{"id":"https://openalex.org/W2029926860","doi":"https://doi.org/10.1109/cdc.2007.4434950","title":"On the computation of local invariant sets for nonlinear systems","display_name":"On the computation of local invariant sets for nonlinear systems","publication_year":2007,"publication_date":"2007-01-01","ids":{"openalex":"https://openalex.org/W2029926860","doi":"https://doi.org/10.1109/cdc.2007.4434950","mag":"2029926860"},"language":"en","primary_location":{"id":"doi:10.1109/cdc.2007.4434950","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2007.4434950","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2007 46th IEEE Conference on Decision and Control","raw_type":"proceedings-article"},"type":"article","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/A5035566586","display_name":"Mirko Fiacchini","orcid":"https://orcid.org/0000-0002-3601-0302"},"institutions":[{"id":"https://openalex.org/I79238269","display_name":"Universidad de Sevilla","ror":"https://ror.org/03yxnpp24","country_code":"ES","type":"education","lineage":["https://openalex.org/I79238269"]}],"countries":["ES"],"is_corresponding":true,"raw_author_name":"M. Fiacchini","raw_affiliation_strings":["Departamento de Ingenier\u00eda de Sistemas y Autom\u00e1tica, Escuela Superior de Ingenieros, Universidad de Sevilla, Seville, Spain","Univ. de Sevilla, Sevilla"],"affiliations":[{"raw_affiliation_string":"Departamento de Ingenier\u00eda de Sistemas y Autom\u00e1tica, Escuela Superior de Ingenieros, Universidad de Sevilla, Seville, Spain","institution_ids":["https://openalex.org/I79238269"]},{"raw_affiliation_string":"Univ. de Sevilla, Sevilla","institution_ids":["https://openalex.org/I79238269"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5014219486","display_name":"Teodoro \u00c1lamo","orcid":"https://orcid.org/0000-0002-0623-8146"},"institutions":[{"id":"https://openalex.org/I79238269","display_name":"Universidad de Sevilla","ror":"https://ror.org/03yxnpp24","country_code":"ES","type":"education","lineage":["https://openalex.org/I79238269"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"T. Alamo","raw_affiliation_strings":["Departamento de Ingenier\u00eda de Sistemas y Autom\u00e1tica, Escuela Superior de Ingenieros, Universidad de Sevilla, Seville, Spain","Univ. de Sevilla, Sevilla"],"affiliations":[{"raw_affiliation_string":"Departamento de Ingenier\u00eda de Sistemas y Autom\u00e1tica, Escuela Superior de Ingenieros, Universidad de Sevilla, Seville, Spain","institution_ids":["https://openalex.org/I79238269"]},{"raw_affiliation_string":"Univ. de Sevilla, Sevilla","institution_ids":["https://openalex.org/I79238269"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5089211717","display_name":"Eduardo F. Camacho","orcid":"https://orcid.org/0000-0002-9636-5666"},"institutions":[{"id":"https://openalex.org/I79238269","display_name":"Universidad de Sevilla","ror":"https://ror.org/03yxnpp24","country_code":"ES","type":"education","lineage":["https://openalex.org/I79238269"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"E.F. Camacho","raw_affiliation_strings":["Departamento de Ingenier\u00eda de Sistemas y Autom\u00e1tica, Escuela Superior de Ingenieros, Universidad de Sevilla, Seville, Spain","Univ. de Sevilla, Sevilla"],"affiliations":[{"raw_affiliation_string":"Departamento de Ingenier\u00eda de Sistemas y Autom\u00e1tica, Escuela Superior de Ingenieros, Universidad de Sevilla, Seville, Spain","institution_ids":["https://openalex.org/I79238269"]},{"raw_affiliation_string":"Univ. de Sevilla, Sevilla","institution_ids":["https://openalex.org/I79238269"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5035566586"],"corresponding_institution_ids":["https://openalex.org/I79238269"],"apc_list":null,"apc_paid":null,"fwci":1.69506945,"has_fulltext":false,"cited_by_count":12,"citation_normalized_percentile":{"value":0.86988381,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":null,"issue":null,"first_page":"3989","last_page":"3994"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10791","display_name":"Advanced Control Systems Optimization","score":1.0,"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/T10791","display_name":"Advanced Control Systems Optimization","score":1.0,"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/T11236","display_name":"Control Systems and Identification","score":0.9954000115394592,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9948999881744385,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/invariant","display_name":"Invariant (physics)","score":0.7334954738616943},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6836039423942566},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.5772454142570496},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5130523443222046},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.49571263790130615},{"id":"https://openalex.org/keywords/exponential-stability","display_name":"Exponential stability","score":0.4662783145904541},{"id":"https://openalex.org/keywords/lti-system-theory","display_name":"LTI system