{"id":"https://openalex.org/W2966932052","doi":"https://doi.org/10.23919/ecc.2019.8796108","title":"Approximating Viability Kernels of High-Dimensional Linear Systems","display_name":"Approximating Viability Kernels of High-Dimensional Linear Systems","publication_year":2019,"publication_date":"2019-06-01","ids":{"openalex":"https://openalex.org/W2966932052","doi":"https://doi.org/10.23919/ecc.2019.8796108","mag":"2966932052"},"language":"en","primary_location":{"id":"doi:10.23919/ecc.2019.8796108","is_oa":false,"landing_page_url":"https://doi.org/10.23919/ecc.2019.8796108","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2019 18th European Control Conference (ECC)","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/A5058882992","display_name":"A.M. Carvalho","orcid":null},"institutions":[{"id":"https://openalex.org/I4387152517","display_name":"Instituto Superior T\u00e9cnico","ror":"https://ror.org/03db2by73","country_code":null,"type":"education","lineage":["https://openalex.org/I141596103","https://openalex.org/I4387152517"]}],"countries":["PT"],"is_corresponding":true,"raw_author_name":"Andre M. Carvalho","raw_affiliation_strings":["Instituto Superior T\u00e9cnico, Lisbon, Portugal"],"affiliations":[{"raw_affiliation_string":"Instituto Superior T\u00e9cnico, Lisbon, Portugal","institution_ids":["https://openalex.org/I4387152517"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5045724042","display_name":"Jo\u00e3o Sequeira","orcid":"https://orcid.org/0000-0002-6706-5365"},"institutions":[{"id":"https://openalex.org/I4387152517","display_name":"Instituto Superior T\u00e9cnico","ror":"https://ror.org/03db2by73","country_code":null,"type":"education","lineage":["https://openalex.org/I141596103","https://openalex.org/I4387152517"]},{"id":"https://openalex.org/I4210166615","display_name":"INESC TEC","ror":"https://ror.org/05fa8ka61","country_code":"PT","type":"nonprofit","lineage":["https://openalex.org/I4210125590","https://openalex.org/I4210166615"]}],"countries":["PT"],"is_corresponding":false,"raw_author_name":"Joao S. Sequeira","raw_affiliation_strings":["Instituto Superior T\u00e9cnico, Institute for Systems and Robotics, Lisbon, Portugal"],"affiliations":[{"raw_affiliation_string":"Instituto Superior T\u00e9cnico, Institute for Systems and Robotics, Lisbon, Portugal","institution_ids":["https://openalex.org/I4210166615","https://openalex.org/I4387152517"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5058882992"],"corresponding_institution_ids":["https://openalex.org/I4387152517"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.1249519,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":null,"issue":null,"first_page":"4289","last_page":"4294"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10142","display_name":"Formal Methods in Verification","score":0.9980999827384949,"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":0.9980999827384949,"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/T10586","display_name":"Robotic Path Planning Algorithms","score":0.9947999715805054,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/T10524","display_name":"Traffic control and management","score":0.977400004863739,"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/controllability","display_name":"Controllability","score":0.7707948684692383},{"id":"https://openalex.org/keywords/kernel","display_name":"Kernel (algebra)","score":0.6461468935012817},{"id":"https://openalex.org/keywords/trajectory","display_name":"Trajectory","score":0.49592551589012146},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4945480525493622},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.481652170419693},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4687986969947815},{"id":"https://openalex.org/keywords/range","display_name":"Range (aeronautics)","score":0.4636237621307373},{"id":"https://openalex.org/keywords/robot","display_name":"Robot","score":0.4601818323135376},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.45075106620788574},{"id":"https://openalex.org/keywords/robotics","display_name":"Robotics","score":0.4495309293270111},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.44897782802581787},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.436898410320282},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3931080996990204},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.33244141936302185},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.20545849204063416},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.13600993156433105},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.12712055444717407}],"concepts":[{"id":"https://openalex.org/C48209547","wikidata":"https://www.wikidata.org/wiki/Q1331104","display_name":"Controllability","level":2,"score":0.7707948684692383},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.6461468935012817},{"id":"https://openalex.org/C13662910","wikidata":"https://www.wikidata.org/wiki/Q193139","display_name":"Trajectory","level":2,"score":0.49592551589012146},