{"id":"https://openalex.org/W2891089985","doi":"https://doi.org/10.1109/cdc.2018.8619647","title":"Tight Continuous-Time Reachtubes for Lagrangian Reachability","display_name":"Tight Continuous-Time Reachtubes for Lagrangian Reachability","publication_year":2018,"publication_date":"2018-12-01","ids":{"openalex":"https://openalex.org/W2891089985","doi":"https://doi.org/10.1109/cdc.2018.8619647","mag":"2891089985"},"language":"en","primary_location":{"id":"doi:10.1109/cdc.2018.8619647","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2018.8619647","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2018 IEEE 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/A5067266084","display_name":"Jacek Cyranka","orcid":"https://orcid.org/0000-0001-5719-0616"},"institutions":[{"id":"https://openalex.org/I36258959","display_name":"University of California, San Diego","ror":"https://ror.org/0168r3w48","country_code":"US","type":"education","lineage":["https://openalex.org/I36258959"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Jacek Cyranka","raw_affiliation_strings":["University of California, San Diego"],"affiliations":[{"raw_affiliation_string":"University of California, San Diego","institution_ids":["https://openalex.org/I36258959"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100781410","display_name":"Md. Ariful Islam","orcid":"https://orcid.org/0009-0006-7622-8863"},"institutions":[{"id":"https://openalex.org/I12315562","display_name":"Texas Tech University","ror":"https://ror.org/0405mnx93","country_code":"US","type":"education","lineage":["https://openalex.org/I12315562"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Md. Ariful Islam","raw_affiliation_strings":["Texas Tech University"],"affiliations":[{"raw_affiliation_string":"Texas Tech University","institution_ids":["https://openalex.org/I12315562"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5039202410","display_name":"Scott A. Smolka","orcid":"https://orcid.org/0000-0002-7348-630X"},"institutions":[{"id":"https://openalex.org/I59553526","display_name":"Stony Brook University","ror":"https://ror.org/05qghxh33","country_code":"US","type":"education","lineage":["https://openalex.org/I59553526"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Scott A. Smolka","raw_affiliation_strings":["Stony Brook University"],"affiliations":[{"raw_affiliation_string":"Stony Brook University","institution_ids":["https://openalex.org/I59553526"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5081085178","display_name":"Sicun Gao","orcid":"https://orcid.org/0000-0003-2524-4960"},"institutions":[{"id":"https://openalex.org/I36258959","display_name":"University of California, San Diego","ror":"https://ror.org/0168r3w48","country_code":"US","type":"education","lineage":["https://openalex.org/I36258959"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Sicun Gao","raw_affiliation_strings":["University of California, San Diego"],"affiliations":[{"raw_affiliation_string":"University of California, San Diego","institution_ids":["https://openalex.org/I36258959"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5034362557","display_name":"Radu Grosu","orcid":"https://orcid.org/0000-0001-5715-2142"},"institutions":[{"id":"https://openalex.org/I145847075","display_name":"TU Wien","ror":"https://ror.org/04d836q62","country_code":"AT","type":"education","lineage":["https://openalex.org/I145847075"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Radu Grosu","raw_affiliation_strings":["Vienna University of Technology"],"affiliations":[{"raw_affiliation_string":"Vienna University of Technology","institution_ids":["https://openalex.org/I145847075"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5067266084"],"corresponding_institution_ids":["https://openalex.org/I36258959"],"apc_list":null,"apc_paid":null,"fwci":0.7541,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.71288753,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"20","issue":null,"first_page":"6854","last_page":"6861"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9947999715805054,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9947999715805054,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10142","display_name":"Formal Methods in Verification","score":0.9783999919891357,"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":0.9776999950408936,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/reachability","display_name":"Reachability","score":0.794302225112915},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.48711657524108887},{"id":"https://openalex.org/keywords/interval","display_name":"Interval (graph