{"id":"https://openalex.org/W4393301219","doi":"https://doi.org/10.23919/ecc64448.2024.10591284","title":"Inverse Optimal Cardano-Lyapunov Feedback for PDEs with Convection","display_name":"Inverse Optimal Cardano-Lyapunov Feedback for PDEs with Convection","publication_year":2024,"publication_date":"2024-06-25","ids":{"openalex":"https://openalex.org/W4393301219","doi":"https://doi.org/10.23919/ecc64448.2024.10591284"},"language":"en","primary_location":{"id":"doi:10.23919/ecc64448.2024.10591284","is_oa":false,"landing_page_url":"https://doi.org/10.23919/ecc64448.2024.10591284","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2024 European Control Conference (ECC)","raw_type":"proceedings-article"},"type":"conference-paper","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2404.00370","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5047203075","display_name":"Mohamed Camil Belhadjoudja","orcid":null},"institutions":[{"id":"https://openalex.org/I106785703","display_name":"Institut polytechnique de Grenoble","ror":"https://ror.org/05sbt2524","country_code":"FR","type":"education","lineage":["https://openalex.org/I106785703","https://openalex.org/I899635006"]},{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I4210124956","display_name":"GIPSA-Lab","ror":"https://ror.org/02wrme198","country_code":"FR","type":"facility","lineage":["https://openalex.org/I106785703","https://openalex.org/I1294671590","https://openalex.org/I4210124956","https://openalex.org/I899635006","https://openalex.org/I899635006"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"M. C. Belhadjoudja","raw_affiliation_strings":["Université Grenoble Alpes, Grenoble-INP,CNRS, GIPSA-lab,Grenoble,France,F-38000"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Université Grenoble Alpes, Grenoble-INP,CNRS, GIPSA-lab,Grenoble,France,F-38000","institution_ids":["https://openalex.org/I106785703","https://openalex.org/I1294671590","https://openalex.org/I4210124956"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5018293076","display_name":"Miroslav Krsti\u0107","orcid":"https://orcid.org/0000-0002-5523-941X"},"institutions":[{"id":"https://openalex.org/I36258959","display_name":"University of California San Diego","ror":"https://ror.org/0168r3w48","country_code":"US","type":"education","lineage":["https://openalex.org/I36258959"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"M. Krsti\u0107","raw_affiliation_strings":["University of California San Diego,Department of Mechanical and Aerospace Engineering,San Diego,USA,92093","UC San Diego - University of California [San Diego] (UCSD, 9500 Gilman Dr., La Jolla, CA 92093 USA - United States)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of California San Diego,Department of Mechanical and Aerospace Engineering,San Diego,USA,92093","institution_ids":["https://openalex.org/I36258959"]},{"raw_affiliation_string":"UC San Diego - University of California [San Diego] (UCSD, 9500 Gilman Dr., La Jolla, CA 92093 USA - United States)","institution_ids":["https://openalex.org/I36258959"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5012623469","display_name":"M. Maghenem","orcid":null},"institutions":[{"id":"https://openalex.org/I106785703","display_name":"Institut polytechnique de Grenoble","ror":"https://ror.org/05sbt2524","country_code":"FR","type":"education","lineage":["https://openalex.org/I106785703","https://openalex.org/I899635006"]},{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I4210124956","display_name":"GIPSA-Lab","ror":"https://ror.org/02wrme198","country_code":"FR","type":"facility","lineage":["https://openalex.org/I106785703","https://openalex.org/I1294671590","https://openalex.org/I4210124956","https://openalex.org/I899635006","https://openalex.org/I899635006"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"M. Maghenem","raw_affiliation_strings":["Université Grenoble Alpes, Grenoble-INP,CNRS, GIPSA-lab,Grenoble,France,F-38000"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Université Grenoble Alpes, Grenoble-INP,CNRS, GIPSA-lab,Grenoble,France,F-38000","institution_ids":["https://openalex.org/I106785703","https://openalex.org/I1294671590","https://openalex.org/I4210124956"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5024933923","display_name":"E. Witrant","orcid":null},"institutions":[{"id":"https://openalex.org/I106785703","display_name":"Institut polytechnique de Grenoble","ror":"https://ror.org/05sbt2524","country_code":"FR","type":"education","lineage":["https://openalex.org/I106785703","https://openalex.org/I899635006"]},{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I129902397","display_name":"Dalhousie