Analysis of RHC for Stabilization of Nonautonomous Parabolic Equations Under Uncertainty

Azmi, Behzad; Herrmann, Lukas; Kunisch, Karl

Analysis of RHC for Stabilization of Nonautonomous Parabolic Equations Under Uncertainty

Dateien

Zu diesem Dokument gibt es keine Dateien.

Datum

2024

Autor:innen

Azmi, Behzad

Herrmann, Lukas

Kunisch, Karl

DOI (zitierfähiger Link)

https://doi.org/10.1137/23m1550876

Sammlungen

Mathematik und Statistik

Publikationstyp

Zeitschriftenartikel

Publikationsstatus

Published

Erschienen in

SIAM Journal on Control and Optimization. Society for Industrial & Applied Mathematics (SIAM). 2024, 62(1), pp. 220-242. ISSN 0363-0129. eISSN 1095-7138. Available under: doi: 10.1137/23m1550876

Zusammenfassung

Stabilization of a class of time-varying parabolic equations with uncertain input datausing receding horizon control (RHC) is investigated. The diffusion coefficient and the initial functionare prescribed as random fields. We consider both cases: uniform and log-normal distributions ofthe diffusion coefficient. The controls are chosen to be finite-dimensional and enter into the systemas a linear combination of finitely many indicator functions (actuators) supported in open subsetsof the spatial domain. Under suitable regularity assumptions, we study the expected (averaged)stabilizability of the RHC-controlled system with respect to the number of actuators. An upperbound is also obtained for the failure probability of RHC in relation to the choice of the number ofactuators and parameters in the equation.

Fachgebiet (DDC)

510 Mathematik

Schlagwörter

eceding horizon control, random evolution PDEs, uncertainty, averaged stabiliz-ability, random fields, nonautonomous parabolic equations

Zitieren

ISO 690

AZMI, Behzad, Lukas HERRMANN, Karl KUNISCH, 2024. Analysis of RHC for Stabilization of Nonautonomous Parabolic Equations Under Uncertainty. In: SIAM Journal on Control and Optimization. Society for Industrial & Applied Mathematics (SIAM). 2024, 62(1), pp. 220-242. ISSN 0363-0129. eISSN 1095-7138. Available under: doi: 10.1137/23m1550876

BibTex

@article{Azmi2024-02-29Analy-69788,
  year={2024},
  doi={10.1137/23m1550876},
  title={Analysis of RHC for Stabilization of Nonautonomous Parabolic Equations Under Uncertainty},
  number={1},
  volume={62},
  issn={0363-0129},
  journal={SIAM Journal on Control and Optimization},
  pages={220--242},
  author={Azmi, Behzad and Herrmann, Lukas and Kunisch, Karl}
}

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/123456789/69788">
    <dcterms:title>Analysis of RHC for Stabilization of Nonautonomous Parabolic Equations Under Uncertainty</dcterms:title>
    <dc:contributor>Herrmann, Lukas</dc:contributor>
    <bibo:uri rdf:resource="https://kops.uni-konstanz.de/handle/123456789/69788"/>
    <dcterms:issued>2024-02-29</dcterms:issued>
    <void:sparqlEndpoint rdf:resource="http://localhost/fuseki/dspace/sparql"/>
    <dcterms:isPartOf rdf:resource="https://kops.uni-konstanz.de/server/rdf/resource/123456789/39"/>
    <dc:creator>Herrmann, Lukas</dc:creator>
    <dc:date rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2024-04-17T09:23:46Z</dc:date>
    <dc:contributor>Azmi, Behzad</dc:contributor>
    <foaf:homepage rdf:resource="http://localhost:8080/"/>
    <dspace:isPartOfCollection rdf:resource="https://kops.uni-konstanz.de/server/rdf/resource/123456789/39"/>
    <dc:contributor>Kunisch, Karl</dc:contributor>
    <dcterms:abstract>Stabilization of a class of time-varying parabolic equations with uncertain input datausing receding horizon control (RHC) is investigated.  The diffusion coefficient and the initial functionare prescribed as random fields.  We consider both cases:  uniform and log-normal distributions ofthe diffusion coefficient.  The controls are chosen to be finite-dimensional and enter into the systemas a linear combination of finitely many indicator functions (actuators) supported in open subsetsof  the  spatial  domain.   Under  suitable  regularity  assumptions,  we  study  the  expected  (averaged)stabilizability  of  the  RHC-controlled  system  with  respect  to  the  number  of  actuators.   An  upperbound is also obtained for the failure probability of RHC in relation to the choice of the number ofactuators and parameters in the equation.</dcterms:abstract>
    <dc:creator>Azmi, Behzad</dc:creator>
    <dcterms:available rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2024-04-17T09:23:46Z</dcterms:available>
    <dc:language>eng</dc:language>
    <dc:creator>Kunisch, Karl</dc:creator>
  </rdf:Description>
</rdf:RDF>

Universitätsbibliographie

Ja

Begutachtet

Ja