{"id":"https://openalex.org/W3010680740","doi":"https://doi.org/10.1109/cdc40024.2019.9028932","title":"Safety Verification of Nonlinear Polynomial System via Occupation Measures","display_name":"Safety Verification of Nonlinear Polynomial System via Occupation Measures","publication_year":2019,"publication_date":"2019-12-01","ids":{"openalex":"https://openalex.org/W3010680740","doi":"https://doi.org/10.1109/cdc40024.2019.9028932","mag":"3010680740"},"language":"en","primary_location":{"id":"doi:10.1109/cdc40024.2019.9028932","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc40024.2019.9028932","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2019 IEEE 58th Conference on Decision and Control (CDC)","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/A5101404831","display_name":"Ximing Chen","orcid":"https://orcid.org/0000-0001-8670-8031"},"institutions":[{"id":"https://openalex.org/I79576946","display_name":"University of Pennsylvania","ror":"https://ror.org/00b30xv10","country_code":"US","type":"education","lineage":["https://openalex.org/I79576946"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Ximing Chen","raw_affiliation_strings":["Department of Electrical and Systems Engineering, University of Pennsylvania, Philadelphia, PA"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Systems Engineering, University of Pennsylvania, Philadelphia, PA","institution_ids":["https://openalex.org/I79576946"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5011696469","display_name":"Shaoru Chen","orcid":"https://orcid.org/0000-0001-9416-0627"},"institutions":[{"id":"https://openalex.org/I79576946","display_name":"University of Pennsylvania","ror":"https://ror.org/00b30xv10","country_code":"US","type":"education","lineage":["https://openalex.org/I79576946"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Shaoru Chen","raw_affiliation_strings":["Department of Electrical and Systems Engineering, University of Pennsylvania, Philadelphia, PA"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Systems Engineering, University of Pennsylvania, Philadelphia, PA","institution_ids":["https://openalex.org/I79576946"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5057261458","display_name":"V\u00edctor M. Preciado","orcid":"https://orcid.org/0000-0001-9998-8730"},"institutions":[{"id":"https://openalex.org/I79576946","display_name":"University of Pennsylvania","ror":"https://ror.org/00b30xv10","country_code":"US","type":"education","lineage":["https://openalex.org/I79576946"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Victor M. Preciado","raw_affiliation_strings":["Department of Electrical and Systems Engineering, University of Pennsylvania, Philadelphia, PA"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Systems Engineering, University of Pennsylvania, Philadelphia, PA","institution_ids":["https://openalex.org/I79576946"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5101404831"],"corresponding_institution_ids":["https://openalex.org/I79576946"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.23177865,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"31","issue":null,"first_page":"1159","last_page":"1164"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10142","display_name":"Formal Methods in Verification","score":0.9994999766349792,"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/T10142","display_name":"Formal Methods in Verification","score":0.9994999766349792,"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/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9733999967575073,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10791","display_name":"Advanced Control Systems Optimization","score":0.9542999863624573,"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/hierarchy","display_name":"Hierarchy","score":0.6814353466033936},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6766482591629028},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.6412156820297241},{"id":"https://openalex.org/keywords/context","display_name":"Context (archaeology)","score":0.6366293430328369},{"id":"https://openalex.org/keywords/monotonic-function","display_name":"Monotonic function","score":0.5736919045448303},{"id":"https://openalex.org/keywords/semidefinite-programming","display_name":"Semidefinite