{"id":"https://openalex.org/W2557289702","doi":"https://doi.org/10.1109/tac.2016.2633724","title":"Iterative Learning and Extremum Seeking for Repetitive Time-Varying Mappings","display_name":"Iterative Learning and Extremum Seeking for Repetitive Time-Varying Mappings","publication_year":2016,"publication_date":"2016-12-01","ids":{"openalex":"https://openalex.org/W2557289702","doi":"https://doi.org/10.1109/tac.2016.2633724","mag":"2557289702"},"language":"en","primary_location":{"id":"doi:10.1109/tac.2016.2633724","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2016.2633724","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":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1509.01912","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5012669091","display_name":"Zhixing Cao","orcid":"https://orcid.org/0000-0003-2600-5806"},"institutions":[{"id":"https://openalex.org/I136199984","display_name":"Harvard University","ror":"https://ror.org/03vek6s52","country_code":"US","type":"education","lineage":["https://openalex.org/I136199984"]},{"id":"https://openalex.org/I200769079","display_name":"Hong Kong University of Science and Technology","ror":"https://ror.org/00q4vv597","country_code":"HK","type":"education","lineage":["https://openalex.org/I200769079"]},{"id":"https://openalex.org/I889458895","display_name":"University of Hong Kong","ror":"https://ror.org/02zhqgq86","country_code":"HK","type":"education","lineage":["https://openalex.org/I889458895"]}],"countries":["HK","US"],"is_corresponding":false,"raw_author_name":"Zhixing Cao","raw_affiliation_strings":["Department of Chemical and Biomolecular Engineering, Hong Kong University of Science and Technology, Hong Kong SAR","Harvard John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, United States"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Chemical and Biomolecular Engineering, Hong Kong University of Science and Technology, Hong Kong SAR","institution_ids":["https://openalex.org/I200769079","https://openalex.org/I889458895"]},{"raw_affiliation_string":"Harvard John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, United States","institution_ids":["https://openalex.org/I136199984"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5046681563","display_name":"Hans-Bernd D\u00fcrr","orcid":null},"institutions":[{"id":"https://openalex.org/I100066346","display_name":"University of Stuttgart","ror":"https://ror.org/04vnq7t77","country_code":"DE","type":"education","lineage":["https://openalex.org/I100066346"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Hans-Bernd Durr","raw_affiliation_strings":["Institute for Systems Theory and Automatic Control, University of Stuttgart, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute for Systems Theory and Automatic Control, University of Stuttgart, Germany","institution_ids":["https://openalex.org/I100066346"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5062156162","display_name":"Christian Ebenbauer","orcid":"https://orcid.org/0000-0002-7414-4299"},"institutions":[{"id":"https://openalex.org/I100066346","display_name":"University of Stuttgart","ror":"https://ror.org/04vnq7t77","country_code":"DE","type":"education","lineage":["https://openalex.org/I100066346"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Christian Ebenbauer","raw_affiliation_strings":["Institute for Systems Theory and Automatic Control, University of Stuttgart, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute for Systems Theory and Automatic Control, University of Stuttgart, Germany","institution_ids":["https://openalex.org/I100066346"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5001090900","display_name":"Frank Allg\u00f6wer","orcid":"https://orcid.org/0000-0002-3702-3658"},"institutions":[{"id":"https://openalex.org/I100066346","display_name":"University of Stuttgart","ror":"https://ror.org/04vnq7t77","country_code":"DE","type":"education","lineage":["https://openalex.org/I100066346"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Frank Allgower","raw_affiliation_strings":["Institute for Systems Theory and Automatic Control, University of Stuttgart, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute for Systems Theory and Automatic Control, University of Stuttgart, Germany","institution_ids":["https://openalex.org/I100066346"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5002154840","display_name":"Furong Gao","orcid":"https://orcid.org/0000-0002-5900-1353"},"institutions":[{"id":"https://openalex.org/I136199984","display_name":"Harvard University","ror":"https://ror.org/03vek6s52","country_code":"US","type":"education","lineage":["https://openalex.org/I136199984"]},{"id":"https://openalex.org/I200769079","display_name":"Hong Kong University of Science and Technology","ror":"https://ror.org/00q4vv597","country_code":"HK","type":"education","lineage":["https://openalex.org/I200769079"]},{"id":"https://openalex.org/I4210159029","display_name":"Guangzhou HKUST Fok Ying Tung Research