{"id":"https://openalex.org/W3112433384","doi":"https://doi.org/10.1109/tac.2021.3130874","title":"Finite-Dimensional Observer-Based PI Regulation Control of a Reaction\u2013Diffusion Equation","display_name":"Finite-Dimensional Observer-Based PI Regulation Control of a Reaction\u2013Diffusion Equation","publication_year":2021,"publication_date":"2021-11-25","ids":{"openalex":"https://openalex.org/W3112433384","doi":"https://doi.org/10.1109/tac.2021.3130874","mag":"3112433384"},"language":"en","primary_location":{"id":"doi:10.1109/tac.2021.3130874","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2021.3130874","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Automatic Control","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2012.05062","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5068283066","display_name":"Hugo Lhachemi","orcid":"https://orcid.org/0000-0002-2782-4208"},"institutions":[{"id":"https://openalex.org/I4210107720","display_name":"CentraleSup\u00e9lec","ror":"https://ror.org/019tcpt25","country_code":"FR","type":"facility","lineage":["https://openalex.org/I277688954","https://openalex.org/I4210107720"]},{"id":"https://openalex.org/I4210097418","display_name":"Laboratoire des signaux et syst\u00e8mes","ror":"https://ror.org/00skw9v43","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I277688954","https://openalex.org/I277688954","https://openalex.org/I4210097418","https://openalex.org/I4210107720"]},{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"funder","lineage":["https://openalex.org/I1294671590"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Hugo Lhachemi","raw_affiliation_strings":["Université Paris-Saclay, CNRS, CentraleSupélec, Laboratoire des signaux et systèmes, Gif-sur-Yvette, France","[Laboratoire des signaux et systmes (L2S), CentraleSupelec, Gif sur Yvette, France, 91192 (e-mail: hugo.lhachemi@centralesupelec.fr)]"],"affiliations":[{"raw_affiliation_string":"Université Paris-Saclay, CNRS, CentraleSupélec, Laboratoire des signaux et systèmes, Gif-sur-Yvette, France","institution_ids":["https://openalex.org/I4210097418","https://openalex.org/I1294671590"]},{"raw_affiliation_string":"[Laboratoire des signaux et systmes (L2S), CentraleSupelec, Gif sur Yvette, France, 91192 (e-mail: hugo.lhachemi@centralesupelec.fr)]","institution_ids":["https://openalex.org/I4210107720"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5083387069","display_name":"Christophe Prieur","orcid":"https://orcid.org/0000-0002-4456-2019"},"institutions":[{"id":"https://openalex.org/I4210124956","display_name":"Grenoble Images Parole Signal Automatique","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"]},{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"funder","lineage":["https://openalex.org/I1294671590"]},{"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"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Christophe Prieur","raw_affiliation_strings":["Université Grenoble Alpes, CNRS, Grenoble-INP, GIPSA-lab, Grenoble, France","[Gipsa-lab, Department of Automatic Control, CNRS, Saint Martin d'Hres, France, France, 38402 (e-mail: christophe.prieur@gipsa-lab.fr)]"],"affiliations":[{"raw_affiliation_string":"Université Grenoble Alpes, CNRS, Grenoble-INP, GIPSA-lab, Grenoble, France","institution_ids":["https://openalex.org/I4210124956","https://openalex.org/I1294671590","https://openalex.org/I106785703"]},{"raw_affiliation_string":"[Gipsa-lab, Department of Automatic Control, CNRS, Saint Martin d'Hres, France, France, 38402 (e-mail: christophe.prieur@gipsa-lab.fr)]","institution_ids":["https://openalex.org/I4210124956","https://openalex.org/I1294671590"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5068283066"],"corresponding_institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I4210097418","https://openalex.org/I4210107720"],"apc_list":null,"apc_paid":null,"fwci":0.6913,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.67889749,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":93,"max":97},"biblio":{"volume":"67","issue":"11","first_page":"6143","last_page":"6150"},"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9994000196456909,"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/T11416","display_name":"Numerical methods for differential equations","score":0.9944000244140625,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.7700923681259155},{"id":"https://openalex.org/keywords/observer","display_name":"Observer (physics)","score":0.5950164794921875},{"id":"https://openalex.org/keywords/reaction\u2013diffusion-system","display_name":"Reaction\u2013diffusion system","score":0.5230494737625122},{"id":"https://openalex.org/keywords/context","display_name":"Context (archaeology)","score":0.49210208654403687},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4763341546058655},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.4752469062805176},{"id":"https://openalex.org/keywords/controller","display_name":"Controller (irrigation)","score":0.45257729291915894},{"id":"https://openalex.org/keywords/dirichlet-distribution","display_name":"Dirichlet distribution","score":0.4348015785217285},{"id":"https://openalex.org/keywords/dirichlet-boundary-condition","display_name":"Dirichlet boundary condition","score":0.4300697445869446},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.38952022790908813},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.3620380759239197},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3301716446876526},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.329992413520813},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2899533212184906},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1968030035495758}],"concepts":[{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.7700923681259155},{"id":"https://openalex.org/C2780704645","wikidata":"https://www.wikidata.org/wiki/Q9251458","display_name":"Observer (physics)","level":2,"score":0.5950164794921875},{"id":"https://openalex.org/C121231716","wikidata":"https://www.wikidata.org/wiki/Q901210","display_name":"Reaction\u2013diffusion system","level":2,"score":0.5230494737625122},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.49210208654403687},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4763341546058655},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.4752469062805176},{"id":"https://openalex.org/C203479927","wikidata":"https://www.wikidata.org/wiki/Q5165939","display_name":"Controller (irrigation)","level":2,"score":0.45257729291915894},{"id":"https://openalex.org/C169214877","wikidata":"https://www.wikidata.org/wiki/Q981016","display_name":"Dirichlet distribution","level":3,"score":0.4348015785217285},{"id":"https://openalex.org/C110167270","wikidata":"https://www.wikidata.org/wiki/Q1193699","display_name":"Dirichlet boundary condition","level":3,"score":0.4300697445869446},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.38952022790908813},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.3620380759239197},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3301716446876526},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.329992413520813},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2899533212184906},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1968030035495758},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C6557445","wikidata":"https://www.wikidata.org/wiki/Q173113","display_name":"Agronomy","level":1,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","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/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1109/tac.2021.3130874","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2021.3130874","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Automatic Control","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2012.05062","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2012.05062","pdf_url":"https://arxiv.org/pdf/2012.05062","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":null,"raw_type":"text"},{"id":"pmh:oai:HAL:hal-03472730v1","is_oa":true,"landing_page_url":"https://hal.science/hal-03472730","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"https://ieeexplore.ieee.org/abstract/document/9627534","raw_type":"Journal articles"},{"id":"doi:10.48550/arxiv.2012.05062","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2012.05062","pdf_url":null,"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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article-journal"},{"id":"mag:3112433384","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":null}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2012.05062","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2012.05062","pdf_url":"https://arxiv.org/pdf/2012.05062","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":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":34,"referenced_works":["https://openalex.org/W287703190","https://openalex.org/W1498121547","https://openalex.org/W1527296550","https://openalex.org/W1987089714","https://openalex.org/W2020622868","https://openalex.org/W2036831763","https://openalex.org/W2058666951","https://openalex.org/W2058945808","https://openalex.org/W2066096538","https://openalex.org/W2086906338","https://openalex.org/W2095095978","https://openalex.org/W2118360955","https://openalex.org/W2151460005","https://openalex.org/W2478643659","https://openalex.org/W2499641798","https://openalex.org/W2586061796","https://openalex.org/W2606481864","https://openalex.org/W2613784664","https://openalex.org/W2791510101","https://openalex.org/W2900809057","https://openalex.org/W2913168032","https://openalex.org/W2928782170","https://openalex.org/W2973783944","https://openalex.org/W2994113221","https://openalex.org/W2998425443","https://openalex.org/W3026683940","https://openalex.org/W3033071521","https://openalex.org/W3089241465","https://openalex.org/W3100914771","https://openalex.org/W3193762640","https://openalex.org/W3207582864","https://openalex.org/W4205585472","https://openalex.org/W4234350010","https://openalex.org/W4248729779"],"related_works":["https://openalex.org/W3041386942","https://openalex.org/W3146952500","https://openalex.org/W2095095978","https://openalex.org/W2077384691","https://openalex.org/W2105360994","https://openalex.org/W2076841007","https://openalex.org/W1771645225","https://openalex.org/W2116034181","https://openalex.org/W2912883787","https://openalex.org/W2952316992","https://openalex.org/W2547120152","https://openalex.org/W2551678863","https://openalex.org/W2104834337","https://openalex.org/W2137810725","https://openalex.org/W2969966497","https://openalex.org/W3153886863","https://openalex.org/W2967382115","https://openalex.org/W1963762944","https://openalex.org/W3161330240","https://openalex.org/W2738466507"],"abstract_inverted_index":{"This":[0],"article":[1],"investigates":[2],"the":[3,32,46,57,69,72,88,91,94,98],"output":[4],"feedback":[5],"setpoint":[6,48,95],"regulation":[7,49,96],"control":[8,28,50],"of":[9,15,31,34,51,71,90,97],"a":[10,35,39],"reaction\u2013diffusion":[11,20],"equation":[12],"by":[13],"means":[14],"boundary":[16,47],"control.":[17],"The":[18,26],"considered":[19],"plant":[21,92],"may":[22],"be":[23,77],"open-loop":[24],"unstable.":[25],"proposed":[27],"strategy":[29],"consists":[30],"coupling":[33],"finite-dimensional":[36,73],"observer":[37,74],"and":[38,59,93],"PI":[40],"controller":[41],"in":[42],"order":[43,70],"to":[44,85],"achieve":[45,86],"various":[52],"system":[53,99],"outputs":[54],"such":[55],"as":[56],"Dirichlet":[58],"Neumann":[60],"traces.":[61],"In":[62],"this":[63],"context,":[64],"it":[65],"is":[66],"shown":[67],"that":[68],"can":[75],"always":[76],"selected":[78],"large":[79],"enough,":[80],"with":[81],"an":[82],"explicit":[83],"criterion,":[84],"both":[87],"stabilization":[89],"output.":[100]},"counts_by_year":[{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":2}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}