programming","score":0.500009298324585},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.48146048188209534},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4598129689693451},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4491892457008362},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.44214412569999695},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.4283137321472168},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.2797206938266754},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.14629912376403809}],"concepts":[{"id":"https://openalex.org/C31170391","wikidata":"https://www.wikidata.org/wiki/Q188619","display_name":"Hierarchy","level":2,"score":0.6814353466033936},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6766482591629028},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.6412156820297241},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.6366293430328369},{"id":"https://openalex.org/C72169020","wikidata":"https://www.wikidata.org/wiki/Q194404","display_name":"Monotonic function","level":2,"score":0.5736919045448303},{"id":"https://openalex.org/C101901036","wikidata":"https://www.wikidata.org/wiki/Q2269096","display_name":"Semidefinite programming","level":2,"score":0.500009298324585},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.48146048188209534},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4598129689693451},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4491892457008362},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.44214412569999695},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.4283137321472168},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2797206938266754},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.14629912376403809},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C34447519","wikidata":"https://www.wikidata.org/wiki/Q179522","display_name":"Market economy","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/cdc40024.2019.9028932","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc40024.2019.9028932","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2019 IEEE 58th Conference on Decision and Control (CDC)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":34,"referenced_works":["https://openalex.org/W404764422","https://openalex.org/W1498519438","https://openalex.org/W1540897666","https://openalex.org/W1553812175","https://openalex.org/W1563147540","https://openalex.org/W1582811927","https://openalex.org/W1598855039","https://openalex.org/W1607353007","https://openalex.org/W1987679122","https://openalex.org/W1990337648","https://openalex.org/W2000714860","https://openalex.org/W2024249108","https://openalex.org/W2033118636","https://openalex.org/W2036031393","https://openalex.org/W2045814149","https://openalex.org/W2052446317","https://openalex.org/W2055088712","https://openalex.org/W2057789475","https://openalex.org/W2099354898","https://openalex.org/W2106993639","https://openalex.org/W2123951162","https://openalex.org/W2131441094","https://openalex.org/W2133404041","https://openalex.org/W2319348511","https://openalex.org/W2536620281","https://openalex.org/W2921936808","https://openalex.org/W2964208569","https://openalex.org/W2964320632","https://openalex.org/W3022938717","https://openalex.org/W4251032486","https://openalex.org/W4255442211","https://openalex.org/W6633104559","https://openalex.org/W6679392325","https://openalex.org/W6760463104"],"related_works":["https://openalex.org/W2077314575","https://openalex.org/W4315701745","https://openalex.org/W1990290471","https://openalex.org/W1983756092","https://openalex.org/W4380682190","https://openalex.org/W2005710836","https://openalex.org/W2102386043","https://openalex.org/W2945307361","https://openalex.org/W2116636209","https://openalex.org/W1774334694"],"abstract_inverted_index":{"In":[0,52],"this":[1,29,53,98],"paper,":[2],"we":[3,55,114],"introduce":[4],"a":[5,39,47,85],"flexible":[6],"notion":[7],"of":[8,35,49,60,87,118],"safety":[9],"verification":[10],"for":[11],"nonlinear":[12,36],"autonomous":[13],"systems":[14,37],"by":[15,46],"measuring":[16],"how":[17],"much":[18],"time":[19,61],"the":[20,32,58,64,68,78,81,95,106,110,116],"system":[21],"spends":[22],"in":[23,31,63,97],"given":[24],"unsafe":[25,43,65],"regions.":[26],"We":[27,76],"consider":[28],"problem":[30],"particular":[33],"case":[34],"with":[38],"polynomial":[40,50],"dynamics":[41],"and":[42],"regions":[44,66],"described":[45],"collection":[48],"inequalities.":[51],"context,":[54],"can":[56],"quantify":[57],"amount":[59],"spent":[62],"as":[67],"solution":[69,79,108],"to":[70,80,94,109],"an":[71],"infinite-dimensional":[72,82,111],"linear":[73],"program":[74],"(LP).":[75],"approximate":[77],"LP":[83],"using":[84,121],"hierarchy":[86,99],"finite-dimensional":[88],"semidefinite":[89],"programs":[90],"(SDPs).":[91],"The":[92],"solutions":[93],"SDPs":[96],"provide":[100],"monotonically":[101],"converging":[102],"upper":[103],"bounds":[104],"on":[105],"optimal":[107],"LP.":[112],"Finally,":[113],"validate":[115],"performance":[117],"our":[119],"framework":[120],"numerical":[122],"simulations.":[123]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}