{"id":"https://openalex.org/W2739215887","doi":"https://doi.org/10.1142/s0218127417501048","title":"From Hopf Bifurcation to Limit Cycles Control in Underactuated Mechanical Systems","display_name":"From Hopf Bifurcation to Limit Cycles Control in Underactuated Mechanical Systems","publication_year":2017,"publication_date":"2017-06-30","ids":{"openalex":"https://openalex.org/W2739215887","doi":"https://doi.org/10.1142/s0218127417501048","mag":"2739215887"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127417501048","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127417501048","pdf_url":null,"source":{"id":"https://openalex.org/S81011612","display_name":"International Journal of Bifurcation and Chaos","issn_l":"0218-1274","issn":["0218-1274","1793-6551"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Bifurcation and Chaos","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://hal-lirmm.ccsd.cnrs.fr/lirmm-01723915","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5032274048","display_name":"Nahla Khraief Haddad","orcid":null},"institutions":[{"id":"https://openalex.org/I63596082","display_name":"Tunis El Manar University","ror":"https://ror.org/029cgt552","country_code":"TN","type":"education","lineage":["https://openalex.org/I63596082"]},{"id":"https://openalex.org/I108714496","display_name":"Tunis University","ror":"https://ror.org/02q1spa57","country_code":"TN","type":"education","lineage":["https://openalex.org/I108714496"]}],"countries":["TN"],"is_corresponding":true,"raw_author_name":"Nahla Khraief Haddad","raw_affiliation_strings":["RISC Lab, National School of Engineers of Tunis, University of Tunis El Manar, BP.37, le Belv\u00e9d\u00e9re, 1002 Tunis, Tunisia"],"affiliations":[{"raw_affiliation_string":"RISC Lab, National School of Engineers of Tunis, University of Tunis El Manar, BP.37, le Belv\u00e9d\u00e9re, 1002 Tunis, Tunisia","institution_ids":["https://openalex.org/I108714496","https://openalex.org/I63596082"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5056759341","display_name":"Safya Belghith","orcid":"https://orcid.org/0000-0001-7408-7848"},"institutions":[{"id":"https://openalex.org/I63596082","display_name":"Tunis El Manar University","ror":"https://ror.org/029cgt552","country_code":"TN","type":"education","lineage":["https://openalex.org/I63596082"]},{"id":"https://openalex.org/I108714496","display_name":"Tunis University","ror":"https://ror.org/02q1spa57","country_code":"TN","type":"education","lineage":["https://openalex.org/I108714496"]}],"countries":["TN"],"is_corresponding":false,"raw_author_name":"Safya Belghith","raw_affiliation_strings":["RISC Lab, National School of Engineers of Tunis, University of Tunis El Manar, BP.37, le Belv\u00e9d\u00e9re, 1002 Tunis, Tunisia"],"affiliations":[{"raw_affiliation_string":"RISC Lab, National School of Engineers of Tunis, University of Tunis El Manar, BP.37, le Belv\u00e9d\u00e9re, 1002 Tunis, Tunisia","institution_ids":["https://openalex.org/I108714496","https://openalex.org/I63596082"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5019458989","display_name":"Hass\u00e8ne Gritli","orcid":"https://orcid.org/0000-0002-5643-134X"},"institutions":[{"id":"https://openalex.org/I63596082","display_name":"Tunis El Manar University","ror":"https://ror.org/029cgt552","country_code":"TN","type":"education","lineage":["https://openalex.org/I63596082"]},{"id":"https://openalex.org/I108714496","display_name":"Tunis University","ror":"https://ror.org/02q1spa57","country_code":"TN","type":"education","lineage":["https://openalex.org/I108714496"]}],"countries":["TN"],"is_corresponding":false,"raw_author_name":"Hass\u00e8ne Gritli","raw_affiliation_strings":["RISC Lab, National School of Engineers of Tunis, University of Tunis El Manar, BP.37, le Belv\u00e9d\u00e9re, 1002 Tunis, Tunisia"],"affiliations":[{"raw_affiliation_string":"RISC Lab, National School of Engineers of Tunis, University of Tunis El Manar, BP.37, le Belv\u00e9d\u00e9re, 1002 Tunis, Tunisia","institution_ids":["https://openalex.org/I108714496","https://openalex.org/I63596082"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5026408399","display_name":"Ahmed Chemori","orcid":"https://orcid.org/0000-0001-9739-9473"},"institutions":[{"id":"https://openalex.org/I19894307","display_name":"Universit\u00e9 de Montpellier","ror":"https://ror.org/051escj72","country_code":"FR","type":"education","lineage":["https://openalex.org/I19894307"]},{"id":"https://openalex.org/I4210101743","display_name":"Laboratoire d'Informatique, de