{"id":"https://openalex.org/W2038498011","doi":"https://doi.org/10.1145/2629424","title":"Exact Safety Verification of Hybrid Systems Based on Bilinear SOS Representation","display_name":"Exact Safety Verification of Hybrid Systems Based on Bilinear SOS Representation","publication_year":2015,"publication_date":"2015-01-21","ids":{"openalex":"https://openalex.org/W2038498011","doi":"https://doi.org/10.1145/2629424","mag":"2038498011"},"language":"en","primary_location":{"id":"doi:10.1145/2629424","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2629424","pdf_url":null,"source":{"id":"https://openalex.org/S136160450","display_name":"ACM Transactions on Embedded Computing Systems","issn_l":"1539-9087","issn":["1539-9087","1558-3465"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Embedded Computing Systems","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/A5103026076","display_name":"Zhengfeng Yang","orcid":"https://orcid.org/0000-0001-6316-1723"},"institutions":[{"id":"https://openalex.org/I66867065","display_name":"East China Normal University","ror":"https://ror.org/02n96ep67","country_code":"CN","type":"education","lineage":["https://openalex.org/I66867065"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhengfeng Yang","raw_affiliation_strings":["East China Normal University, Shanghai, China","East China Normal University, SHANGHAI, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"East China Normal University, Shanghai, China","institution_ids":["https://openalex.org/I66867065"]},{"raw_affiliation_string":"East China Normal University, SHANGHAI, China","institution_ids":["https://openalex.org/I66867065"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100703491","display_name":"Wang Lin","orcid":"https://orcid.org/0000-0003-4467-2186"},"institutions":[{"id":"https://openalex.org/I146620803","display_name":"Wenzhou University","ror":"https://ror.org/020hxh324","country_code":"CN","type":"education","lineage":["https://openalex.org/I146620803"]},{"id":"https://openalex.org/I66867065","display_name":"East China Normal University","ror":"https://ror.org/02n96ep67","country_code":"CN","type":"education","lineage":["https://openalex.org/I66867065"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Wang Lin","raw_affiliation_strings":["Wenzhou University and East China Normal University, China","Wenzhou University and East China Normal University, China#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Wenzhou University and East China Normal University, China","institution_ids":["https://openalex.org/I146620803","https://openalex.org/I66867065"]},{"raw_affiliation_string":"Wenzhou University and East China Normal University, China#TAB#","institution_ids":["https://openalex.org/I66867065"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100688016","display_name":"Min Wu","orcid":"https://orcid.org/0000-0002-2776-8218"},"institutions":[{"id":"https://openalex.org/I66867065","display_name":"East China Normal University","ror":"https://ror.org/02n96ep67","country_code":"CN","type":"education","lineage":["https://openalex.org/I66867065"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Min Wu","raw_affiliation_strings":["East China Normal University, Shanghai, China","East China Normal University, SHANGHAI, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"East China Normal University, Shanghai, China","institution_ids":["https://openalex.org/I66867065"]},{"raw_affiliation_string":"East China Normal University, SHANGHAI, China","institution_ids":["https://openalex.org/I66867065"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":4.8478,"has_fulltext":false,"cited_by_count":32,"citation_normalized_percentile":{"value":0.95374506,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"14","issue":"1","first_page":"1","last_page":"19"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10142","display_name":"Formal Methods in Verification","score":0.9993000030517578,"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":0.9993000030517578,"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/T10791","display_name":"Advanced Control Systems Optimization","score":0.9915000200271606,"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/T14083","display_name":"Extremum Seeking Control Systems","score":0.9735000133514404,"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/bilinear-interpolation","display_name":"Bilinear interpolation","score":0.6981825828552246},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6738201379776001},{"id":"https://openalex.org/keywords/solver","display_name":"Solver","score":0.6244167685508728},{"id":"https://openalex.org/keywords/hybrid-system","display_name":"Hybrid system","score":0.6030370593070984},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.5420210957527161},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5100734829902649},{"id":"https://openalex.org/keywords/symbolic-computation","display_name":"Symbolic computation","score":0.5008716583251953},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.48223575949668884},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.43673253059387207},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3749346137046814},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.36168286204338074},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3441818654537201},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.24291089177131653},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.138674795627594},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.08607670664787292}],"concepts":[{"id":"https://openalex.org/C205203396","wikidata":"https://www.wikidata.org/wiki/Q612143","display_name":"Bilinear