{"id":"https://openalex.org/W2035309264","doi":"https://doi.org/10.1137/070698580","title":"Symbolic Models for Nonlinear Control Systems: Alternating Approximate Bisimulations","display_name":"Symbolic Models for Nonlinear Control Systems: Alternating Approximate Bisimulations","publication_year":2009,"publication_date":"2009-01-01","ids":{"openalex":"https://openalex.org/W2035309264","doi":"https://doi.org/10.1137/070698580","mag":"2035309264"},"language":"en","primary_location":{"id":"doi:10.1137/070698580","is_oa":false,"landing_page_url":"https://doi.org/10.1137/070698580","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Control and Optimization","raw_type":"journal-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/A5084720300","display_name":"Giordano Pola","orcid":"https://orcid.org/0000-0002-2213-6051"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Giordano Pola","raw_affiliation_strings":["pola@ee.ucla.edu and tabuada@ee.ucla.edu#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"pola@ee.ucla.edu and tabuada@ee.ucla.edu#TAB#","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5047674203","display_name":"Paulo Tabuada","orcid":"https://orcid.org/0000-0002-3417-0951"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Paulo Tabuada","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":11.8703,"has_fulltext":false,"cited_by_count":161,"citation_normalized_percentile":{"value":0.99020573,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":100},"biblio":{"volume":"48","issue":"2","first_page":"719","last_page":"733"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11125","display_name":"Petri Nets in System Modeling","score":0.9991000294685364,"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"}},"topics":[{"id":"https://openalex.org/T11125","display_name":"Petri Nets in System Modeling","score":0.9991000294685364,"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/T10142","display_name":"Formal Methods in Verification","score":0.9983000159263611,"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/T12772","display_name":"Control and Stability of Dynamical Systems","score":0.998199999332428,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.6067660450935364},{"id":"https://openalex.org/keywords/context","display_name":"Context (archaeology)","score":0.588169515132904},{"id":"https://openalex.org/keywords/bisimulation","display_name":"Bisimulation","score":0.5554662942886353},{"id":"https://openalex.org/keywords/controller","display_name":"Controller (irrigation)","score":0.5497671365737915},{"id":"https://openalex.org/keywords/symbolic-trajectory-evaluation","display_name":"Symbolic trajectory evaluation","score":0.5340425372123718},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5198769569396973},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5099145174026489},{"id":"https://openalex.org/keywords/symbolic-data-analysis","display_name":"Symbolic data analysis","score":0.4565657079219818},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.4479583203792572},{"id":"https://openalex.org/keywords/supervisory-control","display_name":"Supervisory control","score":0.4413449764251709},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.43951311707496643},{"id":"https://openalex.org/keywords/the-symbolic","display_name":"The Symbolic","score":0.4251480996608734},{"id":"https://openalex.org/keywords/control-system","display_name":"Control system","score":0.4165270924568176},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3748680353164673},{"id":"https://openalex.org/keywords/model-checking","display_name":"Model checking","score":0.20873013138771057},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.15838205814361572}],"concepts":[{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.6067660450935364},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.588169515132904},{"id":"https://openalex.org/C135315306","wikidata":"https://www.wikidata.org/wiki/Q866364","display_name":"Bisimulation","level":2,"score":0.5554662942886353},{"id":"https://openalex.org/C203479927","wikidata":"https://www.wikidata.org/wiki/Q5165939","display_name":"Controller (irrigation)","level":2,"score":0.5497671365737915},{"id":"https://openalex.org/C23123167","wikidata":"https://www.wikidata.org/wiki/Q7661193","display_name":"Symbolic trajectory evaluation","level":3,"score":0.5340425372123718},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5198769569396973},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5099145174026489},{"id":"https://openalex.org/C65620979","wikidata":"https://www.wikidata.org/wiki/Q7661176","display_name":"Symbolic data analysis","level":2,"score":0.4565657079219818},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.4479583203792572},{"id":"https://openalex.org/C92991967","wikidata":"https://www.wikidata.org/wiki/Q7644329","display_name":"Supervisory control","level":3,"score":0.4413449764251709},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.43951311707496643},{"id":"https://openalex.org/C2776095079","wikidata":"https://www.wikidata.org/wiki/Q489538","display_name":"The