Robotique et de Micro\u00e9lectronique de Montpellier","ror":"https://ror.org/013yean28","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I151295451","https://openalex.org/I19894307","https://openalex.org/I4210101743","https://openalex.org/I4210159245","https://openalex.org/I4412460525"]},{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"funder","lineage":["https://openalex.org/I1294671590"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Ahmed Chemori","raw_affiliation_strings":["LIRMM, CNRS, University of Montpellier, 161 rue Ada, 34095 Montpellier Cedex 5, France"],"affiliations":[{"raw_affiliation_string":"LIRMM, CNRS, University of Montpellier, 161 rue Ada, 34095 Montpellier Cedex 5, France","institution_ids":["https://openalex.org/I19894307","https://openalex.org/I4210101743","https://openalex.org/I1294671590"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5032274048"],"corresponding_institution_ids":["https://openalex.org/I108714496","https://openalex.org/I63596082"],"apc_list":null,"apc_paid":null,"fwci":1.0058,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.7735829,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"27","issue":"07","first_page":"1750104","last_page":"1750104"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12772","display_name":"Control and Stability of Dynamical 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/T12772","display_name":"Control and Stability of Dynamical 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/T11394","display_name":"Dynamics and Control of Mechanical Systems","score":0.9939000010490417,"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/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.9761999845504761,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/center-manifold","display_name":"Center manifold","score":0.7514636516571045},{"id":"https://openalex.org/keywords/hopf-bifurcation","display_name":"Hopf bifurcation","score":0.7198764085769653},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.6895522475242615},{"id":"https://openalex.org/keywords/pitchfork-bifurcation","display_name":"Pitchfork bifurcation","score":0.6035302877426147},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5617330074310303},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.5444033145904541},{"id":"https://openalex.org/keywords/saddle-node-bifurcation","display_name":"Saddle-node bifurcation","score":0.4451856017112732},{"id":"https://openalex.org/keywords/biological-applications-of-bifurcation-theory","display_name":"Biological applications of bifurcation theory","score":0.43706944584846497},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.4357036352157593},{"id":"https://openalex.org/keywords/limit-cycle","display_name":"Limit cycle","score":0.424665242433548},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.31002527475357056},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2287670373916626},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.22269421815872192},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.2006472945213318},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.18902277946472168}],"concepts":[{"id":"https://openalex.org/C74774103","wikidata":"https://www.wikidata.org/wiki/Q4504202","display_name":"Center manifold","level":5,"score":0.7514636516571045},{"id":"https://openalex.org/C172435161","wikidata":"https://www.wikidata.org/wiki/Q531126","display_name":"Hopf bifurcation","level":4,"score":0.7198764085769653},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.6895522475242615},{"id":"https://openalex.org/C155092403","wikidata":"https://www.wikidata.org/wiki/Q1785924","display_name":"Pitchfork bifurcation","level":5,"score":0.6035302877426147},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5617330074310303},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.5444033145904541},{"id":"https://openalex.org/C101225446","wikidata":"https://www.wikidata.org/wiki/Q740190","display_name":"Saddle-node bifurcation","level":4,"score":0.4451856017112732},{"id":"https://openalex.org/C174914120","wikidata":"https://www.wikidata.org/wiki/Q4914973","display_name":"Biological applications of bifurcation theory","level":5,"score":0.43706944584846497},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.4357036352157593},{"id":"https://openalex.org/C93357160","wikidata":"https://www.wikidata.org/wiki/Q1545916","display_name":"Limit