University","ror":"https://ror.org/01e6qks80","country_code":"CA","type":"education","lineage":["https://openalex.org/I129902397"]},{"id":"https://openalex.org/I4210124956","display_name":"GIPSA-Lab","ror":"https://ror.org/02wrme198","country_code":"FR","type":"facility","lineage":["https://openalex.org/I106785703","https://openalex.org/I1294671590","https://openalex.org/I4210124956","https://openalex.org/I899635006","https://openalex.org/I899635006"]}],"countries":["CA","FR"],"is_corresponding":false,"raw_author_name":"E. Witrant","raw_affiliation_strings":["Université Grenoble Alpes, Grenoble-INP,CNRS, GIPSA-lab,Grenoble,France,F-38000","Dalhousie University [Halifax] (6299 South St, Halifax, NS B3H 4R2 - Canada)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Université Grenoble Alpes, Grenoble-INP,CNRS, GIPSA-lab,Grenoble,France,F-38000","institution_ids":["https://openalex.org/I106785703","https://openalex.org/I1294671590","https://openalex.org/I4210124956"]},{"raw_affiliation_string":"Dalhousie University [Halifax] (6299 South St, Halifax, NS B3H 4R2 - Canada)","institution_ids":["https://openalex.org/I129902397"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":5,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.7753,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.80532122,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":95,"max":96},"biblio":{"volume":null,"issue":null,"first_page":"3823","last_page":"3828"},"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/T12772","display_name":"Control and Stability of Dynamical Systems","score":0.9966999888420105,"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/T10791","display_name":"Advanced Control Systems Optimization","score":0.9871000051498413,"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/mathematics","display_name":"Mathematics","score":0.6997515559196472},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.4989337921142578},{"id":"https://openalex.org/keywords/lyapunov-function","display_name":"Lyapunov function","score":0.4873862862586975},{"id":"https://openalex.org/keywords/inverse","display_name":"Inverse","score":0.45747777819633484},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4533979892730713},{"id":"https://openalex.org/keywords/linear-quadratic-regulator","display_name":"Linear-quadratic regulator","score":0.43478280305862427},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.43209123611450195},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.42778488993644714},{"id":"https://openalex.org/keywords/partial-derivative","display_name":"Partial derivative","score":0.41911524534225464},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.41349726915359497},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.38397443294525146},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.21832022070884705},{"id":"https://openalex.org/keywords/law","display_name":"Law","score":0.17446410655975342},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.14880886673927307},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.12481847405433655},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.096617192029953},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.09483134746551514},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.0890163779258728}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6997515559196472},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.4989337921142578},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.4873862862586975},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.45747777819633484},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4533979892730713},{"id":"https://openalex.org/C98779006","wikidata":"https://www.wikidata.org/wiki/Q2520550","display_name":"Linear-quadratic regulator","level":3,"score":0.43478280305862427},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.43209123611450195},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.42778488993644714},{"id":"https://openalex.org/C53846429","wikidata":"https://www.wikidata.org/wiki/Q186475","display_name":"Partial derivative","level":2,"score":0.41911524534225464},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.41349726915359497},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.38397443294525146},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.21832022070884705},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.17446410655975342},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.14880886673927307},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.12481847405433655},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.096617192029953},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.09483134746551514},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0890163779258728},{"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/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","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}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.23919/ecc64448.2024.10591284","is_oa":false,"landing_page_url":"https://doi.org/10.23919/ecc64448.2024.10591284","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2024 