{"id":"https://openalex.org/W4321366483","doi":"https://doi.org/10.1109/tcst.2023.3242199","title":"A Graphical Approach to Examining Classical Extremum Seeking Using Bifurcation Analysis","display_name":"A Graphical Approach to Examining Classical Extremum Seeking Using Bifurcation Analysis","publication_year":2023,"publication_date":"2023-02-20","ids":{"openalex":"https://openalex.org/W4321366483","doi":"https://doi.org/10.1109/tcst.2023.3242199"},"language":"en","primary_location":{"id":"doi:10.1109/tcst.2023.3242199","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcst.2023.3242199","pdf_url":null,"source":{"id":"https://openalex.org/S133363738","display_name":"IEEE Transactions on Control Systems Technology","issn_l":"1063-6536","issn":["1063-6536","1558-0865","2374-0159"],"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 Control Systems Technology","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://hdl.handle.net/1983/a47eed94-79dc-4280-87e9-37115af3de90","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5016934804","display_name":"Duc H. Nguyen","orcid":"https://orcid.org/0000-0002-6871-7919"},"institutions":[{"id":"https://openalex.org/I36234482","display_name":"University of Bristol","ror":"https://ror.org/0524sp257","country_code":"GB","type":"education","lineage":["https://openalex.org/I36234482"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Duc H. Nguyen","raw_affiliation_strings":["Department of Aerospace Engineering, University of Bristol, Bristol, U.K"],"affiliations":[{"raw_affiliation_string":"Department of Aerospace Engineering, University of Bristol, Bristol, U.K","institution_ids":["https://openalex.org/I36234482"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5102771078","display_name":"Mark Lowenberg","orcid":"https://orcid.org/0000-0002-1373-8237"},"institutions":[{"id":"https://openalex.org/I36234482","display_name":"University of Bristol","ror":"https://ror.org/0524sp257","country_code":"GB","type":"education","lineage":["https://openalex.org/I36234482"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Mark H. Lowenberg","raw_affiliation_strings":["Department of Aerospace Engineering, University of Bristol, Bristol, U.K"],"affiliations":[{"raw_affiliation_string":"Department of Aerospace Engineering, University of Bristol, Bristol, U.K","institution_ids":["https://openalex.org/I36234482"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5006012432","display_name":"Simon A. Neild","orcid":"https://orcid.org/0000-0003-4122-4513"},"institutions":[{"id":"https://openalex.org/I36234482","display_name":"University of Bristol","ror":"https://ror.org/0524sp257","country_code":"GB","type":"education","lineage":["https://openalex.org/I36234482"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Simon A. Neild","raw_affiliation_strings":["Department of Aerospace Engineering, University of Bristol, Bristol, U.K"],"affiliations":[{"raw_affiliation_string":"Department of Aerospace Engineering, University of Bristol, Bristol, U.K","institution_ids":["https://openalex.org/I36234482"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5016934804"],"corresponding_institution_ids":["https://openalex.org/I36234482"],"apc_list":null,"apc_paid":null,"fwci":0.5406,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.63285942,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"31","issue":"3","first_page":"1324","last_page":"1335"},"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/T10553","display_name":"Combustion and flame dynamics","score":0.9610999822616577,"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/control-theory","display_name":"Control theory (sociology)","score":0.7505095601081848},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.6763660907745361},{"id":"https://openalex.org/keywords/limit-cycle","display_name":"Limit cycle","score":0.6504262685775757},{"id":"https://openalex.org/keywords/attractor","display_name":"Attractor","score":0.6006729602813721},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5601034164428711},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.5549220442771912},{"id":"https://openalex.org/keywords/multistability","display_name":"Multistability","score":0.5210089683532715},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5167412161827087},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.5062050223350525},{"id":"https://openalex.org/keywords/bifurcation-theory","display_name":"Bifurcation theory","score":0.4435340464115143},{"id":"https://openalex.org/keywords/complement","display_name":"Complement (music)","score":0.43145716190338135},{"id":"https://openalex.org/keywords/filter","display_name":"Filter (signal processing)","score":0.4117540419101715},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.3643350899219513},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3097030520439148},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.2019321322441101},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.14829903841018677},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.10414993762969971}],"concepts":[{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.7505095601081848},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.6763660907745361},{"id":"https://openalex.org/C93357160","wikidata":"https://www.wikidata.org/wiki/Q1545916","display_name":"Limit