Symbolic","level":2,"score":0.4251480996608734},{"id":"https://openalex.org/C17500928","wikidata":"https://www.wikidata.org/wiki/Q959968","display_name":"Control system","level":2,"score":0.4165270924568176},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3748680353164673},{"id":"https://openalex.org/C110251889","wikidata":"https://www.wikidata.org/wiki/Q1569697","display_name":"Model checking","level":2,"score":0.20873013138771057},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.15838205814361572},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"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/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","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/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.0},{"id":"https://openalex.org/C119599485","wikidata":"https://www.wikidata.org/wiki/Q43035","display_name":"Electrical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"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/C11171543","wikidata":"https://www.wikidata.org/wiki/Q41630","display_name":"Psychoanalysis","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/070698580","is_oa":false,"landing_page_url":"https://doi.org/10.1137/070698580","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Control and Optimization","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G5761302642","display_name":"CAREER:     Automated Synthesis of Embedded Control Software","funder_award_id":"0717188","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6671297155","display_name":null,"funder_award_id":"CAREER","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":36,"referenced_works":["https://openalex.org/W27464976","https://openalex.org/W55814457","https://openalex.org/W1500294907","https://openalex.org/W1503973138","https://openalex.org/W1507306347","https://openalex.org/W1525512650","https://openalex.org/W1553335074","https://openalex.org/W1569692898","https://openalex.org/W1586568018","https://openalex.org/W1586805319","https://openalex.org/W1726255445","https://openalex.org/W1972945640","https://openalex.org/W1979349468","https://openalex.org/W1995691455","https://openalex.org/W2000086176","https://openalex.org/W2006118386","https://openalex.org/W2011979623","https://openalex.org/W2044323243","https://openalex.org/W2054099039","https://openalex.org/W2055960145","https://openalex.org/W2060375000","https://openalex.org/W2079042739","https://openalex.org/W2085838366","https://openalex.org/W2101508170","https://openalex.org/W2107889076","https://openalex.org/W2109080678","https://openalex.org/W2115042355","https://openalex.org/W2117079884","https://openalex.org/W2117218135","https://openalex.org/W2130578594","https://openalex.org/W2151136609","https://openalex.org/W2153026088","https://openalex.org/W2159461839","https://openalex.org/W2912462169","https://openalex.org/W2913459036","https://openalex.org/W2950028064"],"related_works":["https://openalex.org/W2186150309","https://openalex.org/W1552151841","https://openalex.org/W2132514413","https://openalex.org/W2096406490","https://openalex.org/W1951895578","https://openalex.org/W131471094","https://openalex.org/W624889113","https://openalex.org/W1489085734","https://openalex.org/W130519657","https://openalex.org/W1710909947"],"abstract_inverted_index":{"Symbolic":[0],"models":[1,32,45],"are":[2],"abstract":[3],"descriptions":[4],"of":[5,13,30,49,55,73,76],"continuous":[6,14],"systems":[7,80,100,117],"in":[8,27,39,52],"which":[9],"symbols":[10],"represent":[11],"aggregates":[12],"states.":[15],"In":[16,42,85],"the":[17,28,47,53,66,71],"last":[18],"few":[19],"years":[20],"there":[21],"has":[22],"been":[23],"a":[24,34],"growing":[25],"interest":[26],"use":[29,48],"symbolic":[31,44,83,121],"as":[33],"tool":[35],"for":[36,62],"mitigating":[37],"complexity":[38],"control":[40,57,79,99,116],"design.":[41],"fact,":[43],"enable":[46],"well-known":[50],"algorithms":[51],"context":[54],"supervisory":[56],"and":[58,78],"algorithmic":[59],"game":[60],"theory":[61],"controller":[63],"synthesis.":[64],"Since":[65],"1990s":[67],"many":[68],"researchers":[69],"faced":[70],"problem":[72],"identifying":[74],"classes":[75],"dynamical":[77],"that":[81,110],"admit":[82,120],"models.":[84,122],"this":[86,93],"paper":[87],"we":[88],"make":[89],"further":[90],"progress":[91],"along":[92],"research":[94],"line":[95],"by":[96,102],"focusing":[97],"on":[98],"affected":[101],"disturbances.":[103],"Our":[104],"main":[105],"contribution":[106],"is":[107],"to":[108],"show":[109],"incrementally":[111],"globally":[112],"asymptotically":[113],"stable":[114],"nonlinear":[115],"with":[118],"disturbances":[119]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":6},{"year":2023,"cited_by_count":6},{"year":2022,"cited_by_count":6},{"year":2021,"cited_by_count":14},{"year":2020,"cited_by_count":10},{"year":2019,"cited_by_count":7},{"year":2018,"cited_by_count":9},{"year":2017,"cited_by_count":13},{"year":2016,"cited_by_count":11},{"year":2015,"cited_by_count":6},{"year":2014,"cited_by_count":16},{"year":2013,"cited_by_count":13},{"year":2012,"cited_by_count":18}],"updated_date":"2026-08-12T21:12:35.861297","created_date":"2025-10-10T00:00:00"}