interpolation","level":2,"score":0.6981825828552246},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6738201379776001},{"id":"https://openalex.org/C2778770139","wikidata":"https://www.wikidata.org/wiki/Q1966904","display_name":"Solver","level":2,"score":0.6244167685508728},{"id":"https://openalex.org/C50897621","wikidata":"https://www.wikidata.org/wiki/Q2665508","display_name":"Hybrid system","level":2,"score":0.6030370593070984},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.5420210957527161},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5100734829902649},{"id":"https://openalex.org/C110812573","wikidata":"https://www.wikidata.org/wiki/Q175515","display_name":"Symbolic computation","level":2,"score":0.5008716583251953},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.48223575949668884},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.43673253059387207},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3749346137046814},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.36168286204338074},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3441818654537201},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.24291089177131653},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.138674795627594},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.08607670664787292},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","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/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.0},{"id":"https://openalex.org/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","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}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1145/2629424","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2629424","pdf_url":null,"source":{"id":"https://openalex.org/S136160450","display_name":"ACM Transactions on Embedded Computing Systems","issn_l":"1539-9087","issn":["1539-9087","1558-3465"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Embedded Computing Systems","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.761.7358","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.761.7358","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/1201.4219.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G562285834","display_name":"\u57fa\u4e8e\u7b26\u53f7-\u6570\u503c\u6df7\u5408\u8ba1\u7b97\u7684\u7ebf\u6027\u5fae\u5206-\u5dee\u5206\u65b9\u7a0b\u7684\u7406\u8bba\u53ca\u7b97\u6cd5\u7814\u7a76","funder_award_id":"11371143","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6188726043","display_name":null,"funder_award_id":"LQ13F020041 and LY13F030005","funder_id":"https://openalex.org/F4320338464","funder_display_name":"Natural Science Foundation of Zhejiang Province"}],"funders":[{"id":"https://openalex.org/F4320309370","display_name":"University of Pennsylvania","ror":"https://ror.org/00b30xv10"},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320338464","display_name":"Natural Science Foundation of Zhejiang Province","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":38,"referenced_works":["https://openalex.org/W1479840958","https://openalex.org/W1523211942","https://openalex.org/W1552875110","https://openalex.org/W1559197676","https://openalex.org/W1568518466","https://openalex.org/W1573837784","https://openalex.org/W1607353007","https://openalex.org/W1967091946","https://openalex.org/W1967184028","https://openalex.org/W1967969202","https://openalex.org/W1979646426","https://openalex.org/W1981745143","https://openalex.org/W1982216340","https://openalex.org/W1986264093","https://openalex.org/W1994475353","https://openalex.org/W1999629321","https://openalex.org/W2013621063","https://openalex.org/W2016389104","https://openalex.org/W2036031393","https://openalex.org/W2047246610","https://openalex.org/W2053812965","https://openalex.org/W2053849443","https://openalex.org/W2066257627","https://openalex.org/W2076229375","https://openalex.org/W2083862837","https://openalex.org/W2087749124","https://openalex.org/W2093554898","https://openalex.org/W2106606898","https://openalex.org/W2111847594","https://openalex.org/W2131395649","https://openalex.org/W2131441094","https://openalex.org/W2142283990","https://openalex.org/W2147340401","https://openalex.org/W2150529683","https://openalex.org/W2154128151","https://openalex.org/W2155724501","https://openalex.org/W2911280679","https://openalex.org/W3150028190"],"related_works":["https://openalex.org/W2963810603","https://openalex.org/W2132921246","https://openalex.org/W1693001741","https://openalex.org/W2049100639","https://openalex.org/W1973033761","https://openalex.org/W1965116753","https://openalex.org/W1515890570","https://openalex.org/W1980363707","https://openalex.org/W3105877772","https://openalex.org/W3021364813"],"abstract_inverted_index":{"In":[0],"this":[1],"article,":[2],"we":[3],"address":[4],"the":[5,46,53,75,87],"problem":[6],"of":[7,10,25,32,77,89],"safety":[8],"verification":[9],"nonlinear":[11],"hybrid":[12,15,26,34],"systems.":[13],"A":[14],"symbolic-numeric":[16],"method":[17],"is":[18],"presented":[19],"to":[20,64,85],"compute":[21],"exact":[22,66],"inequality":[23],"invariants":[24,31,68],"systems":[27],"efficiently.":[28],"Some":[29],"numerical":[30],"a":[33,41],"system":[35],"can":[36],"be":[37],"obtained":[38],"by":[39],"solving":[40],"bilinear":[42],"SOS":[43],"programming":[44],"via":[45],"PENBMI":[47],"solver":[48],"or":[49],"iterative":[50],"method,":[51],"then":[52],"modified":[54],"Newton":[55],"refinement":[56],"and":[57],"rational":[58,70],"vector":[59],"recovery":[60],"techniques":[61],"are":[62,83],"applied":[63],"obtain":[65],"polynomial":[67],"with":[69],"coefficients,":[71],"which":[72],"exactly":[73],"satisfy":[74],"conditions":[76],"invariants.":[78],"Experiments":[79],"on":[80],"some":[81],"benchmarks":[82],"given":[84],"illustrate":[86],"efficiency":[88],"our":[90],"algorithm.":[91]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":8},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":2}],"updated_date":"2026-08-26T07:47:46.906454","created_date":"2025-10-10T00:00:00"}