European Control Conference (ECC)","raw_type":"proceedings-article"},{"id":"pmh:oai:arXiv.org:2404.00370","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2404.00370","pdf_url":"https://arxiv.org/pdf/2404.00370","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},{"id":"pmh:oai:HAL:hal-04523966v1","is_oa":true,"landing_page_url":"https://hal.science/hal-04523966","pdf_url":"https://hal.science/hal-04523966v1/file/Inv_Optimal_Cardano.pdf","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.science/hal-04523966","raw_type":"info:eu-repo/semantics/preprint"},{"id":"doi:10.48550/arxiv.2404.00370","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2404.00370","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2404.00370","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2404.00370","pdf_url":"https://arxiv.org/pdf/2404.00370","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},"sustainable_development_goals":[{"score":0.41999998688697815,"id":"https://metadata.un.org/sdg/7","display_name":"Affordable and clean energy"}],"awards":[],"funders":[{"id":"https://openalex.org/F4320333359","display_name":"College of Natural Resources and Sciences, Humboldt State University","ror":null}],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4393301219.pdf"},"referenced_works_count":19,"referenced_works":["https://openalex.org/W83782864","https://openalex.org/W1548148540","https://openalex.org/W1970916399","https://openalex.org/W2041076275","https://openalex.org/W2099197607","https://openalex.org/W2111549913","https://openalex.org/W2141784777","https://openalex.org/W2153392494","https://openalex.org/W2157331901","https://openalex.org/W2169932488","https://openalex.org/W2170544117","https://openalex.org/W2172490084","https://openalex.org/W4225366624","https://openalex.org/W4377224316","https://openalex.org/W4381187680","https://openalex.org/W4382935846","https://openalex.org/W4393213779","https://openalex.org/W6862806175","https://openalex.org/W6863260392"],"related_works":["https://openalex.org/W2482034469","https://openalex.org/W2048648086","https://openalex.org/W1969601161","https://openalex.org/W2028893122","https://openalex.org/W1892002403","https://openalex.org/W4309005041","https://openalex.org/W3017943390","https://openalex.org/W2962746246","https://openalex.org/W2203843426","https://openalex.org/W2049369111"],"abstract_inverted_index":{"We":[0,59,181],"consider":[1,21,61],"the":[2,16,55,83,90,93,107,110,113,121,130,134,142,146,149,154,172,190,194],"problem":[3],"of":[4,24,92,112,138,148,177],"inverse":[5,97],"optimal":[6],"control":[7,39,57,84,195],"design":[8],"for":[9,34,69,128],"systems":[10],"that":[11,161,169],"are":[12],"not":[13],"affine":[14],"in":[15,54,82,120,153],"control.":[17],"In":[18],"particular,":[19],"we":[20,95,123,156],"some":[22],"classes":[23],"partial":[25],"differential":[26],"equations":[27],"(PDEs)":[28],"with":[29,64,99],"quadratic":[30,52,80,152,179],"convection":[31],"and":[32],"counter-convection,":[33],"which":[35,70,129],"the$L^{2}$norm":[36],"is":[37,73,133,151,162],"a":[38,47,51,71,74,79,102,116,125,139,158,178],"Lyapunov":[40],"function":[41],"(CLF)":[42],"whose":[43,76],"derivative":[44,77,91,111,147],"has":[45,78,115],"either":[46],"depressed":[48,117],"cubic":[49,118,140],"or":[50,65],"dependence":[53,81,119],"boundary":[56],"input.":[58,85],"also":[60],"diffusive":[62],"PDEs":[63],"without":[66],"linear":[67],"convection,":[68],"weighted$L^{2}$norm":[72],"CLF":[75,114,150],"For":[86,106],"each":[87],"structure":[88],"on":[89],"CLF,":[94],"achieve":[96],"optimality":[98],"respect":[100],"to":[101,171,184,189,192],"meaningful":[103],"cost":[104,126,159],"functional.":[105],"case":[108],"where":[109],"control,":[122,155],"construct":[124,157],"functional":[127,160],"unique":[131,135],"minimizer":[132],"real":[136,175],"root":[137,188],"polynomial:":[141],"Cardano-Lyapunov":[143],"controller.":[144],"When":[145],"minimized":[163],"by":[164],"two":[165,173],"distinct":[166,174],"feedback":[167],"laws,":[168],"correspond":[170],"roots":[176],"equation.":[180],"show":[182],"how":[183],"switch":[185],"from":[186],"one":[187],"other":[191],"reduce":[193],"effort.":[196]},"counts_by_year":[{"year":2025,"cited_by_count":2}],"updated_date":"2026-07-29T14:22:42.915294","created_date":"2024-03-29T00:00:00"}