{"id":"https://openalex.org/W2098603504","doi":"https://doi.org/10.1109/cdc.2013.6760459","title":"Null controllability of the 2D heat equation using flatness","display_name":"Null controllability of the 2D heat equation using flatness","publication_year":2013,"publication_date":"2013-12-01","ids":{"openalex":"https://openalex.org/W2098603504","doi":"https://doi.org/10.1109/cdc.2013.6760459","mag":"2098603504"},"language":"en","primary_location":{"id":"doi:10.1109/cdc.2013.6760459","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2013.6760459","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"52nd IEEE Conference on Decision and Control","raw_type":"proceedings-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1304.5426","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5059519742","display_name":"Philippe Martin","orcid":"https://orcid.org/0000-0001-8638-6829"},"institutions":[{"id":"https://openalex.org/I2746051580","display_name":"Universit\u00e9 Paris Sciences et Lettres","ror":"https://ror.org/013cjyk83","country_code":"FR","type":"education","lineage":["https://openalex.org/I2746051580"]},{"id":"https://openalex.org/I70768539","display_name":"\u00c9cole Nationale Sup\u00e9rieure des Mines de Paris","ror":"https://ror.org/04y8cs423","country_code":"FR","type":"education","lineage":["https://openalex.org/I190752583","https://openalex.org/I2746051580","https://openalex.org/I70768539"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Philippe Martin","raw_affiliation_strings":["Centre Autornatique et Systemes, MINES ParisTech, Paris, France","Centre Automatique et Syst\u00e8mes, Mines ParisTech, PSL Research University, 60, boulevard Saint-Michel, 75272 Paris cedex 06, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Centre Autornatique et Systemes, MINES ParisTech, Paris, France","institution_ids":["https://openalex.org/I70768539"]},{"raw_affiliation_string":"Centre Automatique et Syst\u00e8mes, Mines ParisTech, PSL Research University, 60, boulevard Saint-Michel, 75272 Paris cedex 06, France","institution_ids":["https://openalex.org/I70768539","https://openalex.org/I2746051580"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5015767026","display_name":"Lionel Rosier","orcid":"https://orcid.org/0000-0002-5602-9799"},"institutions":[{"id":"https://openalex.org/I2746051580","display_name":"Universit\u00e9 Paris Sciences et Lettres","ror":"https://ror.org/013cjyk83","country_code":"FR","type":"education","lineage":["https://openalex.org/I2746051580"]},{"id":"https://openalex.org/I3017839442","display_name":"Institut \u00c9lie Cartan de Lorraine","ror":"https://ror.org/04rvw8791","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I3017839442","https://openalex.org/I4210141950","https://openalex.org/I90183372"]},{"id":"https://openalex.org/I70768539","display_name":"\u00c9cole Nationale Sup\u00e9rieure des Mines de Paris","ror":"https://ror.org/04y8cs423","country_code":"FR","type":"education","lineage":["https://openalex.org/I190752583","https://openalex.org/I2746051580","https://openalex.org/I70768539"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Lionel Rosier","raw_affiliation_strings":["Institut Elie Cartan de Lorraine, Vandmuvre-l\u00e8s-Nancy, BP, France","Centre Automatique et Syst\u00e8mes, Mines ParisTech, PSL Research University, 60, boulevard Saint-Michel, 75272 Paris cedex 06, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institut Elie Cartan de Lorraine, Vandmuvre-l\u00e8s-Nancy, BP, France","institution_ids":["https://openalex.org/I3017839442"]},{"raw_affiliation_string":"Centre Automatique et Syst\u00e8mes, Mines ParisTech, PSL Research University, 60, boulevard Saint-Michel, 75272 Paris cedex 06, France","institution_ids":["https://openalex.org/I70768539","https://openalex.org/I2746051580"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5065752316","display_name":"Pierre Rouchon","orcid":"https://orcid.org/0000-0001-6160-5634"},"institutions":[{"id":"https://openalex.org/I2746051580","display_name":"Universit\u00e9 Paris Sciences et Lettres","ror":"https://ror.org/013cjyk83","country_code":"FR","type":"education","lineage":["https://openalex.org/I2746051580"]},{"id":"https://openalex.org/I70768539","display_name":"\u00c9cole Nationale Sup\u00e9rieure des Mines de