{"id":"https://openalex.org/W2127615550","doi":"https://doi.org/10.1137/15m1040670","title":"Impulse and Sampled-Data Optimal Control of Heat Equations, and Error Estimates","display_name":"Impulse and Sampled-Data Optimal Control of Heat Equations, and Error Estimates","publication_year":2016,"publication_date":"2016-01-01","ids":{"openalex":"https://openalex.org/W2127615550","doi":"https://doi.org/10.1137/15m1040670","mag":"2127615550"},"language":"en","primary_location":{"id":"doi:10.1137/15m1040670","is_oa":false,"landing_page_url":"https://doi.org/10.1137/15m1040670","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":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1509.05932","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5089339704","display_name":"Emmanuel Tr\u00e9lat","orcid":"https://orcid.org/0000-0002-0656-7003"},"institutions":[{"id":"https://openalex.org/I4210158291","display_name":"Laboratoire Jacques-Louis Lions","ror":"https://ror.org/04xmteb38","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I204730241","https://openalex.org/I39804081","https://openalex.org/I4210141950","https://openalex.org/I4210158291"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Emmanuel Tr\u00e9lat","raw_affiliation_strings":["Laboratoire Jacques-Louis Lions"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Laboratoire Jacques-Louis Lions","institution_ids":["https://openalex.org/I4210158291"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100436501","display_name":"Lijuan Wang","orcid":"https://orcid.org/0000-0002-2517-2728"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Lijuan Wang","raw_affiliation_strings":["School of Mathematics and Statistics [Wuhan]"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics [Wuhan]","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5076622154","display_name":"Yubiao Zhang","orcid":"https://orcid.org/0000-0002-3843-3384"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yubiao Zhang","raw_affiliation_strings":["School of Mathematics and Statistics [Wuhan]"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics [Wuhan]","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5089339704"],"corresponding_institution_ids":["https://openalex.org/I4210158291"],"apc_list":null,"apc_paid":null,"fwci":3.5095,"has_fulltext":false,"cited_by_count":30,"citation_normalized_percentile":{"value":0.92516738,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"54","issue":"5","first_page":"2787","last_page":"2819"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.9993000030517578,"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"}},"topics":[{"id":"https://openalex.org/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.9993000030517578,"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/T11205","display_name":"Numerical methods in inverse problems","score":0.9932000041007996,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.9868999719619751,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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/optimal-control","display_name":"Optimal control","score":0.8323793411254883},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8172892332077026},{"id":"https://openalex.org/keywords/impulse","display_name":"Impulse (physics)","score":0.660110354423523},{"id":"https://openalex.org/keywords/impulse-control","display_name":"Impulse control","score":0.655058741569519},{"id":"https://openalex.org/keywords/heat-equation","display_name":"Heat equation","score":0.5570943355560303},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5348109006881714},{"id":"https://openalex.org/keywords/maximum-principle","display_name":"Maximum principle","score":0.5185204744338989},{"id":"https://openalex.org/keywords/pontryagins-minimum-principle","display_name":"Pontryagin's minimum principle","score":0.5170881748199463},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.4657711982727051},{"id":"https://openalex.org/keywords/approximations-of-\u03c0","display_name":"Approximations of \u03c0","score":0.4199492335319519},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4163965880870819},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.40592172741889954},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3348413109779358},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.22504964470863342},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.11669141054153442}],"concepts":[{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.8323793411254883},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8172892332077026},{"id":"https://openalex.org/C70836080","wikidata":"https://www.wikidata.org/wiki/Q837940","display_name":"Impulse (physics)","level":2,"score":0.660110354423523},{"id":"https://openalex.org/C3018727167","wikidata":"https://www.wikidata.org/wiki/Q6033829","display_name":"Impulse control","level":2,"score":0.655058741569519},{"id":"https://openalex.org/C202787564","wikidata":"https://www.wikidata.org/wiki/Q6510488","display_name":"Heat equation","level":2,"score":0.5570943355560303},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5348109006881714},{"id":"https://openalex.org/C31010330","wikidata":"https://www.wikidata.org/wiki/Q1914255","display_name":"Maximum principle","level":3,"score":0.5185204744338989},{"id":"https://openalex.org/C141803461","wikidata":"https://www.wikidata.org/wiki/Q3491629","display_name":"Pontryagin's