{"id":"https://openalex.org/W2528933731","doi":"https://doi.org/10.1109/tac.2016.2615599","title":"Reach-Avoid Verification for Nonlinear Systems Based on Boundary Analysis","display_name":"Reach-Avoid Verification for Nonlinear Systems Based on Boundary Analysis","publication_year":2016,"publication_date":"2016-10-06","ids":{"openalex":"https://openalex.org/W2528933731","doi":"https://doi.org/10.1109/tac.2016.2615599","mag":"2528933731"},"language":"en","primary_location":{"id":"doi:10.1109/tac.2016.2615599","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2016.2615599","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Automatic Control","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/A5100781916","display_name":"Xue Bai","orcid":"https://orcid.org/0000-0001-9717-846X"},"institutions":[{"id":"https://openalex.org/I129877168","display_name":"Carl von Ossietzky Universit\u00e4t Oldenburg","ror":"https://ror.org/033n9gh91","country_code":"DE","type":"education","lineage":["https://openalex.org/I129877168"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Bai Xue","raw_affiliation_strings":["Carl von Ossietzky Universit\u00e4t Oldenburg, Germany"],"affiliations":[{"raw_affiliation_string":"Carl von Ossietzky Universit\u00e4t Oldenburg, Germany","institution_ids":["https://openalex.org/I129877168"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5054946593","display_name":"Arvind Easwaran","orcid":"https://orcid.org/0000-0002-9628-3847"},"institutions":[{"id":"https://openalex.org/I172675005","display_name":"Nanyang Technological University","ror":"https://ror.org/02e7b5302","country_code":"SG","type":"education","lineage":["https://openalex.org/I172675005"]}],"countries":["SG"],"is_corresponding":false,"raw_author_name":"Arvind Easwaran","raw_affiliation_strings":["Nanyang Technological University, Singapore"],"affiliations":[{"raw_affiliation_string":"Nanyang Technological University, Singapore","institution_ids":["https://openalex.org/I172675005"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5066515999","display_name":"Nam\u2010Joon Cho","orcid":"https://orcid.org/0000-0002-8692-8955"},"institutions":[{"id":"https://openalex.org/I172675005","display_name":"Nanyang Technological University","ror":"https://ror.org/02e7b5302","country_code":"SG","type":"education","lineage":["https://openalex.org/I172675005"]}],"countries":["SG"],"is_corresponding":false,"raw_author_name":"Nam-Joon Cho","raw_affiliation_strings":["Nanyang Technological University, Singapore"],"affiliations":[{"raw_affiliation_string":"Nanyang Technological University, Singapore","institution_ids":["https://openalex.org/I172675005"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5089746112","display_name":"Martin Fr\u00e4nzle","orcid":"https://orcid.org/0000-0002-9138-8340"},"institutions":[{"id":"https://openalex.org/I129877168","display_name":"Carl von Ossietzky Universit\u00e4t Oldenburg","ror":"https://ror.org/033n9gh91","country_code":"DE","type":"education","lineage":["https://openalex.org/I129877168"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Martin Franzle","raw_affiliation_strings":["Carl von Ossietzky Universit\u00e4t Oldenburg, Germany"],"affiliations":[{"raw_affiliation_string":"Carl von Ossietzky Universit\u00e4t Oldenburg, Germany","institution_ids":["https://openalex.org/I129877168"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5100781916"],"corresponding_institution_ids":["https://openalex.org/I129877168"],"apc_list":null,"apc_paid":null,"fwci":4.1817,"has_fulltext":false,"cited_by_count":33,"citation_normalized_percentile":{"value":0.94456421,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"62","issue":"7","first_page":"3518","last_page":"3523"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10142","display_name":"Formal Methods in Verification","score":0.9991999864578247,"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":0.9991999864578247,"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/T11697","display_name":"Numerical Methods and Algorithms","score":0.9948999881744385,"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/T11689","display_name":"Adversarial Robustness in Machine Learning","score":0.9897000193595886,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/reachability","display_name":"Reachability","score":0.7370753884315491},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.7103185653686523},{"id":"https://openalex.org/keywords/extrapolation","display_name":"Extrapolation","score":0.5921072363853455},{"id":"https://openalex.org/keywords/parametric-statistics","display_name":"Parametric statistics","score":0.5639973878860474},{"id":"https://openalex.org/keywords/set-operations","display_name":"Set operations","score":0.5284421443939209},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5167338252067566},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5078256726264954},{"id":"https://openalex.org/keywords/ellipsoid","display_name":"Ellipsoid","score":0.4915343225002289},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4534001052379608},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.44943323731422424},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4461899995803833},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.43787962198257446},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3435591459274292},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.14454934000968933}],"concepts":[{"id":"https://openalex.org/C136643341","wikidata":"https://www.wikidata.org/wiki/Q1361526","display_name":"Reachability","level":2,"score":0.7370753884315491},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.7103185653686523},{"id":"https://openalex.org/C132459708","wikidata":"https://www.wikidata.org/wiki/Q744069","display_name":"Extrapolation","level":2,"score":0.5921072363853455},{"id":"https://openalex.org/C117251300","wikidata":"https://www.wikidata.org/wiki/Q1849855","display_name":"Parametric