Paris","ror":"https://ror.org/04y8cs423","country_code":"FR","type":"education","lineage":["https://openalex.org/I190752583","https://openalex.org/I2746051580","https://openalex.org/I70768539"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Pierre Rouchon","raw_affiliation_strings":["Centre Autornatique et Systemes, MINES ParisTech, Paris, France","Centre Automatique et Syst\u00e8mes, Mines ParisTech, PSL Research University, 60, boulevard Saint-Michel, 75272 Paris cedex 06, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Centre Autornatique et Systemes, MINES ParisTech, Paris, France","institution_ids":["https://openalex.org/I70768539"]},{"raw_affiliation_string":"Centre Automatique et Syst\u00e8mes, Mines ParisTech, PSL Research University, 60, boulevard Saint-Michel, 75272 Paris cedex 06, France","institution_ids":["https://openalex.org/I70768539","https://openalex.org/I2746051580"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.5023,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.74094526,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"32","issue":null,"first_page":"3738","last_page":"3743"},"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":0.9998000264167786,"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":0.9998000264167786,"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":0.9934999942779541,"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":0.9861000180244446,"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/controllability","display_name":"Controllability","score":0.9680521488189697},{"id":"https://openalex.org/keywords/flatness","display_name":"Flatness (cosmology)","score":0.9492080807685852},{"id":"https://openalex.org/keywords/heat-equation","display_name":"Heat equation","score":0.6928904056549072},{"id":"https://openalex.org/keywords/null","display_name":"Null (SQL)","score":0.6741007566452026},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6025068163871765},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.5746516585350037},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5120018124580383},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.4422111511230469},{"id":"https://openalex.org/keywords/series","display_name":"Series (stratigraphy)","score":0.43029719591140747},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.41582751274108887},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.36381399631500244},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2823389768600464},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.15263378620147705}],"concepts":[{"id":"https://openalex.org/C48209547","wikidata":"https://www.wikidata.org/wiki/Q1331104","display_name":"Controllability","level":2,"score":0.9680521488189697},{"id":"https://openalex.org/C2778530986","wikidata":"https://www.wikidata.org/wiki/Q5457948","display_name":"Flatness (cosmology)","level":3,"score":0.9492080807685852},{"id":"https://openalex.org/C202787564","wikidata":"https://www.wikidata.org/wiki/Q6510488","display_name":"Heat equation","level":2,"score":0.6928904056549072},{"id":"https://openalex.org/C203763787","wikidata":"https://www.wikidata.org/wiki/Q371029","display_name":"Null (SQL)","level":2,"score":0.6741007566452026},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6025068163871765},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.5746516585350037},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5120018124580383},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.4422111511230469},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.43029719591140747},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.41582751274108887},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.36381399631500244},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2823389768600464},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.15263378620147705},{"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/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C26405456","wikidata":"https://www.wikidata.org/wiki/Q338","display_name":"Cosmology","level":2,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"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":8,"locations":[{"id":"doi:10.1109/cdc.2013.6760459","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2013.6760459","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"52nd IEEE Conference on Decision and