{"id":"https://openalex.org/W2612716718","doi":"https://doi.org/10.1137/17m1115253","title":"Null Controllability of a Linearized Korteweg--de Vries Equation by Backstepping Approach","display_name":"Null Controllability of a Linearized Korteweg--de Vries Equation by Backstepping Approach","publication_year":2019,"publication_date":"2019-01-01","ids":{"openalex":"https://openalex.org/W2612716718","doi":"https://doi.org/10.1137/17m1115253","mag":"2612716718"},"language":"en","primary_location":{"id":"doi:10.1137/17m1115253","is_oa":false,"landing_page_url":"https://doi.org/10.1137/17m1115253","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":true,"oa_status":"green","oa_url":"https://hal.archives-ouvertes.fr/hal-01468750","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5002179101","display_name":"Shuhuang Xiang","orcid":"https://orcid.org/0000-0002-6727-6170"},"institutions":[{"id":"https://openalex.org/I39804081","display_name":"Sorbonne Universit\u00e9","ror":"https://ror.org/02en5vm52","country_code":"FR","type":"education","lineage":["https://openalex.org/I39804081"]},{"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":"S. Xiang","raw_affiliation_strings":["LJLL (UMR_7598) - Laboratoire Jacques-Louis Lions (Sorbonne-Universit\u00e9, Bo\u00eete courrier 187 - 75252 Paris Cedex 05 - France)","CaGE  - Control And GEometry (France)","SU - Sorbonne Universite\u0301 (21 rue de l\u2019\u00c9cole de m\u00e9decine - 75006 Paris - France)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"LJLL (UMR_7598) - Laboratoire Jacques-Louis Lions (Sorbonne-Universit\u00e9, Bo\u00eete courrier 187 - 75252 Paris Cedex 05 - France)","institution_ids":["https://openalex.org/I39804081","https://openalex.org/I4210158291"]},{"raw_affiliation_string":"CaGE  - Control And GEometry (France)","institution_ids":[]},{"raw_affiliation_string":"SU - Sorbonne Universite\u0301 (21 rue de l\u2019\u00c9cole de m\u00e9decine - 75006 Paris - France)","institution_ids":["https://openalex.org/I39804081"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5002179101"],"corresponding_institution_ids":["https://openalex.org/I39804081","https://openalex.org/I4210158291"],"apc_list":null,"apc_paid":null,"fwci":2.6277,"has_fulltext":false,"cited_by_count":28,"citation_normalized_percentile":{"value":0.89734413,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":95,"max":98},"biblio":{"volume":"57","issue":"2","first_page":"1493","last_page":"1515"},"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":0.9998999834060669,"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":0.9998999834060669,"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/T11654","display_name":"Advanced Mathematical Physics Problems","score":0.9991999864578247,"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9943000078201294,"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/controllability","display_name":"Controllability","score":0.9272605180740356},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.864825963973999},{"id":"https://openalex.org/keywords/backstepping","display_name":"Backstepping","score":0.7385711073875427},{"id":"https://openalex.org/keywords/korteweg\u2013de-vries-equation","display_name":"Korteweg\u2013de Vries equation","score":0.6361279487609863},{"id":"https://openalex.org/keywords/null","display_name":"Null (SQL)","score":0.551555335521698},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.541344165802002},{"id":"https://openalex.org/keywords/dirichlet-distribution","display_name":"Dirichlet distribution","score":0.5022008419036865},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.45517778396606445},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4465635418891907},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.3582158088684082},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.3410349190235138},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.3057963252067566},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.22850704193115234},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.06886440515518188},{"id":"https://openalex.org/keywords/adaptive-control","display_name":"Adaptive control","score":0.06769928336143494},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.06358128786087036}],"concepts":[{"id":"https://openalex.org/C48209547","wikidata":"https://www.wikidata.org/wiki/Q1331104","display_name":"Controllability","level":2,"score":0.9272605180740356},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.864825963973999},{"id":"https://openalex.org/C72218879","wikidata":"https://www.wikidata.org/wiki/Q4839759","display_name":"Backstepping","level":4,"score":0.7385711073875427},{"id":"https://openalex.org/C146630112","wikidata":"https://www.wikidata.org/wiki/Q601796","display_name":"Korteweg\u2013de Vries equation","level":3,"score":0.6361279487609863},{"id":"https://openalex.org/C203763787","wikidata":"https://www.wikidata.org/wiki/Q371029","display_name":"Null (SQL)","level":2,"score":0.551555335521698},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.541344165802002},{"id":"https://openalex.org/C169214877","wikidata":"https://www.wikidata.org/wiki/Q981016","display_name":"Dirichlet distribution","level":3,"score":0.5022008419036865},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.45517778396606445},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4465635418891907},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.3582158088684082},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.3410349190235138},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.3057963252067566},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.22850704193115234},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.06886440515518188},{"id":"https://openalex.org/C107464732","wikidata":"https://www.wikidata.org/wiki/Q235781","display_name":"Adaptive control","level":3,"score":0.06769928336143494},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.06358128786087036},{"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/17m1115253","is_oa":false,"landing_page_url":"https://doi.org/10.1137/17m1115253","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-01468750v1","is_oa":true,"landing_page_url":"https://hal.archives-ouvertes.fr/hal-01468750","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":"https://hal.archives-ouvertes.fr/hal-01468750","raw_type":"\\ninfo:eu-repo/semantics/preprint\\n"},{"id":"pmh:oai:HAL:hal-01468750v2","is_oa":true,"landing_page_url":"https://hal.science/hal-01468750","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, 2019, &#x27E8;10.1137/17M1115253&#x27E9;","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:HAL:hal-01468750v1","is_oa":true,"landing_page_url":"https://hal.archives-ouvertes.fr/hal-01468750","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":"https://hal.archives-ouvertes.fr/hal-01468750","raw_type":"\\ninfo:eu-repo/semantics/preprint\\n"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3271926106","display_name":null,"funder_award_id":"ANR 15-CE23-0007","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G6997608508","display_name":"Finite Time Control and Estimation for System of Systems","funder_award_id":"ANR-15-CE23-0007","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"}],"funders":[{"id":"https://openalex.org/F4320320883","display_name":"Agence Nationale de la Recherche","ror":"https://ror.org/00rbzpz17"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":42,"referenced_works":["https://openalex.org/W46317803","https://openalex.org/W245278405","https://openalex.org/W1571539429","https://openalex.org/W1966249877","https://openalex.org/W1980351610","https://openalex.org/W1980366322","https://openalex.org/W1981539165","https://openalex.org/W1988720984","https://openalex.org/W1990834757","https://openalex.org/W2002744405","https://openalex.org/W2019091709","https://openalex.org/W2066888772","https://openalex.org/W2074058833","https://openalex.org/W2084749319","https://openalex.org/W2088371633","https://openalex.org/W2091019995","https://openalex.org/W2094889090","https://openalex.org/W2101694485","https://openalex.org/W2110837625","https://openalex.org/W2114920878","https://openalex.org/W2128039433","https://openalex.org/W2134733687","https://openalex.org/W2136187884","https://openalex.org/W2140122171","https://openalex.org/W2148668375","https://openalex.org/W2157127092","https://openalex.org/W2170544117","https://openalex.org/W2178205091","https://openalex.org/W2522650499","https://openalex.org/W2559953699","https://openalex.org/W2563249773","https://openalex.org/W2580519087","https://openalex.org/W2610818604","https://openalex.org/W2612682187","https://openalex.org/W2757755218","https://openalex.org/W2792398305","https://openalex.org/W2963588029","https://openalex.org/W2963666812","https://openalex.org/W2963961449","https://openalex.org/W3021872353","https://openalex.org/W3103235081","https://openalex.org/W3151680498"],"related_works":["https://openalex.org/W4225722709","https://openalex.org/W2036697162","https://openalex.org/W2051029143","https://openalex.org/W2131379161","https://openalex.org/W4312823883","https://openalex.org/W3185750406","https://openalex.org/W3215273227","https://openalex.org/W2018039518","https://openalex.org/W1480788855","https://openalex.org/W2079322307"],"abstract_inverted_index":{"We":[0],"prove":[1],"the":[2,16,27],"null":[3],"controllability":[4],"of":[5,20],"a":[6,12,33,38],"linearized":[7],"Korteweg--de":[8],"Vries":[9],"equation":[10],"with":[11],"Dirichlet":[13],"control":[14],"on":[15],"left":[17],"boundary.":[18],"Instead":[19],"considering":[21],"classical":[22],"methods,":[23],"i.e.,":[24],"Carleman":[25],"estimates,":[26],"moment":[28],"method,":[29],"etc.,":[30],"we":[31],"use":[32],"backstepping":[34],"approach,":[35],"which":[36],"is":[37],"method":[39],"usually":[40],"used":[41],"to":[42],"handle":[43],"stabilization":[44],"problems.":[45]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":3}],"updated_date":"2026-07-13T07:31:44.756512","created_date":"2025-10-10T00:00:00"}