statistics","level":2,"score":0.5639973878860474},{"id":"https://openalex.org/C2777168461","wikidata":"https://www.wikidata.org/wiki/Q42196253","display_name":"Set operations","level":3,"score":0.5284421443939209},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5167338252067566},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5078256726264954},{"id":"https://openalex.org/C57489055","wikidata":"https://www.wikidata.org/wiki/Q190046","display_name":"Ellipsoid","level":2,"score":0.4915343225002289},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4534001052379608},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.44943323731422424},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4461899995803833},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.43787962198257446},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3435591459274292},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.14454934000968933},{"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/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","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/C1276947","wikidata":"https://www.wikidata.org/wiki/Q333","display_name":"Astronomy","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tac.2016.2615599","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2016.2615599","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Automatic Control","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G557630777","display_name":null,"funder_award_id":"ARG/14015","funder_id":"https://openalex.org/F4320320766","funder_display_name":"Nanyang Technological University"}],"funders":[{"id":"https://openalex.org/F4320320766","display_name":"Nanyang Technological University","ror":"https://ror.org/02e7b5302"},{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"},{"id":"https://openalex.org/F4320324232","display_name":"RWTH Aachen University","ror":"https://ror.org/04xfq0f34"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W172589331","https://openalex.org/W216834189","https://openalex.org/W635879892","https://openalex.org/W1499853177","https://openalex.org/W1535866048","https://openalex.org/W1569692898","https://openalex.org/W1598855039","https://openalex.org/W1726255445","https://openalex.org/W2084859862","https://openalex.org/W2096326343","https://openalex.org/W2100081537","https://openalex.org/W2116364955","https://openalex.org/W2123357397","https://openalex.org/W2131332110","https://openalex.org/W2131441094","https://openalex.org/W2145201569","https://openalex.org/W2147936671","https://openalex.org/W2158451642","https://openalex.org/W4249492311","https://openalex.org/W6607093319","https://openalex.org/W6679885043"],"related_works":["https://openalex.org/W2127267268","https://openalex.org/W2156446763","https://openalex.org/W2136512912","https://openalex.org/W2067910792","https://openalex.org/W2150194458","https://openalex.org/W1968270095","https://openalex.org/W2143461633","https://openalex.org/W2889071233","https://openalex.org/W4321471459","https://openalex.org/W2220129715"],"abstract_inverted_index":{"In":[0,34],"this":[1],"technical":[2],"note,":[3],"we":[4],"propose":[5],"a":[6,31,69,138],"set-boundary":[7],"based":[8],"method":[9,55,103,151],"to":[10,36,61,68,123],"verify":[11],"reach-avoid":[12,86,153],"properties":[13],"of":[14,49,71,114,132,141],"non-linear":[15],"dynamical":[16],"systems":[17],"with":[18,92,108],"parametric":[19],"uncertainty,":[20],"which":[21],"works":[22],"under":[23],"the":[24,27,37,46,50,62,130,133],"assumption":[25],"that":[26],"initial":[28,51,63,94],"set":[29,70,134],"is":[30,135],"compact":[32],"set.":[33],"comparison":[35],"conventional":[38],"approach":[39],"employing":[40],"safely":[41],"overapproximating":[42],"state":[43,58],"extrapolation":[44,59],"on":[45],"full":[47],"volume":[48],"set,":[52],"our":[53,101,149],"boundary-based":[54,102,150],"applies":[56],"such":[57,142],"only":[60],"set's":[64],"boundary,":[65],"and":[66,80],"thus":[67],"significantly":[72],"smaller":[73],"volume.":[74],"This":[75],"can":[76],"help":[77],"enhance":[78],"precision":[79],"reduce":[81],"computational":[82],"burden":[83],"when":[84],"solving":[85],"verification":[87,154],"problems,":[88],"especially":[89],"for":[90],"cases":[91],"large":[93,97],"sets":[95,116],"and/or":[96],"time":[98],"horizons.":[99],"Furthermore,":[100],"lifts":[104],"existing":[105],"reachability-analysis":[106],"techniques":[107],"their":[109],"often":[110],"confined":[111],"geometric":[112,127],"representations":[113],"reachable":[115],"(like":[117],"interval":[118],"boxes,":[119],"zonotopes,":[120],"polyhedra,":[121],"ellipsoids)":[122],"considerably":[124],"more":[125],"complex":[126],"shapes,":[128],"where":[129],"boundary":[131],"representable":[136],"as":[137],"finite":[139],"union":[140],"shapes.":[143],"The":[144],"resulting":[145],"benefits":[146],"brought":[147],"by":[148],"in":[152],"are":[155],"illustrated":[156],"through":[157],"several":[158],"examples.":[159]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":6},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":6},{"year":2017,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}