{"id":"https://openalex.org/W4415548699","doi":"https://doi.org/10.1093/imamci/dnaf033","title":"Homogeneous boundary control design for a one-dimensional viscous Burgers equation: modal decomposition approach","display_name":"Homogeneous boundary control design for a one-dimensional viscous Burgers equation: modal decomposition approach","publication_year":2025,"publication_date":"2025-09-25","ids":{"openalex":"https://openalex.org/W4415548699","doi":"https://doi.org/10.1093/imamci/dnaf033"},"language":"en","primary_location":{"id":"doi:10.1093/imamci/dnaf033","is_oa":false,"landing_page_url":"https://doi.org/10.1093/imamci/dnaf033","pdf_url":null,"source":{"id":"https://openalex.org/S162756791","display_name":"IMA Journal of Mathematical Control and Information","issn_l":"0265-0754","issn":["0265-0754","1471-6887"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311648","host_organization_name":"Oxford University Press","host_organization_lineage":["https://openalex.org/P4310311648","https://openalex.org/P4310311647"],"host_organization_lineage_names":["Oxford University Press","University of Oxford"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IMA Journal of Mathematical Control and Information","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/A5093716772","display_name":"Mericel Ayamou","orcid":null},"institutions":[{"id":"https://openalex.org/I2279609970","display_name":"Universit\u00e9 de Lille","ror":"https://ror.org/02kzqn938","country_code":"FR","type":"education","lineage":["https://openalex.org/I2279609970"]},{"id":"https://openalex.org/I7454413","display_name":"\u00c9cole Centrale de Lille","ror":"https://ror.org/01x441g73","country_code":"FR","type":"education","lineage":["https://openalex.org/I7454413"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Mericel Ayamou","raw_affiliation_strings":["Univ. Lille, CNRS , Inria, Centrale Lille, UMR 9189 CRIStAL, F-59000 Lille ,"],"affiliations":[{"raw_affiliation_string":"Univ. Lille, CNRS , Inria, Centrale Lille, UMR 9189 CRIStAL, F-59000 Lille ,","institution_ids":["https://openalex.org/I7454413","https://openalex.org/I2279609970"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Andrey Polyakov","orcid":null},"institutions":[{"id":"https://openalex.org/I2279609970","display_name":"Universit\u00e9 de Lille","ror":"https://ror.org/02kzqn938","country_code":"FR","type":"education","lineage":["https://openalex.org/I2279609970"]},{"id":"https://openalex.org/I7454413","display_name":"\u00c9cole Centrale de Lille","ror":"https://ror.org/01x441g73","country_code":"FR","type":"education","lineage":["https://openalex.org/I7454413"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Andrey Polyakov","raw_affiliation_strings":["Univ. Lille , CNRS, Inria, Centrale Lille, UMR 9189 CRIStAL, F-59000 Lille ,"],"affiliations":[{"raw_affiliation_string":"Univ. Lille , CNRS, Inria, Centrale Lille, UMR 9189 CRIStAL, F-59000 Lille ,","institution_ids":["https://openalex.org/I7454413","https://openalex.org/I2279609970"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5064356260","display_name":"Nicol\u00e1s Espitia","orcid":"https://orcid.org/0000-0001-8241-0633"},"institutions":[{"id":"https://openalex.org/I7454413","display_name":"\u00c9cole Centrale de Lille","ror":"https://ror.org/01x441g73","country_code":"FR","type":"education","lineage":["https://openalex.org/I7454413"]},{"id":"https://openalex.org/I2279609970","display_name":"Universit\u00e9 de Lille","ror":"https://ror.org/02kzqn938","country_code":"FR","type":"education","lineage":["https://openalex.org/I2279609970"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Nicolas Espitia","raw_affiliation_strings":["Univ. Lille , CNRS, Centrale Lille, UMR 9189 CRIStAL, F-59000 Lille ,"],"affiliations":[{"raw_affiliation_string":"Univ. Lille , CNRS, Centrale Lille, UMR 9189 CRIStAL, F-59000 Lille ,","institution_ids":["https://openalex.org/I7454413","https://openalex.org/I2279609970"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5007830129","display_name":"Emilia Fridman","orcid":"https://orcid.org/0000-0002-8773-9494"},"institutions":[{"id":"https://openalex.org/I16391192","display_name":"Tel Aviv University","ror":"https://ror.org/04mhzgx49","country_code":"IL","type":"education","lineage":["https://openalex.org/I16391192"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Emilia Fridman","raw_affiliation_strings":["School of Electrical Engineering, Tel Aviv University , Tel Aviv 69978 ,"],"affiliations":[{"raw_affiliation_string":"School of Electrical Engineering, Tel Aviv University , Tel Aviv 69978 ,","institution_ids":["https://openalex.org/I16391192"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5093716772"],"corresponding_institution_ids":["https://openalex.org/I2279609970","https://openalex.org/I7454413"],"apc_list":{"value":2582,"currency":"GBP","value_usd":3167},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.41648005,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"42","issue":"4","first_page":null,"last_page":null},"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":1.0,"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":1.0,"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/T11206","display_name":"Model Reduction and Neural Networks","score":0.9976000189781189,"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/T11654","display_name":"Advanced Mathematical Physics Problems","score":0.9930999875068665,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.7056000232696533},{"id":"https://openalex.org/keywords/homogeneous","display_name":"Homogeneous","score":0.669700026512146},{"id":"https://openalex.org/keywords/modal","display_name":"Modal","score":0.6452999711036682},{"id":"https://openalex.org/keywords/controller","display_name":"Controller (irrigation)","score":0.4952000081539154},{"id":"https://openalex.org/keywords/observer","display_name":"Observer (physics)","score":0.4948999881744385},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.48080000281333923},{"id":"https://openalex.org/keywords/lyapunov-function","display_name":"Lyapunov function","score":0.4675000011920929},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.4672999978065491},{"id":"https://openalex.org/keywords/stability-theory","display_name":"Stability theory","score":0.45879998803138733}],"concepts":[{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.7056000232696533},{"id":"https://openalex.org/C66882249","wikidata":"https://www.wikidata.org/wiki/Q169336","display_name":"Homogeneous","level":2,"score":0.669700026512146},{"id":"https://openalex.org/C71139939","wikidata":"https://www.wikidata.org/wiki/Q910194","display_name":"Modal","level":2,"score":0.6452999711036682},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5889000296592712},{"id":"https://openalex.org/C203479927","wikidata":"https://www.wikidata.org/wiki/Q5165939","display_name":"Controller (irrigation)","level":2,"score":0.4952000081539154},{"id":"https://openalex.org/C2780704645","wikidata":"https://www.wikidata.org/wiki/Q9251458","display_name":"Observer (physics)","level":2,"score":0.4948999881744385},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.48080000281333923},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.4675000011920929},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.4672999978065491},{"id":"https://openalex.org/C41949839","wikidata":"https://www.wikidata.org/wiki/Q1756677","display_name":"Stability theory","level":3,"score":0.45879998803138733},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.4359999895095825},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.40230000019073486},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3668999969959259},{"id":"https://openalex.org/C167964875","wikidata":"https://www.wikidata.org/wiki/Q17011487","display_name":"Exponential stability","level":3,"score":0.3630000054836273},{"id":"https://openalex.org/C124681953","wikidata":"https://www.wikidata.org/wiki/Q339062","display_name":"Decomposition","level":2,"score":0.3531000018119812},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.328900009393692},{"id":"https://openalex.org/C2777032711","wikidata":"https://www.wikidata.org/wiki/Q5318993","display_name":"Dynamic mode decomposition","level":2,"score":0.3073999881744385},{"id":"https://openalex.org/C2984730371","wikidata":"https://www.wikidata.org/wiki/Q6501221","display_name":"Feedback controller","level":3,"score":0.3018999993801117},{"id":"https://openalex.org/C3018651601","wikidata":"https://www.wikidata.org/wiki/Q183635","display_name":"Feedback control","level":2,"score":0.2906000018119812},{"id":"https://openalex.org/C2780801425","wikidata":"https://www.wikidata.org/wiki/Q5164392","display_name":"Construct (python library)","level":2,"score":0.274399995803833},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.27059999108314514},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.2694000005722046},{"id":"https://openalex.org/C129747778","wikidata":"https://www.wikidata.org/wiki/Q1014918","display_name":"Burgers' equation","level":3,"score":0.25769999623298645},{"id":"https://openalex.org/C2778258933","wikidata":"https://www.wikidata.org/wiki/Q16918986","display_name":"Decomposition method (queueing theory)","level":2,"score":0.2549999952316284},{"id":"https://openalex.org/C2776829284","wikidata":"https://www.wikidata.org/wiki/Q1341651","display_name":"Lyapunov