cycle","level":3,"score":0.424665242433548},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.31002527475357056},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2287670373916626},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.22269421815872192},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2006472945213318},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.18902277946472168},{"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/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1142/s0218127417501048","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127417501048","pdf_url":null,"source":{"id":"https://openalex.org/S81011612","display_name":"International Journal of Bifurcation and Chaos","issn_l":"0218-1274","issn":["0218-1274","1793-6551"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Bifurcation and Chaos","raw_type":"journal-article"},{"id":"pmh:oai:HAL:lirmm-01723915v1","is_oa":true,"landing_page_url":"https://hal-lirmm.ccsd.cnrs.fr/lirmm-01723915","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"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":"International journal of bifurcation and chaos in applied sciences and engineering , 2017, 27 (07), ⟨10.1142/S0218127417501048⟩","raw_type":"Journal articles"}],"best_oa_location":{"id":"pmh:oai:HAL:lirmm-01723915v1","is_oa":true,"landing_page_url":"https://hal-lirmm.ccsd.cnrs.fr/lirmm-01723915","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"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":"International journal of bifurcation and chaos in applied sciences and engineering , 2017, 27 (07), ⟨10.1142/S0218127417501048⟩","raw_type":"Journal articles"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions","score":0.7799999713897705}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W60729464","https://openalex.org/W1496777766","https://openalex.org/W1556270104","https://openalex.org/W2017564142","https://openalex.org/W2026609162","https://openalex.org/W2035695789","https://openalex.org/W2054080358","https://openalex.org/W2058418005","https://openalex.org/W2076841780","https://openalex.org/W2078958425","https://openalex.org/W2081696580","https://openalex.org/W2089876099","https://openalex.org/W2125968092","https://openalex.org/W2157018854","https://openalex.org/W2322754464","https://openalex.org/W2965444194","https://openalex.org/W3106525534","https://openalex.org/W4205625716","https://openalex.org/W4206651839","https://openalex.org/W4298039342","https://openalex.org/W4310301864"],"related_works":["https://openalex.org/W2546487931","https://openalex.org/W2356715721","https://openalex.org/W2019027784","https://openalex.org/W2078078632","https://openalex.org/W4312595290","https://openalex.org/W4250493900","https://openalex.org/W2737309493","https://openalex.org/W2319958367","https://openalex.org/W2319695500","https://openalex.org/W2358021809"],"abstract_inverted_index":{"This":[0],"paper":[1],"deals":[2],"with":[3,19,37,112],"the":[4,20,33,43,53,68,74,79,85,94,104,119],"problem":[5],"of":[6,12,24,67,89],"obtaining":[7],"stable":[8],"and":[9,60,78,87],"robust":[10],"oscillations":[11],"underactuated":[13],"mechanical":[14],"systems.":[15],"It":[16],"is":[17],"concerned":[18],"Hopf":[21,62,95],"bifurcation":[22,63],"analysis":[23],"a":[25,38],"Controlled":[26],"Inertia":[27],"Wheel":[28],"Inverted":[29],"Pendulum":[30],"(C-IWIP).":[31],"Firstly,":[32],"stabilization":[34],"was":[35],"achieved":[36],"control":[39,69,116],"law":[40],"based":[41],"on":[42],"Interconnection,":[44],"Damping,":[45],"Assignment":[46],"Passive":[47],"Based":[48],"Control":[49],"method":[50],"(IDA-PBC).":[51],"Interestingly,":[52],"considered":[54],"closed-loop":[55],"system":[56],"exhibits":[57],"both":[58],"supercritical":[59],"subcritical":[61],"for":[64],"certain":[65],"gains":[66],"law.":[70],"Secondly,":[71],"we":[72,114],"used":[73],"center":[75],"manifold":[76],"theorem":[77],"normal":[80],"form":[81],"technique":[82],"to":[83,102,109],"study":[84],"stability":[86],"instability":[88],"limit":[90,128],"cycles":[91],"emerging":[92],"from":[93],"bifurcation.":[96],"Finally,":[97],"numerical":[98],"simulations":[99],"were":[100],"conducted":[101],"validate":[103],"analytical":[105],"results":[106],"in":[107],"order":[108],"prove":[110],"that":[111],"IDA-PBC":[113],"can":[115],"not":[117],"only":[118],"unstable":[120],"equilibrium":[121],"but":[122],"also":[123],"some":[124],"trajectories":[125],"such":[126],"as":[127],"cycles.":[129]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":3},{"year":2018,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2017-07-31T00:00:00"}