theory)","score":0.4652242362499237},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4349152445793152},{"id":"https://openalex.org/keywords/infinitesimal","display_name":"Infinitesimal","score":0.42629989981651306},{"id":"https://openalex.org/keywords/correctness","display_name":"Correctness","score":0.4255005717277527},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.41125333309173584},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.38268429040908813},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.33119940757751465},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.32990193367004395},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1925143301486969},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.13569816946983337},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.09774905443191528}],"concepts":[{"id":"https://openalex.org/C136643341","wikidata":"https://www.wikidata.org/wiki/Q1361526","display_name":"Reachability","level":2,"score":0.794302225112915},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.48711657524108887},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.4652242362499237},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4349152445793152},{"id":"https://openalex.org/C91229774","wikidata":"https://www.wikidata.org/wiki/Q193885","display_name":"Infinitesimal","level":2,"score":0.42629989981651306},{"id":"https://openalex.org/C55439883","wikidata":"https://www.wikidata.org/wiki/Q360812","display_name":"Correctness","level":2,"score":0.4255005717277527},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.41125333309173584},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.38268429040908813},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.33119940757751465},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.32990193367004395},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1925143301486969},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.13569816946983337},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.09774905443191528},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/cdc.2018.8619647","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2018.8619647","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2018 IEEE Conference on Decision and Control (CDC)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":27,"referenced_works":["https://openalex.org/W172589331","https://openalex.org/W306903215","https://openalex.org/W315739085","https://openalex.org/W574472091","https://openalex.org/W1496681274","https://openalex.org/W1538215585","https://openalex.org/W1974537499","https://openalex.org/W2024171867","https://openalex.org/W2047179434","https://openalex.org/W2055325291","https://openalex.org/W2072500636","https://openalex.org/W2084859862","https://openalex.org/W2112289054","https://openalex.org/W2148952098","https://openalex.org/W2153803621","https://openalex.org/W2166280160","https://openalex.org/W2509505087","https://openalex.org/W2539282332","https://openalex.org/W2576277975","https://openalex.org/W2620736690","https://openalex.org/W2963669205","https://openalex.org/W2963688046","https://openalex.org/W2964040381","https://openalex.org/W3032611786","https://openalex.org/W3037031223","https://openalex.org/W3149233563","https://openalex.org/W6731923558"],"related_works":["https://openalex.org/W2136512912","https://openalex.org/W2127267268","https://openalex.org/W2156446763","https://openalex.org/W2067910792","https://openalex.org/W2150194458","https://openalex.org/W2143461633","https://openalex.org/W2889071233","https://openalex.org/W4321471459","https://openalex.org/W4221156924","https://openalex.org/W2754251478"],"abstract_inverted_index":{"We":[0,47,120],"introduce":[1],"continuous":[2,154],"Lagrangian":[3],"reachability":[4],"(CLRT),":[5],"a":[6,13,23,95,134],"new":[7],"algorithm":[8],"for":[9,18,54,58],"the":[10,19,35,38,55,98,109,112,116,126,129,153],"computation":[11],"of":[12,22,37,111,128,136,152],"tight":[14],"and":[15,86],"continuous-time":[16],"reachtube":[17,155],"solution":[20,39,113],"flows":[21],"nonlinear,":[24],"time-variant":[25],"dynamical":[26],"system.":[27],"CLRT":[28,71,140],"employs":[29],"finite":[30],"strain":[31,75],"theory":[32,76],"to":[33,44,64,77,90,124,144],"determine":[34],"deformation":[36],"set":[40,100],"from":[41],"time":[42,45,81,102],"$t_{i}$":[43,85,103],"$t_{i+1}$.":[46],"have":[48],"developed":[49],"simple":[50],"explicit":[51],"analytic":[52],"formulas":[53],"optimal":[56,80],"metric":[57],"this":[59,61],"deformation;":[60],"is":[62],"superior":[63],"prior":[65],"work,":[66],"which":[67],"used":[68],"semi-definite":[69],"programming.":[70],"also":[72],"uses":[73],"infinitesimal":[74],"derive":[78],"an":[79],"increment":[82],"$h_{i}$":[83],"between":[84],"$t_{i+1}$,":[87],"nonlinear":[88],"optimization":[89],"minimally":[91],"bloat":[92],"(i.e.,":[93],"using":[94],"minimal":[96],"radius)":[97],"state":[99],"at":[101],"such":[104,147],"that":[105,139],"it":[106],"includes":[107],"all":[108],"states":[110],"flow":[114],"in":[115,150],"interval":[117],"$[t_{i},\\":[118],"t_{i+1}]$.":[119],"use":[121],"$\\delta$":[122],"-satisfiability":[123],"ensure":[125],"correctness":[127],"bloating.":[130],"Our":[131],"results":[132],"on":[133],"series":[135],"benchmarks":[137],"show":[138],"performs":[141],"favorably":[142],"compared":[143],"state-of-the-art":[145],"tools":[146],"as":[148],"CAPD":[149],"terms":[151],"volumes":[156],"they":[157],"compute.":[158]},"counts_by_year":[{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":3},{"year":2017,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}