Institute","ror":"https://ror.org/05cvbj479","country_code":"CN","type":"facility","lineage":["https://openalex.org/I200769079","https://openalex.org/I4210159029"]},{"id":"https://openalex.org/I889458895","display_name":"University of Hong Kong","ror":"https://ror.org/02zhqgq86","country_code":"HK","type":"education","lineage":["https://openalex.org/I889458895"]}],"countries":["CN","HK","US"],"is_corresponding":false,"raw_author_name":"Furong Gao","raw_affiliation_strings":["Department of Chemical and Biomolecular Engineering, Hong Kong University of Science and Technology Hong Kong SAR, the Harvard John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, USA","Fok Ying Tung Research Institute, Hong Kong University of Science and Technology, Guangzhou, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Chemical and Biomolecular Engineering, Hong Kong University of Science and Technology Hong Kong SAR, the Harvard John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, USA","institution_ids":["https://openalex.org/I136199984","https://openalex.org/I200769079","https://openalex.org/I889458895"]},{"raw_affiliation_string":"Fok Ying Tung Research Institute, Hong Kong University of Science and Technology, Guangzhou, China","institution_ids":["https://openalex.org/I200769079","https://openalex.org/I4210159029"]}]}],"institutions":[],"countries_distinct_count":4,"institutions_distinct_count":5,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.7857,"has_fulltext":false,"cited_by_count":22,"citation_normalized_percentile":{"value":0.85994285,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"62","issue":"7","first_page":"3339","last_page":"3353"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11749","display_name":"Iterative Learning Control Systems","score":0.9991999864578247,"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/T11749","display_name":"Iterative Learning Control Systems","score":0.9991999864578247,"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/T14083","display_name":"Extremum Seeking Control Systems","score":0.9969000220298767,"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/T11429","display_name":"Semiconductor Lasers and Optical Devices","score":0.9778000116348267,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic 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/iterative-learning-control","display_name":"Iterative learning control","score":0.9087620973587036},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.6156237125396729},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5654709935188293},{"id":"https://openalex.org/keywords/tracking-error","display_name":"Tracking error","score":0.5103217959403992},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.4915240705013275},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.4757349491119385},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.46158674359321594},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.42827823758125305},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.37692388892173767},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3642599582672119},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.19393733143806458},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.15186473727226257},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.139992356300354},{"id":"https://openalex.org/keywords/law","display_name":"Law","score":0.0932236909866333}],"concepts":[{"id":"https://openalex.org/C117619785","wikidata":"https://www.wikidata.org/wiki/Q6094414","display_name":"Iterative learning control","level":3,"score":0.9087620973587036},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.6156237125396729},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5654709935188293},{"id":"https://openalex.org/C183356978","wikidata":"https://www.wikidata.org/wiki/Q1779213","display_name":"Tracking error","level":3,"score":0.5103217959403992},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.4915240705013275},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.4757349491119385},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.46158674359321594},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.42827823758125305},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.37692388892173767},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3642599582672119},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.19393733143806458},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.15186473727226257},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.139992356300354},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0932236909866333},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","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}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1109/tac.2016.2633724","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2016.2633724","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:arXiv.org:1509.01912","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1509.01912","pdf_url":"https://arxiv.org/pdf/1509.01912","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:repository.hkust.edu.hk:1783.1-85868","is_oa":false,"landing_page_url":"http://repository.hkust.edu.hk/ir/Record/1783.1-85868","pdf_url":null,"source":{"id":"https://openalex.org/S4306401796","display_name":"Rare & Special e-Zone (The Hong Kong University of Science and Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I200769079","host_organization_name":"Hong Kong University of Science and Technology","host_organization_lineage":["https://openalex.org/I200769079"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1509.01912","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1509.01912","pdf_url":"https://arxiv.org/pdf/1509.01912","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[{"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16","score":0.8100000023841858}],"awards":[{"id":"https://openalex.org/G4721190839","display_name":"\u9762\u5411\u6ce8\u5851\u8fc7\u7a0b\u7684\u5728\u7ebf\u8d28\u91cf\u68c0\u6d4b\u4eea","funder_award_id":"61227005","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7226277211","display_name":null,"funder_award_id":"12190007","funder_id":"https://openalex.org/F4320334898","funder_display_name":"Guangzhou Science and Technology Program key projects"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320334898","display_name":"Guangzhou Science and Technology Program key projects","ror":"https://ror.org/00tjzgn92"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":35,"referenced_works":["https://openalex.org/W575947117","https://openalex.org/W630552816","https://openalex.org/W1540560684","https://openalex.org/W1654632542","https://openalex.org/W1834204252","https://openalex.org/W1972843576","https://openalex.org/W1984371888","https://openalex.org/W2022777480","https://openalex.org/W2031600073","https://openalex.org/W2037134746","https://openalex.org/W2041242313","https://openalex.org/W2057402039","https://openalex.org/W2058647849","https://openalex.org/W2074633447","https://openalex.org/W2078609652","https://openalex.org/W2084348046","https://openalex.org/W2088104099","https://openalex.org/W2093237314","https://openalex.org/W2095062552","https://openalex.org/W2113539361","https://openalex.org/W2120677931","https://openalex.org/W2127934173","https://openalex.org/W2146396918","https://openalex.org/W2154529221","https://openalex.org/W2156466787","https://openalex.org/W2159038290","https://openalex.org/W2166003201","https://openalex.org/W2168029749","https://openalex.org/W2318012484","https://openalex.org/W2563375064","https://openalex.org/W3109393067","https://openalex.org/W4236403390","https://openalex.org/W4300443332","https://openalex.org/W6636951021","https://openalex.org/W6638967683"],"related_works":["https://openalex.org/W2379960361","https://openalex.org/W2133373519","https://openalex.org/W2478562663","https://openalex.org/W2104608934","https://openalex.org/W2465904370","https://openalex.org/W1498036222","https://openalex.org/W2107729799","https://openalex.org/W4210894462","https://openalex.org/W1972930307","https://openalex.org/W2365680665"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3],"develop":[4],"an":[5,34,48,69,111],"iterative":[6,51,62,73,102,112],"learning":[7,52,63,74,103,113],"control":[8,14,53,64,75,114],"method":[9],"integrated":[10],"with":[11,76,96,115],"extremum":[12,28,66,104],"seeking":[13,29,105],"to":[15,58,157,166],"track":[16],"a":[17,77,92,141,158],"time-varying":[18],"optimizer":[19],"within":[20],"finite":[21],"time":[22],"horizon.":[23],"The":[24,41,55,121,160],"behavior":[25],"of":[26,124,137,162,170],"the":[27,101,116,151,163,167,171,181],"system":[30,45,106,129],"is":[31,46,80,84,148],"analyzed":[32,85],"via":[33,86],"approximating":[35],"system-the":[36],"modified":[37,42,126],"Lie":[38,43,127],"bracket":[39,44,128],"system.":[40],"essentially":[47],"online":[49,70],"integral-type":[50],"law.":[54],"paper":[56],"contributes":[57],"two":[59],"fields,":[60],"namely,":[61],"and":[65,174],"seeking.":[67],"First,":[68],"integral":[71],"type":[72],"forgetting":[78],"factor":[79],"proposed.":[81],"Its":[82],"convergence":[83],"k-dependent":[87],"(iteration-dependent)":[88],"contraction":[89],"mapping":[90],"in":[91,135],"Banach":[93],"space":[94],"equipped":[95],"so":[97],"called":[98],"\u03bb-norm.":[99],"Second,":[100],"can":[107,130,177],"be":[108,131,178],"interpreted":[109],"as":[110,119],"approximation":[117],"error":[118,123,153],"\u201cdisturbance\u201d.":[120],"tracking":[122,152],"its":[125,175],"shown":[132,149],"uniformly":[133],"bounded":[134],"terms":[136],"iterations":[138],"by":[139,180],"selecting":[140],"sufficiently":[142],"large":[143],"dither":[144],"frequency.":[145,182],"Furthermore,":[146],"it":[147],"that":[150],"will":[154],"eventually":[155],"converge":[156],"set.":[159],"center":[161],"set":[164],"corresponds":[165],"limit":[168],"solution":[169],"\u201cdisturbance-free\u201d":[172],"system,":[173],"radius":[176],"controlled":[179]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":3}],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2016-12-08T00:00:00"}