cycle","level":3,"score":0.6504262685775757},{"id":"https://openalex.org/C164380108","wikidata":"https://www.wikidata.org/wiki/Q507187","display_name":"Attractor","level":2,"score":0.6006729602813721},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5601034164428711},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5549220442771912},{"id":"https://openalex.org/C2776966350","wikidata":"https://www.wikidata.org/wiki/Q6935096","display_name":"Multistability","level":3,"score":0.5210089683532715},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5167412161827087},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.5062050223350525},{"id":"https://openalex.org/C85075877","wikidata":"https://www.wikidata.org/wiki/Q1154357","display_name":"Bifurcation theory","level":4,"score":0.4435340464115143},{"id":"https://openalex.org/C112313634","wikidata":"https://www.wikidata.org/wiki/Q7886648","display_name":"Complement (music)","level":5,"score":0.43145716190338135},{"id":"https://openalex.org/C106131492","wikidata":"https://www.wikidata.org/wiki/Q3072260","display_name":"Filter (signal processing)","level":2,"score":0.4117540419101715},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.3643350899219513},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3097030520439148},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.2019321322441101},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.14829903841018677},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.10414993762969971},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C188082640","wikidata":"https://www.wikidata.org/wiki/Q1780899","display_name":"Complementation","level":4,"score":0.0},{"id":"https://openalex.org/C127716648","wikidata":"https://www.wikidata.org/wiki/Q104053","display_name":"Phenotype","level":3,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1109/tcst.2023.3242199","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcst.2023.3242199","pdf_url":null,"source":{"id":"https://openalex.org/S133363738","display_name":"IEEE Transactions on Control Systems Technology","issn_l":"1063-6536","issn":["1063-6536","1558-0865","2374-0159"],"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 Control Systems Technology","raw_type":"journal-article"},{"id":"pmh:oai:research-information.bris.ac.uk:openaire_cris_publications/a47eed94-79dc-4280-87e9-37115af3de90","is_oa":true,"landing_page_url":"https://hdl.handle.net/1983/a47eed94-79dc-4280-87e9-37115af3de90","pdf_url":null,"source":{"id":"https://openalex.org/S4306400895","display_name":"Bristol Research (University of Bristol)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I36234482","host_organization_name":"University of Bristol","host_organization_lineage":["https://openalex.org/I36234482"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"Nguyen, D H, Lowenberg , M H & Neild, S A 2023, 'A Graphical Approach to Examining Classical Extremum Seeking Using Bifurcation Analysis', IEEE Transactions on Control Systems Technology, vol. 31, no. 3, pp. 1324-1335. https://doi.org/10.1109/TCST.2023.3242199","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:research-information.bris.ac.uk:openaire/a47eed94-79dc-4280-87e9-37115af3de90","is_oa":true,"landing_page_url":"https://research-information.bris.ac.uk/en/publications/a47eed94-79dc-4280-87e9-37115af3de90","pdf_url":"https://research-information.bris.ac.uk/files/355574463/TCST3242199.pdf","source":{"id":"https://openalex.org/S4306400895","display_name":"Bristol Research (University of Bristol)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I36234482","host_organization_name":"University of Bristol","host_organization_lineage":["https://openalex.org/I36234482"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Nguyen, D H, Lowenberg , M H & Neild, S A 2023, 'A Graphical Approach to Examining Classical Extremum Seeking Using Bifurcation Analysis', IEEE Transactions on Control Systems Technology, vol. 31, no. 3, pp. 1324-1335. https://doi.org/10.1109/TCST.2023.3242199","raw_type":"info:eu-repo/semantics/publishedVersion"}],"best_oa_location":{"id":"pmh:oai:research-information.bris.ac.uk:openaire_cris_publications/a47eed94-79dc-4280-87e9-37115af3de90","is_oa":true,"landing_page_url":"https://hdl.handle.net/1983/a47eed94-79dc-4280-87e9-37115af3de90","pdf_url":null,"source":{"id":"https://openalex.org/S4306400895","display_name":"Bristol Research (University of Bristol)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I36234482","host_organization_name":"University of Bristol","host_organization_lineage":["https://openalex.org/I36234482"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"Nguyen, D H, Lowenberg , M H & Neild, S A 2023, 'A