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4945480525493622},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.481652170419693},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4687986969947815},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.4636237621307373},{"id":"https://openalex.org/C90509273","wikidata":"https://www.wikidata.org/wiki/Q11012","display_name":"Robot","level":2,"score":0.4601818323135376},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.45075106620788574},{"id":"https://openalex.org/C34413123","wikidata":"https://www.wikidata.org/wiki/Q170978","display_name":"Robotics","level":3,"score":0.4495309293270111},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.44897782802581787},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.436898410320282},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3931080996990204},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.33244141936302185},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.20545849204063416},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.13600993156433105},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.12712055444717407},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","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/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","level":1,"score":0.0},{"id":"https://openalex.org/C1276947","wikidata":"https://www.wikidata.org/wiki/Q333","display_name":"Astronomy","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.23919/ecc.2019.8796108","is_oa":false,"landing_page_url":"https://doi.org/10.23919/ecc.2019.8796108","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2019 18th European Control Conference (ECC)","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":16,"referenced_works":["https://openalex.org/W1524886571","https://openalex.org/W1532859487","https://openalex.org/W1569692898","https://openalex.org/W1987605281","https://openalex.org/W1999497797","https://openalex.org/W2000147742","https://openalex.org/W2015863039","https://openalex.org/W2085744412","https://openalex.org/W2109569369","https://openalex.org/W2123922810","https://openalex.org/W2158451642","https://openalex.org/W2887991064","https://openalex.org/W6633997905","https://openalex.org/W6676366129","https://openalex.org/W6678726515","https://openalex.org/W6753760328"],"related_works":["https://openalex.org/W2054831413","https://openalex.org/W1999673819","https://openalex.org/W1493380407","https://openalex.org/W3209184047","https://openalex.org/W4237454804","https://openalex.org/W1942635442","https://openalex.org/W2170835896","https://openalex.org/W1990421243","https://openalex.org/W2026024153","https://openalex.org/W2539338955"],"abstract_inverted_index":{"Using":[0],"concepts":[1],"from":[2,115],"Viability":[3,30],"Theory,":[4,31],"this":[5],"paper":[6],"presents":[7],"an":[8],"algorithm":[9,114,140,167],"to":[10,129,146],"determine":[11],"a":[12,106,131,171,191,195],"safety":[13],"property":[14],"of":[15,23,46,66,88,108,110,123,137,144,173,199],"linear":[16],"and":[17,156,160,182],"time":[18],"invariant":[19],"systems.":[20],"A":[21,175],"number":[22],"Robotics":[24],"scenarios":[25],"can":[26],"be":[27],"framed":[28],"within":[29],"namely":[32],"applications":[33],"concerning":[34],"autonomous":[35],"vehicles.":[36],"Often":[37],"the":[38,44,47,59,63,81,84,89,95,99,111,116,121,124,138,142,162,180,183,188],"navigation":[39],"problem":[40],"consists":[41],"in":[42,177],"keeping":[43],"trajectory":[45],"system":[48,200],"inside":[49,83,101],"some":[50],"compact":[51],"set":[52,65],"representing":[53],"motion":[54],"constraints.":[55],"This":[56,104],"means":[57],"computing":[58],"viability":[60,125],"kernel":[61],"(i.e.,":[62],"largest":[64],"initial":[67],"states":[68],"for":[69,150,194],"which":[70],"it":[71],"is":[72,141,168],"guaranteed":[73],"that":[74,79,97,187],"there":[75],"are":[76,158],"available":[77],"controls":[78,96],"maintain":[80],"trajectories":[82],"constraint":[85],"set)":[86],"out":[87],"admissible/safe":[90],"areas":[91],"and,":[92],"implicitly,":[93],"find":[94],"keep":[98],"robot":[100],"such":[102],"sets.":[103,148],"represents":[105],"form":[107],"controllability":[109],"system.":[112],"An":[113],"literature,":[117],"based":[118],"on":[119],"sampling":[120],"boundary":[122],"kernel,":[126],"was":[127],"modified":[128],"yield":[130],"faster":[132],"algorithm.":[133],"The":[134,166],"distinctive":[135],"feature":[136],"extended":[139,184],"use":[143],"zonotopes":[145],"represent":[147],"Simulations":[149],"systems":[151],"with":[152,170],"dimensions":[153],"between":[154,179],"n=5":[155],"n=100":[157],"presented":[159],"illustrate":[161],"relative":[163],"performance":[164,178,193],"improvement.":[165],"illustrated":[169],"chain":[172],"integrators.":[174],"comparison":[176],"original":[181],"algorithms":[185],"suggests":[186],"latter":[189],"has":[190],"better":[192],"sufficiently":[196],"wide":[197],"range":[198],"dimensions.":[201]},"counts_by_year":[{"year":2023,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}