stability","level":3,"score":0.25450000166893005},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.2531000077724457},{"id":"https://openalex.org/C17500928","wikidata":"https://www.wikidata.org/wiki/Q959968","display_name":"Control system","level":2,"score":0.25290000438690186}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1093/imamci/dnaf033","is_oa":false,"landing_page_url":"https://doi.org/10.1093/imamci/dnaf033","pdf_url":null,"source":{"id":"https://openalex.org/S162756791","display_name":"IMA Journal of Mathematical Control and Information","issn_l":"0265-0754","issn":["0265-0754","1471-6887"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311648","host_organization_name":"Oxford University Press","host_organization_lineage":["https://openalex.org/P4310311648","https://openalex.org/P4310311647"],"host_organization_lineage_names":["Oxford University Press","University of Oxford"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IMA Journal of Mathematical Control and Information","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":56,"referenced_works":["https://openalex.org/W109546027","https://openalex.org/W587086020","https://openalex.org/W1057021034","https://openalex.org/W1527296550","https://openalex.org/W1556831891","https://openalex.org/W1559539328","https://openalex.org/W1560060148","https://openalex.org/W1954793758","https://openalex.org/W1975716337","https://openalex.org/W1980351610","https://openalex.org/W2026967759","https://openalex.org/W2036831763","https://openalex.org/W2044497027","https://openalex.org/W2055912791","https://openalex.org/W2056621178","https://openalex.org/W2066096538","https://openalex.org/W2080688746","https://openalex.org/W2091019995","https://openalex.org/W2092991598","https://openalex.org/W2098750612","https://openalex.org/W2114920878","https://openalex.org/W2124699533","https://openalex.org/W2127560478","https://openalex.org/W2130921294","https://openalex.org/W2171472659","https://openalex.org/W2172490084","https://openalex.org/W2176923824","https://openalex.org/W2279156231","https://openalex.org/W2499641798","https://openalex.org/W2529406432","https://openalex.org/W2606481864","https://openalex.org/W2786600126","https://openalex.org/W2790447963","https://openalex.org/W2897092541","https://openalex.org/W2902661488","https://openalex.org/W2942948303","https://openalex.org/W2962715862","https://openalex.org/W2997601858","https://openalex.org/W3004059645","https://openalex.org/W3006295337","https://openalex.org/W3089241465","https://openalex.org/W3148800415","https://openalex.org/W3179998438","https://openalex.org/W3207582864","https://openalex.org/W3210839039","https://openalex.org/W4205267168","https://openalex.org/W4225420884","https://openalex.org/W4281855051","https://openalex.org/W4311241294","https://openalex.org/W4313444021","https://openalex.org/W4379514169","https://openalex.org/W4390850455","https://openalex.org/W4398249620","https://openalex.org/W4402508621","https://openalex.org/W4403442848","https://openalex.org/W4413944669"],"related_works":[],"abstract_inverted_index":{"Abstract":[0],"In":[1],"this":[2],"paper,":[3],"we":[4,24,70,112],"address":[5],"the":[6,14,20,31,40,44,60,65,78,84,88,93,96,100,108,118,134],"problem":[7],"of":[8,67,87,95],"non-linear":[9],"boundary":[10],"control":[11,47,105],"design":[12,25,77],"for":[13,30],"one-dimensional":[15],"viscous":[16],"Burgers":[17],"equation.":[18],"Using":[19],"modal":[21],"decomposition":[22],"approach,":[23],"a":[26,72,127],"finite-dimensional":[27,101],"homogeneous":[28,45,62,79,102],"controller":[29,81,125],"controlled":[32],"subsystem":[33],"containing":[34],"unstable":[35],"modes.":[36],"We":[37,91],"prove":[38],"that":[39],"closed-loop":[41,89,97,131],"system":[42,98],"with":[43,99,126],"state-feedback":[46],"is":[48],"locally":[49],"asymptotically":[50],"stable":[51],"by":[52,106],"constructing":[53],"an":[54],"appropriate":[55],"Lyapunov":[56],"functional":[57],"depending":[58],"on":[59],"canonical":[61],"norm":[63],"and":[64,76,121,133],"degree":[66],"homogeneity.":[68],"Next,":[69],"construct":[71],"linear":[73,128],"infinite-dimensional":[74],"observer":[75],"output-feedback":[80],"to":[82,116],"achieve":[83],"local":[85],"stability":[86],"system.":[90],"analyse":[92],"well-posedness":[94],"state/output":[103],"feedback":[104],"using":[107],"Arzela\u2013Ascoli":[109],"theorem.":[110],"Finally,":[111],"present":[113],"numerical":[114],"simulations":[115],"support":[117],"analytical":[119],"results":[120],"compare":[122],"our":[123],"proposed":[124],"one":[129],"regarding":[130],"performance":[132],"peaking":[135],"effect.":[136]},"counts_by_year":[],"updated_date":"2026-03-07T16:01:11.037858","created_date":"2025-10-25T00:00:00"}
