{"id":"https://openalex.org/W2611099779","doi":"https://doi.org/10.23919/acc.2017.7963319","title":"Nonlinear adaptive stabilization of a class of planar slow-fast systems at a non-hyperbolic point","display_name":"Nonlinear adaptive stabilization of a class of planar slow-fast systems at a non-hyperbolic point","publication_year":2017,"publication_date":"2017-05-01","ids":{"openalex":"https://openalex.org/W2611099779","doi":"https://doi.org/10.23919/acc.2017.7963319","mag":"2611099779"},"language":"en","primary_location":{"id":"doi:10.23919/acc.2017.7963319","is_oa":false,"landing_page_url":"https://doi.org/10.23919/acc.2017.7963319","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":true,"oa_status":"green","oa_url":"https://research.rug.nl/en/publications/14d73b01-0cc9-4853-aab3-4c7cc66519f7","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5029419062","display_name":"Hildeberto Jard\u00f3n-Kojakhmetov","orcid":"https://orcid.org/0000-0001-8708-7409"},"institutions":[{"id":"https://openalex.org/I169381384","display_name":"University of Groningen","ror":"https://ror.org/012p63287","country_code":"NL","type":"education","lineage":["https://openalex.org/I169381384"]}],"countries":["NL"],"is_corresponding":true,"raw_author_name":"H. Jardon-Kojakhmetov","raw_affiliation_strings":["Jan C. Willems Center for Systems and Control and the Engineering and Technology Institute (ENTEG), University of Groningen, Groningen, The Netherlands"],"affiliations":[{"raw_affiliation_string":"Jan C. Willems Center for Systems and Control and the Engineering and Technology Institute (ENTEG), University of Groningen, Groningen, The Netherlands","institution_ids":["https://openalex.org/I169381384"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5078364973","display_name":"Jacquelien M.A. Scherpen","orcid":"https://orcid.org/0000-0002-3409-5760"},"institutions":[{"id":"https://openalex.org/I169381384","display_name":"University of Groningen","ror":"https://ror.org/012p63287","country_code":"NL","type":"education","lineage":["https://openalex.org/I169381384"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Jacquelien M.A. Scherpen","raw_affiliation_strings":["Jan C. Willems Center for Systems and Control and the Engineering and Technology Institute (ENTEG), University of Groningen, Groningen, The Netherlands"],"affiliations":[{"raw_affiliation_string":"Jan C. Willems Center for Systems and Control and the Engineering and Technology Institute (ENTEG), University of Groningen, Groningen, The Netherlands","institution_ids":["https://openalex.org/I169381384"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5062972822","display_name":"Dunstano del Puerto-Flores","orcid":"https://orcid.org/0000-0001-7190-6641"},"institutions":[{"id":"https://openalex.org/I193181351","display_name":"Universidad de Guadalajara","ror":"https://ror.org/043xj7k26","country_code":"MX","type":"education","lineage":["https://openalex.org/I193181351"]}],"countries":["MX"],"is_corresponding":false,"raw_author_name":"D. del Puerto-Flores","raw_affiliation_strings":["Department of Mechanical-Electrical Engineering, University of Guadalajara, Guadalajara, Mexico"],"affiliations":[{"raw_affiliation_string":"Department of Mechanical-Electrical Engineering, University of Guadalajara, Guadalajara, Mexico","institution_ids":["https://openalex.org/I193181351"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5029419062"],"corresponding_institution_ids":["https://openalex.org/I169381384"],"apc_list":null,"apc_paid":null,"fwci":0.5248,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.63181914,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":null,"issue":null,"first_page":"2441","last_page":"2446"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11513","display_name":"stochastic dynamics and bifurcation","score":0.9995999932289124,"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"}},"topics":[{"id":"https://openalex.org/T11513","display_name":"stochastic dynamics and bifurcation","score":0.9995999932289124,"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/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9987000226974487,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10244","display_name":"Chaos control and synchronization","score":0.9958000183105469,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6728382706642151},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.6248277425765991},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5703266859054565},{"id":"https://openalex.org/keywords/singular-perturbation","display_name":"Singular