Graphical Approach to Examining Classical Extremum Seeking Using Bifurcation Analysis', IEEE Transactions on Control Systems Technology, vol. 31, no. 3, pp. 1324-1335. https://doi.org/10.1109/TCST.2023.3242199","raw_type":"info:eu-repo/semantics/publishedVersion"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320306101","display_name":"National Aeronautics and Space Administration","ror":"https://ror.org/027ka1x80"},{"id":"https://openalex.org/F4320332378","display_name":"Langley Research Center","ror":"https://ror.org/0399mhs52"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":47,"referenced_works":["https://openalex.org/W593234001","https://openalex.org/W1480785168","https://openalex.org/W1786679580","https://openalex.org/W1999245588","https://openalex.org/W2006391589","https://openalex.org/W2055253862","https://openalex.org/W2074219590","https://openalex.org/W2082228574","https://openalex.org/W2095062552","https://openalex.org/W2112619033","https://openalex.org/W2124646895","https://openalex.org/W2127025124","https://openalex.org/W2127934173","https://openalex.org/W2156466787","https://openalex.org/W2164761951","https://openalex.org/W2166003201","https://openalex.org/W2253564595","https://openalex.org/W2280059822","https://openalex.org/W2326895606","https://openalex.org/W2342277539","https://openalex.org/W2344767529","https://openalex.org/W2407938586","https://openalex.org/W2521100213","https://openalex.org/W2560154500","https://openalex.org/W2766529560","https://openalex.org/W2778765202","https://openalex.org/W2781511698","https://openalex.org/W2781540738","https://openalex.org/W2782348926","https://openalex.org/W2789810054","https://openalex.org/W2908789497","https://openalex.org/W2912085843","https://openalex.org/W3037232681","https://openalex.org/W3083737121","https://openalex.org/W3088778840","https://openalex.org/W3154164276","https://openalex.org/W3167862478","https://openalex.org/W3190288780","https://openalex.org/W4210313665","https://openalex.org/W4213011582","https://openalex.org/W4230906466","https://openalex.org/W4300443332","https://openalex.org/W4303107264","https://openalex.org/W6638967683","https://openalex.org/W6747209573","https://openalex.org/W6747404199","https://openalex.org/W6748145504"],"related_works":["https://openalex.org/W1464403884","https://openalex.org/W2015173963","https://openalex.org/W2108117187","https://openalex.org/W3090703118","https://openalex.org/W2784603025","https://openalex.org/W3015125480","https://openalex.org/W2140187929","https://openalex.org/W4362633503","https://openalex.org/W2083968322","https://openalex.org/W2070724789"],"abstract_inverted_index":{"The":[0,133,165],"majority":[1],"of":[2,31,50,70,93,100,105,149,167,182],"extremum-seeking":[3,42,131,136],"literature":[4],"discusses":[5],"rigorous":[6],"stability":[7,102,179],"analysis,":[8],"thereby":[9,75],"limiting":[10],"its":[11],"audience":[12],"to":[13,36,60,79,125,161],"mathematicians":[14],"and":[15,54,103,122,138,173,180,190],"control":[16,137],"engineers":[17,121],"with":[18,58],"strong":[19],"theoretical":[20],"backgrounds.":[21],"Here,":[22],"we":[23],"complement":[24],"these":[25],"studies":[26],"by":[27],"proposing":[28],"the":[29,67,77,81,163,168,178,183],"use":[30,146],"harmonically":[32,72],"forced":[33,73],"bifurcation":[34],"analysis":[35,114],"evaluate":[37],"parameter":[38],"choices":[39],"in":[40,88,153],"classical":[41,130],"systems.":[43,132],"This":[44],"method":[45],"generates":[46],"a":[47,61,71,154],"graphical":[48],"map":[49],"limit":[51],"cycle":[52],"attractors":[53],"how":[55],"they":[56],"change":[57],"respect":[59],"chosen":[62],"parameter.":[63],"Our":[64],"approach":[65],"retains":[66],"full":[68],"properties":[69],"system,":[74],"avoiding":[76],"requirement":[78],"approximate":[80],"dynamics":[82,159],"as":[83,86,98],"equilibrium":[84],"solutions":[85,107],"done":[87],"previous":[89],"studies.":[90],"Common":[91],"elements":[92],"nonlinear":[94],"dynamical":[95,139],"systems,":[96],"such":[97],"loss":[99],"local":[101],"coexistence":[104],"multiple":[106],"via":[108],"fold":[109],"bifurcations":[110],"are":[111],"observed.":[112],"Bifurcation":[113],"therefore":[115],"provides":[116],"an":[117,147,150],"intuitive":[118],"tool":[119],"for":[120],"new":[123],"adopters":[124],"gain":[126],"further":[127],"insight":[128],"into":[129],"link":[134],"between":[135],"system":[140,152,184],"theory":[141],"is":[142,185],"also":[143],"highlighted.":[144],"We":[145],"example":[148],"auto-trim":[151],"nonlinear,":[155],"longitudinal":[156],"(fourth-order)":[157],"flight":[158],"model":[160],"demonstrate":[162],"method.":[164],"influence":[166],"forcing":[169],"frequency,":[170],"modulation":[171],"phase,":[172],"high-pass":[174],"filter":[175],"frequency":[176],"on":[177],"performance":[181],"examined":[186],"using":[187],"both":[188],"one-":[189],"two-parameter":[191],"continuation.":[192]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1}],"updated_date":"2026-04-18T07:56:08.524223","created_date":"2025-10-10T00:00:00"}