Control","raw_type":"proceedings-article"},{"id":"pmh:oai:arXiv.org:1304.5426","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1304.5426","pdf_url":"https://arxiv.org/pdf/1304.5426","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":"text"},{"id":"mag:2098603504","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1310.6179.pdf","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:oai:HAL:hal-00971484v1","is_oa":false,"landing_page_url":"https://minesparis-psl.hal.science/hal-00971484","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Decision and Control (CDC), 2013 IEEE 52nd Annual Conference on, Dec 2013, Firenze, Italy. pp.3738 - 3743, ⟨10.1109/CDC.2013.6760459⟩","raw_type":"info:eu-repo/semantics/conferenceObject"},{"id":"pmh:oai:HAL:hal-00971487v1","is_oa":false,"landing_page_url":"https://minesparis-psl.hal.science/hal-00971487","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"1st IFAC workshop on Control of Systems Governed by Partial Differential Equations (CPDE2013), Sep 2013, Paris, France. pp.1-7","raw_type":"info:eu-repo/semantics/conferenceObject"},{"id":"pmh:oai:HAL:hal-01112044v1","is_oa":true,"landing_page_url":"https://minesparis-psl.hal.science/hal-01112044","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":"Automatica, 2014, 50 (12), pp.3067--3076. ⟨10.1016/j.automatica.2014.10.049⟩","raw_type":"info:eu-repo/semantics/article"},{"id":"doi:10.48550/arxiv.1303.2344","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1303.2344","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":"Preprint"},{"id":"doi:10.48550/arxiv.1304.5426","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1304.5426","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":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1304.5426","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1304.5426","pdf_url":"https://arxiv.org/pdf/1304.5426","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":"text"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions","score":0.7300000190734863}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W39337161","https://openalex.org/W630764638","https://openalex.org/W1532154335","https://openalex.org/W1594563152","https://openalex.org/W1966686724","https://openalex.org/W1981740375","https://openalex.org/W1984888568","https://openalex.org/W2002744405","https://openalex.org/W2025851055","https://openalex.org/W2030634628","https://openalex.org/W2065272780","https://openalex.org/W2065297540","https://openalex.org/W2070461805","https://openalex.org/W2073755546","https://openalex.org/W2082009002","https://openalex.org/W2094254426","https://openalex.org/W2104243801","https://openalex.org/W2119461276","https://openalex.org/W2243162423","https://openalex.org/W2322173280","https://openalex.org/W2333341447","https://openalex.org/W4238859827","https://openalex.org/W6742150121"],"related_works":["https://openalex.org/W2006207162","https://openalex.org/W3126379647","https://openalex.org/W1577028882","https://openalex.org/W186581679","https://openalex.org/W4659219","https://openalex.org/W1982378928","https://openalex.org/W2741087143","https://openalex.org/W2912530409","https://openalex.org/W2299879947","https://openalex.org/W2019542844","https://openalex.org/W2185816199","https://openalex.org/W2980487745","https://openalex.org/W2950489395","https://openalex.org/W2067126362","https://openalex.org/W2039360330","https://openalex.org/W3108140878","https://openalex.org/W2963799327","https://openalex.org/W3134798866","https://openalex.org/W3023059517","https://openalex.org/W2962971350"],"abstract_inverted_index":{"We":[0,20],"derive":[1],"in":[2,28],"a":[3,13,39],"direct":[4],"and":[5,32],"rather":[6],"straightforward":[7],"way":[8],"the":[9,22,30,33,36,49,57,60],"null":[10],"controllability":[11],"of":[12,38,59],"2-D":[14],"heat":[15],"equation":[16],"with":[17],"boundary":[18],"control.":[19],"use":[21],"so-called":[23],"flatness":[24],"approach,":[25],"which":[26],"consists":[27],"parameterizing":[29],"solution":[31],"control":[34,46],"by":[35],"derivatives":[37],"\u201cflat":[40],"output\u201d.":[41],"This":[42],"provides":[43],"an":[44],"explicit":[45],"law":[47],"achieving":[48],"exact":[50],"steering":[51],"to":[52],"zero.":[53],"Numerical":[54],"experiments":[55],"demonstrate":[56],"relevance":[58],"approach.":[61]},"counts_by_year":[{"year":2014,"cited_by_count":1}],"updated_date":"2026-07-02T09:51:11.867554","created_date":"2025-10-10T00:00:00"}