theory","score":0.44121307134628296},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4333272874355316},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.41304126381874084},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.37587693333625793},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3713567852973938},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.2851487398147583},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.24008595943450928},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.15783533453941345},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.1401636302471161},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.1205534040927887}],"concepts":[{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.7334954738616943},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6836039423942566},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.5772454142570496},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5130523443222046},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.49571263790130615},{"id":"https://openalex.org/C167964875","wikidata":"https://www.wikidata.org/wiki/Q17011487","display_name":"Exponential stability","level":3,"score":0.4662783145904541},{"id":"https://openalex.org/C87698059","wikidata":"https://www.wikidata.org/wiki/Q1808960","display_name":"LTI system theory","level":3,"score":0.44121307134628296},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4333272874355316},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.41304126381874084},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.37587693333625793},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3713567852973938},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.2851487398147583},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.24008595943450928},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.15783533453941345},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.1401636302471161},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.1205534040927887},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/cdc.2007.4434950","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2007.4434950","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2007 46th IEEE Conference on Decision and Control","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":19,"referenced_works":["https://openalex.org/W81972919","https://openalex.org/W292508636","https://openalex.org/W1518078339","https://openalex.org/W1977320922","https://openalex.org/W1978956894","https://openalex.org/W1981367768","https://openalex.org/W1988705663","https://openalex.org/W1998915836","https://openalex.org/W2001041931","https://openalex.org/W2003001623","https://openalex.org/W2032155434","https://openalex.org/W2044475509","https://openalex.org/W2101138302","https://openalex.org/W2127580532","https://openalex.org/W2152754654","https://openalex.org/W2162269500","https://openalex.org/W2171505650","https://openalex.org/W2567281007","https://openalex.org/W3102923851"],"related_works":["https://openalex.org/W4231775656","https://openalex.org/W2046435967","https://openalex.org/W2383646825","https://openalex.org/W1593898832","https://openalex.org/W2371018915","https://openalex.org/W2354191502","https://openalex.org/W1972225038","https://openalex.org/W2756324413","https://openalex.org/W2142048021","https://openalex.org/W3169827016"],"abstract_inverted_index":{"The":[0,131],"importance":[1],"of":[2,17,40,74,86],"invariant":[3,42,67,119,141],"sets":[4],"in":[5,121],"control":[6,32],"is":[7,45,134,147],"due":[8],"to":[9,37,128,136],"the":[10,18,38,47,91,144],"fact":[11,92],"that":[12,80,93],"they":[13],"define":[14],"a":[15,61,65,117,138],"region":[16],"space":[19],"where":[20],"stability,":[21],"and":[22,90],"potentially":[23],"asymptotic":[24],"convergence,":[25],"are":[26,35,78],"assured.":[27],"For":[28],"this":[29],"reason":[30],"many":[31],"design":[33],"strategies":[34,53],"related":[36],"computation":[39],"an":[41,113],"set.":[43],"This":[44,58],"particularly":[46],"case":[48],"for":[49,63,69,115],"receding":[50],"horizon":[51],"based":[52],"as":[54,84,101],"model":[55],"predictive":[56],"control.":[57],"paper":[59],"presents":[60],"method":[62],"computing":[64,116],"convex":[66,88],"set":[68,120,142],"nonlinear":[70,96,145],"systems.":[71],"Using":[72],"properties":[73],"D.C.":[75,102],"functions,":[76,89,103],"which":[77,122],"functions":[79],"can":[81,98],"be":[82,99,129],"expressed":[83,100],"difference":[85],"two":[87],"any":[94],"continuous":[95],"function":[97],"or,":[104],"at":[105],"least,":[106],"well":[107],"approximated":[108],"by":[109],"them,":[110],"we":[111],"propose":[112],"algorithm":[114],"polyhedral":[118],"no":[123],"global":[124],"optimization":[125],"problem":[126],"has":[127],"solved.":[130],"proposed":[132],"strategy":[133],"guaranteed":[135],"provide":[137],"non-empty":[139],"local":[140],"provided":[143],"system":[146],"locally":[148],"stable.":[149]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":3},{"year":2014,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-25T21:42:39.735039","created_date":"2025-10-10T00:00:00"}