{"id":"https://openalex.org/W2125711107","doi":"https://doi.org/10.1109/cdc.2007.4434911","title":"Symbolic models for nonlinear control systems using approximate bisimulation","display_name":"Symbolic models for nonlinear control systems using approximate bisimulation","publication_year":2007,"publication_date":"2007-01-01","ids":{"openalex":"https://openalex.org/W2125711107","doi":"https://doi.org/10.1109/cdc.2007.4434911","mag":"2125711107"},"language":"en","primary_location":{"id":"doi:10.1109/cdc.2007.4434911","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2007.4434911","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":"preprint","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/A5084720300","display_name":"Giordano Pola","orcid":"https://orcid.org/0000-0002-2213-6051"},"institutions":[{"id":"https://openalex.org/I161318765","display_name":"University of California, Los Angeles","ror":"https://ror.org/046rm7j60","country_code":"US","type":"education","lineage":["https://openalex.org/I161318765"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Giordano Pola","raw_affiliation_strings":["Department of Electrical Engineering, University of California, Los Angeles, Los Angeles, CA, USA","University of California\u2013Los Angeles"],"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, University of California, Los Angeles, Los Angeles, CA, USA","institution_ids":["https://openalex.org/I161318765"]},{"raw_affiliation_string":"University of California\u2013Los Angeles","institution_ids":["https://openalex.org/I161318765"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5081751699","display_name":"Antoine Girard","orcid":"https://orcid.org/0000-0002-4075-9041"},"institutions":[{"id":"https://openalex.org/I4210149092","display_name":"Laboratoire Jean Kuntzmann","ror":"https://ror.org/04ett5b41","country_code":"FR","type":"facility","lineage":["https://openalex.org/I106785703","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I4210149092","https://openalex.org/I899635006","https://openalex.org/I899635006"]},{"id":"https://openalex.org/I177483745","display_name":"Universit\u00e9 Joseph Fourier","ror":"https://ror.org/02aj0kh94","country_code":"FR","type":"education","lineage":["https://openalex.org/I177483745"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Antoine Girard","raw_affiliation_strings":["Laboratoire Jean Kuntzmann, Universit\u00e9 Joseph Fourier de Grenoble, Grenoble, France","Universit\u00e9 Joseph Fourier, Laboratoire Jean Kuntzmann, B.P. 53, 38041, Grenoble, France#TAB#"],"affiliations":[{"raw_affiliation_string":"Laboratoire Jean Kuntzmann, Universit\u00e9 Joseph Fourier de Grenoble, Grenoble, France","institution_ids":["https://openalex.org/I4210149092","https://openalex.org/I177483745"]},{"raw_affiliation_string":"Universit\u00e9 Joseph Fourier, Laboratoire Jean Kuntzmann, B.P. 53, 38041, Grenoble, France#TAB#","institution_ids":["https://openalex.org/I4210149092","https://openalex.org/I177483745"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5047674203","display_name":"Paulo Tabuada","orcid":"https://orcid.org/0000-0002-3417-0951"},"institutions":[{"id":"https://openalex.org/I161318765","display_name":"University of California, Los Angeles","ror":"https://ror.org/046rm7j60","country_code":"US","type":"education","lineage":["https://openalex.org/I161318765"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Paulo Tabuada","raw_affiliation_strings":["Department of Electrical Engineering, University of California, Los Angeles, Los Angeles, CA, USA","Department of Electrical Engineering, University of California at Los Angeles, 90095-1594, USA"],"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, University of California, Los Angeles, Los Angeles, CA, USA","institution_ids":["https://openalex.org/I161318765"]},{"raw_affiliation_string":"Department of Electrical Engineering, University of California at Los Angeles, 90095-1594, USA","institution_ids":["https://openalex.org/I161318765"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5084720300"],"corresponding_institution_ids":["https://openalex.org/I161318765"],"apc_list":null,"apc_paid":null,"fwci":7.9006,"has_fulltext":false,"cited_by_count":20,"citation_normalized_percentile":{"value":0.97173404,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":null,"issue":null,"first_page":"4656","last_page":"4661"},"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":0.9991000294685364,"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":0.9991000294685364,"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/T10142","display_name":"Formal Methods in Verification","score":0.996999979019165,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/T10904","display_name":"Embedded Systems Design Techniques","score":0.9954000115394592,"subfield":{"id":"https://openalex.org/subfields/1708","display_name":"Hardware and Architecture"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/bisimulation","display_name":"Bisimulation","score":0.7786575555801392},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6403990983963013},{"id":"https://openalex.org/keywords/interfacing","display_name":"Interfacing","score":0.5476996302604675},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.5365837216377258},{"id":"https://openalex.org/keywords/physical-system","display_name":"Physical system","score":0.531866192817688},{"id":"https://openalex.org/keywords/software","display_name":"Software","score":0.511487603187561},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.4771154224872589},{"id":"https://openalex.org/keywords/a-priori-and-a-posteriori","display_name":"A priori and a posteriori","score":0.46243512630462646},{"id":"https://openalex.org/keywords/equivalence","display_name":"Equivalence (formal languages)","score":0.4378364086151123},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.43729519844055176},{"id":"https://openalex.org/keywords/quantization","display_name":"Quantization (signal