minimum principle","level":3,"score":0.5170881748199463},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.4657711982727051},{"id":"https://openalex.org/C193386753","wikidata":"https://www.wikidata.org/wiki/Q1130396","display_name":"Approximations of \u03c0","level":2,"score":0.4199492335319519},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4163965880870819},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.40592172741889954},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3348413109779358},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.22504964470863342},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.11669141054153442},{"id":"https://openalex.org/C542102704","wikidata":"https://www.wikidata.org/wiki/Q183257","display_name":"Psychotherapist","level":1,"score":0.0},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/15m1040670","is_oa":false,"landing_page_url":"https://doi.org/10.1137/15m1040670","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:arXiv.org:1509.05932","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1509.05932","pdf_url":"https://arxiv.org/pdf/1509.05932","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":null},{"id":"pmh:oai:HAL:hal-01202251v1","is_oa":true,"landing_page_url":"https://hal.science/hal-01202251","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":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM Journal on Control and Optimization, 2016, 54 (5), pp.2787--2819","raw_type":"Journal articles"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1509.05932","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1509.05932","pdf_url":"https://arxiv.org/pdf/1509.05932","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":null},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/7","score":0.6100000143051147,"display_name":"Affordable and clean energy"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":37,"referenced_works":["https://openalex.org/W30907860","https://openalex.org/W89839489","https://openalex.org/W126240089","https://openalex.org/W185172081","https://openalex.org/W187630271","https://openalex.org/W1499788862","https://openalex.org/W1509930179","https://openalex.org/W1524099673","https://openalex.org/W1589236075","https://openalex.org/W1593038947","https://openalex.org/W1628576809","https://openalex.org/W1745577466","https://openalex.org/W1866311589","https://openalex.org/W1968702788","https://openalex.org/W1968834064","https://openalex.org/W1970963843","https://openalex.org/W1984479582","https://openalex.org/W1985491254","https://openalex.org/W1995018531","https://openalex.org/W2000334666","https://openalex.org/W2006681194","https://openalex.org/W2012408233","https://openalex.org/W2012666906","https://openalex.org/W2023940093","https://openalex.org/W2024295674","https://openalex.org/W2033517841","https://openalex.org/W2045354979","https://openalex.org/W2053362105","https://openalex.org/W2053756579","https://openalex.org/W2081581211","https://openalex.org/W2094254426","https://openalex.org/W2103284380","https://openalex.org/W2118481011","https://openalex.org/W2121623735","https://openalex.org/W2171568556","https://openalex.org/W2952284893","https://openalex.org/W2964225436"],"related_works":["https://openalex.org/W2771042763","https://openalex.org/W2155570364","https://openalex.org/W4211240924","https://openalex.org/W4292923857","https://openalex.org/W4302321938","https://openalex.org/W2031281152","https://openalex.org/W2543201876","https://openalex.org/W1500373884","https://openalex.org/W2511035558","https://openalex.org/W2166776080"],"abstract_inverted_index":{"We":[0,49,101],"consider":[1],"the":[2,45,84,89,97,118,125],"optimal":[3,33,55,109,119,122],"control":[4,56],"problem":[5,29,127],"of":[6,15,53,67,71,96,124],"minimizing":[7],"some":[8],"quadratic":[9],"functional":[10],"over":[11],"all":[12],"possible":[13],"solutions":[14],"an":[16,40,62],"internally":[17],"controlled":[18,98],"multidimensional":[19],"heat":[20,73,99],"equation":[21],"with":[22,75,128],"a":[23,31,69,93,107],"periodic":[24],"terminal":[25],"state":[26],"constraint.":[27],"This":[28],"has":[30],"unique":[32,108],"solution,":[34,110],"which":[35],"can":[36],"be":[37],"characterized":[38],"by":[39,83],"optimality":[41],"system":[42,70],"derived":[43],"from":[44],"Pontryagin":[46],"maximum":[47],"principle.":[48],"define":[50],"two":[51],"approximations":[52],"this":[54],"problem.":[57],"The":[58,78],"first":[59],"one":[60,80],"is":[61,81],"impulse":[63,76,132],"approximation":[64,95],"and":[65,111,121,133],"consists":[66],"considering":[68],"linear":[72],"equations":[74],"control.":[77],"second":[79],"obtained":[82],"sample-and-hold":[85],"procedure":[86],"applied":[87],"to":[88,130],"control,":[90],"resulting":[91],"in":[92],"sampled-data":[94,134],"equation.":[100],"prove":[102],"that":[103],"both":[104],"problems":[105],"have":[106],"we":[112],"establish":[113],"precise":[114],"error":[115],"estimates":[116],"for":[117],"controls":[120],"states":[123],"initial":[126],"respect":[129],"its":[131],"approximations.":[135]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":6},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":1}],"updated_date":"2026-05-12T08:28:47.272897","created_date":"2016-06-24T00:00:00"}