perturbation","score":0.5495792627334595},{"id":"https://openalex.org/keywords/planar","display_name":"Planar","score":0.4970863163471222},{"id":"https://openalex.org/keywords/hyperbolic-equilibrium-point","display_name":"Hyperbolic equilibrium point","score":0.4967861771583557},{"id":"https://openalex.org/keywords/lyapunov-function","display_name":"Lyapunov function","score":0.4564807713031769},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4232894778251648},{"id":"https://openalex.org/keywords/controller","display_name":"Controller (irrigation)","score":0.41392359137535095},{"id":"https://openalex.org/keywords/perturbation","display_name":"Perturbation (astronomy)","score":0.41132447123527527},{"id":"https://openalex.org/keywords/hyperbolic-function","display_name":"Hyperbolic function","score":0.37825676798820496},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1721717119216919},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.13554590940475464},{"id":"https://openalex.org/keywords/hyperbolic-manifold","display_name":"Hyperbolic manifold","score":0.12445369362831116},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.1006024181842804}],"concepts":[{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6728382706642151},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.6248277425765991},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5703266859054565},{"id":"https://openalex.org/C165160513","wikidata":"https://www.wikidata.org/wiki/Q7524249","display_name":"Singular perturbation","level":2,"score":0.5495792627334595},{"id":"https://openalex.org/C134786449","wikidata":"https://www.wikidata.org/wiki/Q3391255","display_name":"Planar","level":2,"score":0.4970863163471222},{"id":"https://openalex.org/C51691630","wikidata":"https://www.wikidata.org/wiki/Q3925833","display_name":"Hyperbolic equilibrium point","level":4,"score":0.4967861771583557},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.4564807713031769},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4232894778251648},{"id":"https://openalex.org/C203479927","wikidata":"https://www.wikidata.org/wiki/Q5165939","display_name":"Controller (irrigation)","level":2,"score":0.41392359137535095},{"id":"https://openalex.org/C177918212","wikidata":"https://www.wikidata.org/wiki/Q803623","display_name":"Perturbation (astronomy)","level":2,"score":0.41132447123527527},{"id":"https://openalex.org/C92047909","wikidata":"https://www.wikidata.org/wiki/Q204034","display_name":"Hyperbolic function","level":2,"score":0.37825676798820496},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1721717119216919},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.13554590940475464},{"id":"https://openalex.org/C70984080","wikidata":"https://www.wikidata.org/wiki/Q2619102","display_name":"Hyperbolic manifold","level":3,"score":0.12445369362831116},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.1006024181842804},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","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},{"id":"https://openalex.org/C6557445","wikidata":"https://www.wikidata.org/wiki/Q173113","display_name":"Agronomy","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":3,"locations":[{"id":"doi:10.23919/acc.2017.7963319","is_oa":false,"landing_page_url":"https://doi.org/10.23919/acc.2017.7963319","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"},{"id":"pmh:oai:pure.rug.nl:openaire/14d73b01-0cc9-4853-aab3-4c7cc66519f7","is_oa":true,"landing_page_url":"https://research.rug.nl/en/publications/14d73b01-0cc9-4853-aab3-4c7cc66519f7","pdf_url":null,"source":{"id":"https://openalex.org/S4306400420","display_name":"University of Groningen research database (University of Groningen / Centre for Information Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I169381384","host_organization_name":"University of Groningen","host_organization_lineage":["https://openalex.org/I169381384"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Jard\u00f3n Kojakhmetov, H, Scherpen, J M A & del Puerto-Flores, D 2017, Nonlinear Adaptive Stabilization of a Class of Planar Slow-Fast Systems at a Non-Hyperbolic Point. in Proceedings of the American Control Conference 2017. IEEEXplore, pp. 2441-2446, 2017 American Control Conference, Seattle, United States, 24/05/2017. https://doi.org/10.23919/ACC.2017.7963319","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:pure.rug.nl:publications/14d73b01-0cc9-4853-aab3-4c7cc66519f7","is_oa":true,"landing_page_url":"https://hdl.handle.net/11370/14d73b01-0cc9-4853-aab3-4c7cc66519f7","pdf_url":"https://research.rug.nl/files/50534300/07963319.pdf","source":{"id":"https://openalex.org/S4306400420","display_name":"University of Groningen research database (University of Groningen / Centre for