Publikation: Stabilization of nonautonomous parabolic equations by a single moving actuator
Dateien
Datum
Autor:innen
Herausgeber:innen
ISSN der Zeitschrift
Electronic ISSN
ISBN
Bibliografische Daten
Verlag
Schriftenreihe
Auflagebezeichnung
DOI (zitierfähiger Link)
Internationale Patentnummer
Angaben zur Forschungsförderung
Projekt
Open Access-Veröffentlichung
Sammlungen
Core Facility der Universität Konstanz
Titel in einer weiteren Sprache
Publikationstyp
Publikationsstatus
Erschienen in
Zusammenfassung
It is shown that an internal control based on a moving indicator function is able to stabilize the state of parabolic equations evolving in rectangular domains. For proving the stabilizability result, we start with a control obtained from an oblique projection feedback based on a finite number of static actuators, then we used the continuity of the state when the control varies in a relaxation metric to construct a switching control where at each given instant of time only one of the static actuators is active, finally we construct the moving control by traveling between the static actuators. Numerical computations are performed by a concatenation procedure following a receding horizon control approach. They confirm the stabilizing performance of the moving control.
Zusammenfassung in einer weiteren Sprache
Fachgebiet (DDC)
Schlagwörter
Konferenz
Rezension
Zitieren
ISO 690
AZMI, Behzad, Karl KUNISCH, Sérgio S. RODRIGUES, 2021. Stabilization of nonautonomous parabolic equations by a single moving actuator. In: Discrete and Continuous Dynamical Systems. American Institute of Mathematical Sciences (AIMS). 2021, 41(12), pp. 5789-5824. ISSN 1078-0947. eISSN 1553-5231. Available under: doi: 10.3934/dcds.2021096BibTex
@article{Azmi2021Stabi-58388, year={2021}, doi={10.3934/dcds.2021096}, title={Stabilization of nonautonomous parabolic equations by a single moving actuator}, number={12}, volume={41}, issn={1078-0947}, journal={Discrete and Continuous Dynamical Systems}, pages={5789--5824}, author={Azmi, Behzad and Kunisch, Karl and Rodrigues, Sérgio S.} }
RDF
<rdf:RDF xmlns:dcterms="http://purl.org/dc/terms/" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:bibo="http://purl.org/ontology/bibo/" xmlns:dspace="http://digital-repositories.org/ontologies/dspace/0.1.0#" xmlns:foaf="http://xmlns.com/foaf/0.1/" xmlns:void="http://rdfs.org/ns/void#" xmlns:xsd="http://www.w3.org/2001/XMLSchema#" > <rdf:Description rdf:about="https://kops.uni-konstanz.de/server/rdf/resource/123456789/58388"> <dc:date rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2022-08-26T07:40:11Z</dc:date> <dc:creator>Rodrigues, Sérgio S.</dc:creator> <void:sparqlEndpoint rdf:resource="http://localhost/fuseki/dspace/sparql"/> <bibo:uri rdf:resource="https://kops.uni-konstanz.de/handle/123456789/58388"/> <dc:creator>Azmi, Behzad</dc:creator> <dcterms:abstract xml:lang="eng">It is shown that an internal control based on a moving indicator function is able to stabilize the state of parabolic equations evolving in rectangular domains. For proving the stabilizability result, we start with a control obtained from an oblique projection feedback based on a finite number of static actuators, then we used the continuity of the state when the control varies in a relaxation metric to construct a switching control where at each given instant of time only one of the static actuators is active, finally we construct the moving control by traveling between the static actuators. Numerical computations are performed by a concatenation procedure following a receding horizon control approach. They confirm the stabilizing performance of the moving control.</dcterms:abstract> <dspace:isPartOfCollection rdf:resource="https://kops.uni-konstanz.de/server/rdf/resource/123456789/39"/> <dc:creator>Kunisch, Karl</dc:creator> <dcterms:title>Stabilization of nonautonomous parabolic equations by a single moving actuator</dcterms:title> <dcterms:available rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2022-08-26T07:40:11Z</dcterms:available> <dcterms:rights rdf:resource="https://rightsstatements.org/page/InC/1.0/"/> <dc:contributor>Rodrigues, Sérgio S.</dc:contributor> <dc:rights>terms-of-use</dc:rights> <dcterms:isPartOf rdf:resource="https://kops.uni-konstanz.de/server/rdf/resource/123456789/39"/> <dc:contributor>Kunisch, Karl</dc:contributor> <dc:contributor>Azmi, Behzad</dc:contributor> <dcterms:issued>2021</dcterms:issued> <foaf:homepage rdf:resource="http://localhost:8080/"/> <dc:language>eng</dc:language> </rdf:Description> </rdf:RDF>