{"id":"https://openalex.org/W1996026793","doi":"https://doi.org/10.1137/090769788","title":"On Trajectories Satisfying a State Constraint: $W^{1,1}$ Estimates and Counterexamples","display_name":"On Trajectories Satisfying a State Constraint: $W^{1,1}$ Estimates and Counterexamples","publication_year":2010,"publication_date":"2010-01-01","ids":{"openalex":"https://openalex.org/W1996026793","doi":"https://doi.org/10.1137/090769788","mag":"1996026793"},"language":"en","primary_location":{"id":"doi:10.1137/090769788","is_oa":false,"landing_page_url":"https://doi.org/10.1137/090769788","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Control and Optimization","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/A5109351634","display_name":"Piernicola Bettiol","orcid":"https://orcid.org/0000-0003-4969-6144"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Piernicola Bettiol","raw_affiliation_strings":["p.bettiol@imperial.ac.uk and r.vinter@imperial.ac.uk#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"p.bettiol@imperial.ac.uk and r.vinter@imperial.ac.uk#TAB#","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5048359772","display_name":"Alberto Bressan","orcid":"https://orcid.org/0000-0002-2030-842X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Alberto Bressan","raw_affiliation_strings":["bressan@math.psu.edu#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"bressan@math.psu.edu#TAB#","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5031053402","display_name":"Richard Vinter","orcid":"https://orcid.org/0000-0002-3585-0473"},"institutions":[{"id":"https://openalex.org/I47508984","display_name":"Imperial College London","ror":"https://ror.org/041kmwe10","country_code":"GB","type":"education","lineage":["https://openalex.org/I47508984"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Richard Vinter","raw_affiliation_strings":["Imperial College London,#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Imperial College London,#TAB#","institution_ids":["https://openalex.org/I47508984"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":4.5779,"has_fulltext":false,"cited_by_count":36,"citation_normalized_percentile":{"value":0.94536656,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":88,"max":98},"biblio":{"volume":"48","issue":"7","first_page":"4664","last_page":"4679"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9919999837875366,"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/T10545","display_name":"Optimization and Variational Analysis","score":0.9919999837875366,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9843000173568726,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12158","display_name":"Guidance and Control Systems","score":0.9739999771118164,"subfield":{"id":"https://openalex.org/subfields/2202","display_name":"Aerospace 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/counterexample","display_name":"Counterexample","score":0.9218977689743042},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8439735174179077},{"id":"https://openalex.org/keywords/state","display_name":"State (computer science)","score":0.6389250159263611},{"id":"https://openalex.org/keywords/constraint","display_name":"Constraint (computer-aided design)","score":0.6257838606834412},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4005897641181946},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.3460700213909149},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.34166276454925537},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.31179898977279663},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.15359970927238464},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.12962660193443298}],"concepts":[{"id":"https://openalex.org/C162838799","wikidata":"https://www.wikidata.org/wiki/Q596077","display_name":"Counterexample","level":2,"score":0.9218977689743042},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8439735174179077},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.6389250159263611},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.6257838606834412},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4005897641181946},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.3460700213909149},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.34166276454925537},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.31179898977279663},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.15359970927238464},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.12962660193443298}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/090769788","is_oa":false,"landing_page_url":"https://doi.org/10.1137/090769788","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Control and Optimization","raw_type":"journal-article"},{"id":"pmh:oai:HAL:hal-04404445v1","is_oa":false,"landing_page_url":"https://univ-brest.hal.science/hal-04404445","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"https://epubs.siam.org/doi/10.1137/090769788","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","score":0.8399999737739563,"display_name":"Reduced inequalities"}],"awards":[{"id":"https://openalex.org/G1823500649","display_name":null,"funder_award_id":"EP/G066477/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"}],"funders":[{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":10,"referenced_works":["https://openalex.org/W1592961332","https://openalex.org/W1983536992","https://openalex.org/W1984394420","https://openalex.org/W1994996557","https://openalex.org/W2011822463","https://openalex.org/W2013692585","https://openalex.org/W2056018340","https://openalex.org/W2072575566","https://openalex.org/W2141616022","https://openalex.org/W4240902880"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2349952486","https://openalex.org/W1489260687","https://openalex.org/W2775700832","https://openalex.org/W2587222766","https://openalex.org/W3204670144","https://openalex.org/W2163101548","https://openalex.org/W1988934358","https://openalex.org/W4389574038","https://openalex.org/W2349580982"],"abstract_inverted_index":{"This":[0],"paper":[1],"concerns":[2],"properties":[3],"of":[4,20,27,44,51,57,67,83,86,99,154,157],"solutions":[5],"to":[6,24,65,80,147,176],"a":[7,12,21,97,134,155,169,177],"differential":[8],"inclusion":[9],"(\u201cF-trajectories\u201d)":[10],"satisfying":[11,29],"state":[13,93,121,129,166,192],"constraint.":[14,167],"Estimates":[15],"on":[16],"the":[17,25,30,42,52,58,68,74,81,87],"$W^{1,1}$":[18,75,112,150,200],"distance":[19,76],"given":[22],"F-trajectory":[23],"set":[26],"F-trajectories":[28],"constraint":[31,84,104],"have":[32],"an":[33],"important":[34],"role":[35],"in":[36,55,72,116,179,204],"state-constrained":[37],"optimal":[38],"control":[39],"theory,":[40],"regarding":[41],"derivation":[43],"nondegenerate":[45],"necessary":[46],"conditions,":[47],"sensitivity":[48],"analysis,":[49],"characterization":[50],"value":[53],"function":[54],"terms":[56],"Hamilton\u2013Jacobi":[59],"equation":[60],"and":[61,194],"other":[62],"applications.":[63],"According":[64],"some":[66],"earlier":[69,158],"literature,":[70],"estimates,":[71],"which":[73,199],"is":[77,145,163],"related":[78],"linearly":[79],"degree":[82],"violation":[85],"original":[88],"F-trajectory,":[89],"are":[90,114,202],"valid":[91,118,203],"for":[92,119,173,190],"constraints":[94,193],"defined":[95],"by":[96,108,152],"collection":[98],"one":[100,165],"or":[101],"more":[102],"inequality":[103],"functionals.":[105],"We":[106,123,140],"show,":[107],"counterexample,":[109],"that":[110,143],"linear,":[111,149],"estimates":[113,151,189,201],"not":[115,132],"general":[117],"multiple":[120,191],"constraints.":[122],"also":[124],"identify":[125,195],"cases":[126],"involving":[127],"several":[128],"constraints,":[130],"where":[131],"even":[133],"weaker,":[135],"linear":[136],"$L^{\\infty}$":[137],"estimate":[138],"holds.":[139],"further":[141],"show":[142],"it":[144],"possible":[146],"justify":[148],"means":[153],"modification":[156],"constructive":[159],"techniques,":[160],"when":[161],"there":[162],"only":[164],"In":[168],"future":[170],"companion":[171],"paper[Estimates":[172],"trajectories":[174],"confined":[175],"cone":[178],"$\\mathbb{R}^n$,":[180],"SIAM":[181],"J.":[182],"Control":[183],"Optim.,":[184],"submitted]":[185],"we":[186],"develop":[187],"weaker":[188],"additional":[196],"hypotheses":[197],"under":[198],"this":[205],"broader":[206],"setting.":[207]},"counts_by_year":[{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":3}],"updated_date":"2026-09-04T10:56:28.161419","created_date":"2025-10-10T00:00:00"}