Information Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I169381384","host_organization_name":"University of Groningen","host_organization_lineage":["https://openalex.org/I169381384"],"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":"Jard\u00f3n Kojakhmetov, H, Scherpen, J M A & del Puerto-Flores, D 2017, Nonlinear Adaptive Stabilization of a Class of Planar Slow-Fast Systems at a Non-Hyperbolic Point. in Proceedings of the American Control Conference 2017. IEEEXplore, pp. 2441-2446, 2017 American Control Conference, Seattle, United States, 24/05/2017. https://doi.org/10.23919/ACC.2017.7963319","raw_type":"info:eu-repo/semantics/publishedVersion"}],"best_oa_location":{"id":"pmh:oai:pure.rug.nl:openaire/14d73b01-0cc9-4853-aab3-4c7cc66519f7","is_oa":true,"landing_page_url":"https://research.rug.nl/en/publications/14d73b01-0cc9-4853-aab3-4c7cc66519f7","pdf_url":null,"source":{"id":"https://openalex.org/S4306400420","display_name":"University of Groningen research database (University of Groningen / Centre for Information Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I169381384","host_organization_name":"University of Groningen","host_organization_lineage":["https://openalex.org/I169381384"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Jard\u00f3n Kojakhmetov, H, Scherpen, J M A & del Puerto-Flores, D 2017, Nonlinear Adaptive Stabilization of a Class of Planar Slow-Fast Systems at a Non-Hyperbolic Point. in Proceedings of the American Control Conference 2017. IEEEXplore, pp. 2441-2446, 2017 American Control Conference, Seattle, United States, 24/05/2017. https://doi.org/10.23919/ACC.2017.7963319","raw_type":"info:eu-repo/semantics/publishedVersion"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W99189181","https://openalex.org/W1584245551","https://openalex.org/W1626756714","https://openalex.org/W1976081015","https://openalex.org/W1983920324","https://openalex.org/W1986739294","https://openalex.org/W1995090200","https://openalex.org/W2013272212","https://openalex.org/W2014157641","https://openalex.org/W2015925613","https://openalex.org/W2016767879","https://openalex.org/W2062361291","https://openalex.org/W2063490625","https://openalex.org/W2071313546","https://openalex.org/W2090167557","https://openalex.org/W2197630424","https://openalex.org/W2572508998","https://openalex.org/W2605542659","https://openalex.org/W4206311976","https://openalex.org/W4236765228","https://openalex.org/W4240834412","https://openalex.org/W4295122410","https://openalex.org/W4298290699","https://openalex.org/W6634861456"],"related_works":["https://openalex.org/W4327639758","https://openalex.org/W1998082046","https://openalex.org/W2116787190","https://openalex.org/W2154304710","https://openalex.org/W2019676381","https://openalex.org/W1982149897","https://openalex.org/W2387468633","https://openalex.org/W2006371715","https://openalex.org/W2713536231","https://openalex.org/W1598394172"],"abstract_inverted_index":{"Non-hyperbolic":[0],"points":[1,38],"of":[2,39,60,87,116],"slow-fast":[3,41,61,88],"systems":[4,62],"(also":[5],"known":[6],"as":[7,20],"singularly":[8],"perturbed":[9],"ordinary":[10],"differential":[11],"equations)":[12],"are":[13,132],"responsible":[14],"for":[15],"many":[16],"interesting":[17],"behavior":[18,125],"such":[19],"relaxation":[21],"oscillations,":[22,25],"canards,":[23],"mixed-mode":[24],"etc.":[26],"Recently,":[27],"the":[28,58,69,82,94,114,117,127,135],"authors":[29],"have":[30],"proposed":[31],"a":[32,52,122],"control":[33],"strategy":[34,44],"to":[35,56,73,96,126],"stabilize":[36],"non-hyperbolic":[37,64],"planar":[40],"systems.":[42,89],"Such":[43],"is":[45,51,92,99,103],"based":[46,111],"on":[47,134],"geometric":[48,107],"desingularization,":[49],"which":[50],"well":[53],"suited":[54],"technique":[55,67],"analyze":[57],"dynamics":[59],"near":[63],"points.":[65],"This":[66,79],"transforms":[68],"singular":[70],"perturbation":[71,77],"problem":[72,86],"an":[74],"equivalent":[75],"regular":[76],"problem.":[78],"papers":[80],"treats":[81],"nonlinear":[83],"adaptive":[84],"stabilization":[85],"The":[90,101],"novelty":[91],"that":[93],"point":[95],"be":[97],"stabilized":[98],"non-hyperbolic.":[100],"controller":[102],"designed":[104],"by":[105],"combining":[106],"desingularization":[108],"and":[109],"Lyapunov":[110],"techniques.":[112],"Through":[113],"action":[115],"controller,":[118],"we":[119],"basically":[120],"inject":[121],"normally":[123],"hyperbolic":[124],"fast":[128],"variable.":[129],"Our":[130],"results":[131],"exemplified":[133],"van":[136],"der":[137],"Pol":[138],"oscillator.":[139]},"counts_by_year":[{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1}],"updated_date":"2026-03-17T09:09:15.849793","created_date":"2025-10-10T00:00:00"}