"id":"https://openalex.org/C158535547","wikidata":"https://www.wikidata.org/wiki/Q5165437","display_name":"Continuous-time stochastic process","level":3,"score":0.5005745887756348},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.4744775593280792},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.4525725543498993},{"id":"https://openalex.org/C194387892","wikidata":"https://www.wikidata.org/wiki/Q1747770","display_name":"Stochastic optimization","level":2,"score":0.44597721099853516},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.42458418011665344},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.414081871509552},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3430865406990051},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.12541022896766663},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.06540030241012573},{"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/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"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/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/acc.2010.5530487","is_oa":false,"landing_page_url":"https://doi.org/10.1109/acc.2010.5530487","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2010 American Control Conference","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":14,"referenced_works":["https://openalex.org/W1989145274","https://openalex.org/W2007287229","https://openalex.org/W2008123001","https://openalex.org/W2044387789","https://openalex.org/W2048983163","https://openalex.org/W2091253371","https://openalex.org/W2095062552","https://openalex.org/W2101607950","https://openalex.org/W2102249468","https://openalex.org/W2115220705","https://openalex.org/W2125812768","https://openalex.org/W2139798591","https://openalex.org/W2147574995","https://openalex.org/W2153409886"],"related_works":["https://openalex.org/W2965246392","https://openalex.org/W129738973","https://openalex.org/W2888652631","https://openalex.org/W4200373676","https://openalex.org/W3020818737","https://openalex.org/W2912388972","https://openalex.org/W4238487991","https://openalex.org/W1997769777","https://openalex.org/W2042280983","https://openalex.org/W4224283474"],"abstract_inverted_index":{"We":[0,107],"investigate":[1],"stochastic":[2,22,31,47,71,99,112],"averaging":[3,32],"theory":[4,17],"in":[5,57],"continuous":[6],"time":[7],"for":[8,39,115,119],"locally":[9],"Lipschitz":[10],"systems":[11,45],"and":[12,34,49,80,118],"the":[13,63,70,77,83,87,109],"applications":[14],"of":[15,21,42,62,76,82,86,103,111],"this":[16],"to":[18],"stability":[19,37,75,110],"analysis":[20],"extremum":[23,95,113],"seeking":[24,96,114],"algorithms.":[25],"First,":[26],"we":[27,91],"establish":[28],"a":[29,40,93],"general":[30,120],"principle":[33],"some":[35],"related":[36],"theorems":[38],"class":[41],"continuous-time":[43,94],"nonlinear":[44,64,121],"with":[46,98],"perturbations":[48],"remove":[50],"or":[51],"weaken":[52],"several":[53],"significant":[54],"restrictions":[55],"present":[56],"existing":[58],"results:":[59],"global":[60,73],"Lipschitzness":[61],"vector":[65],"field,":[66],"equilibrium":[67],"preservation":[68],"under":[69],"perturbation,":[72],"exponential":[74],"average":[78],"system,":[79],"compactness":[81],"state":[84],"space":[85],"perturbation":[88],"process.":[89],"Then,":[90],"propose":[92],"algorithm":[97],"excitation":[100],"signals":[101],"instead":[102],"deterministic":[104],"periodic":[105],"signals.":[106],"analyze":[108],"static":[116],"maps":[117],"dynamic":[122],"systems.":[123]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2017,"cited_by_count":1}],"updated_date":"2026-07-29T14:22:42.915294","created_date":"2025-10-10T00:00:00"}