processing)","score":0.42147207260131836},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2790941596031189},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.2708776593208313},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.2353377640247345},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.11279502511024475}],"concepts":[{"id":"https://openalex.org/C135315306","wikidata":"https://www.wikidata.org/wiki/Q866364","display_name":"Bisimulation","level":2,"score":0.7786575555801392},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6403990983963013},{"id":"https://openalex.org/C2776303644","wikidata":"https://www.wikidata.org/wiki/Q1020499","display_name":"Interfacing","level":2,"score":0.5476996302604675},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.5365837216377258},{"id":"https://openalex.org/C116672817","wikidata":"https://www.wikidata.org/wiki/Q1454986","display_name":"Physical system","level":2,"score":0.531866192817688},{"id":"https://openalex.org/C2777904410","wikidata":"https://www.wikidata.org/wiki/Q7397","display_name":"Software","level":2,"score":0.511487603187561},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.4771154224872589},{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.46243512630462646},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.4378364086151123},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.43729519844055176},{"id":"https://openalex.org/C28855332","wikidata":"https://www.wikidata.org/wiki/Q198099","display_name":"Quantization (signal processing)","level":2,"score":0.42147207260131836},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2790941596031189},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2708776593208313},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.2353377640247345},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.11279502511024475},{"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/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","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/C9390403","wikidata":"https://www.wikidata.org/wiki/Q3966","display_name":"Computer hardware","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1109/cdc.2007.4434911","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2007.4434911","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"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.130.8481","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.130.8481","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.ee.ucla.edu/~pola/publications/Pola_CDC2007a.pdf","raw_type":"text"},{"id":"pmh:oai:HAL:hal-00307012v1","is_oa":false,"landing_page_url":"https://hal.science/hal-00307012","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"CDC - 46th IEEE Conference on Decision and Control, Dec 2007, New Orleans, LA, United States. pp.4656-4661, ⟨10.1109/CDC.2007.4434911⟩","raw_type":"Conference papers"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W27464976","https://openalex.org/W258022877","https://openalex.org/W1500294907","https://openalex.org/W1503973138","https://openalex.org/W1547562281","https://openalex.org/W1979349468","https://openalex.org/W2000086176","https://openalex.org/W2011979623","https://openalex.org/W2044323243","https://openalex.org/W2054099039","https://openalex.org/W2060375000","https://openalex.org/W2079042739","https://openalex.org/W2117079884","https://openalex.org/W2130578594","https://openalex.org/W2130590906","https://openalex.org/W2146156468"],"related_works":["https://openalex.org/W2136647108","https://openalex.org/W2350029007","https://openalex.org/W2152662857","https://openalex.org/W1965180958","https://openalex.org/W1973428399","https://openalex.org/W2182594080","https://openalex.org/W2484987020","https://openalex.org/W2017757432","https://openalex.org/W2047994557","https://openalex.org/W3097229793"],"abstract_inverted_index":{"Control":[0],"systems":[1,54],"are":[2,24,33,59,84,161],"usually":[3],"modeled":[4],"by":[5,15],"differential":[6],"equations":[7],"describing":[8,52],"how":[9],"physical":[10,30,43,119],"phenomena":[11],"can":[12,146,175],"be":[13,147,176],"influenced":[14],"certain":[16],"control":[17,53,110,133],"parameters":[18],"or":[19],"inputs.":[20,185],"Although":[21],"these":[22,81],"models":[23,57,83,91,174],"very":[25],"powerful":[26],"when":[27],"dealing":[28],"with":[29,117,142],"phenomena,":[31],"they":[32,101],"less":[34],"suitable":[35,181],"to":[36,70,96,106,139],"describe":[37,97],"software":[38,98,113],"and":[39,99,114,163],"hardware":[40,115],"interfacing":[41],"the":[42,63,77,86,90,118,165,172,184],"world.":[44,120],"This":[45],"has":[46],"spurred":[47],"a":[48,103,143,180],"recent":[49],"interest":[50],"in":[51,76,93,111,158],"through":[55],"symbolic":[56,82,140,173],"that":[58,126,145,153],"abstract":[60],"descriptions":[61],"of":[62,73,85,89,109,168,183],"continuous":[64,74,78],"dynamics,":[65],"where":[66],"each":[67],"\"symbol\"":[68],"corresponds":[69],"an":[71],"\"aggregate\"":[72],"states":[75],"model.":[79],"Since":[80],"same":[87],"nature":[88],"used":[92],"computer":[94],"science":[95],"hardware,":[100],"provided":[102],"unified":[104],"language":[105],"study":[107],"problems":[108],"which":[112,159],"interact":[116],"In":[121],"this":[122],"paper":[123],"we":[124],"show":[125,152],"every":[127],"incrementally":[128],"globally":[129],"asymptotically":[130],"stable":[131],"nonlinear":[132],"system":[134],"is":[135],"approximately":[136],"equivalent":[137],"(bisimilar)":[138],"model":[141],"precision":[144],"chosen":[148],"a-priori.":[149],"We":[150],"also":[151],"for":[154],"digital":[155],"controlled":[156],"systems,":[157],"inputs":[160],"piecewise-constant,":[162],"under":[164],"stronger":[166],"assumption":[167],"incremental":[169],"input-to-state":[170],"stability,":[171],"obtained,":[177],"based":[178],"on":[179],"quantization":[182]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2014,"cited_by_count":2},{"year":2012,"cited_by_count":2}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}