Publikation:

Optimality-Based Control Space Reduction for Infinite-Dimensional Control Spaces

Vorschaubild

Dateien

Zu diesem Dokument gibt es keine Dateien.

Datum

2025

Autor:innen

Herausgeber:innen

Kontakt

ISSN der Zeitschrift

Electronic ISSN

ISBN

Bibliografische Daten

Verlag

Schriftenreihe

Auflagebezeichnung

URI (zitierfähiger Link)
DOI (zitierfähiger Link)
https://doi.org/10.48550/arXiv.2510.14479
ArXiv-ID

Internationale Patentnummer

Angaben zur Forschungsförderung

Institutionen der Bundesrepublik Deutschland: 05M22VSA

Projekt

Open Access-Veröffentlichung

Sammlungen

Mathematik und Statistik: Publikationen
Core Facility der Universität Konstanz

Gesperrt bis

Titel in einer weiteren Sprache

Publikationstyp
Preprint
Publikationsstatus
Published

Erschienen in

Zusammenfassung

We consider linear model reduction in both the control and state variables for unconstrained linear-quadratic optimal control problems subject to time-varying parabolic PDEs. The first-order optimality condition for a state-space reduced model naturally leads to a reduced structure of the optimal control. Thus, we consider a control- and state-reduced problem that admits the same minimizer as the solely state-reduced problem. Lower and upper a posteriori error bounds for the optimal control and a representation for the error in the optimal function value are provided. These bounds are used in an adaptive algorithm to solve the control problem. We prove its convergence and numerically demonstrate the advantage of combined control and state space reduction.

Zusammenfassung in einer weiteren Sprache

Fachgebiet (DDC)
510 Mathematik

Schlagwörter

Linear-quadratic optimization, parabolic PDEs, adaptive model-order reduction, proper orthogonal decomposition, control space reduction, a posteriori error estimates

Konferenz

Rezension
undefined / . - undefined, undefined

Forschungsvorhaben

Organisationseinheiten

Zeitschriftenheft

Zugehörige Datensätze in KOPS

Vorschaubild
Datensatz
michikartmann/control_reduction: V1.0
(2025) Kartmann, Michael

Zitieren

ISO 690KARTMANN, Michael, Stefan VOLKWEIN, 2025. Optimality-Based Control Space Reduction for Infinite-Dimensional Control Spaces
BibTex
@unpublished{Kartmann2025Optim-75350,
  title={Optimality-Based Control Space Reduction for Infinite-Dimensional Control Spaces},
  year={2025},
  doi={10.48550/arXiv.2510.14479},
  author={Kartmann, Michael and Volkwein, Stefan}
}
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/123456789/75350">
    <dc:contributor>Volkwein, Stefan</dc:contributor>
    <dcterms:issued>2025</dcterms:issued>
    <dc:creator>Kartmann, Michael</dc:creator>
    <dc:language>eng</dc:language>
    <void:sparqlEndpoint rdf:resource="http://localhost/fuseki/dspace/sparql"/>
    <dcterms:isPartOf rdf:resource="https://kops.uni-konstanz.de/server/rdf/resource/123456789/39"/>
    <foaf:homepage rdf:resource="http://localhost:8080/"/>
    <dc:creator>Volkwein, Stefan</dc:creator>
    <bibo:uri rdf:resource="https://kops.uni-konstanz.de/handle/123456789/75350"/>
    <dspace:isPartOfCollection rdf:resource="https://kops.uni-konstanz.de/server/rdf/resource/123456789/39"/>
    <dc:date rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2025-12-01T14:54:56Z</dc:date>
    <dcterms:abstract>We consider linear model reduction in both the control and state variables for unconstrained linear-quadratic optimal control problems subject to time-varying parabolic PDEs. The first-order optimality condition for a state-space reduced model naturally leads to a reduced structure of the optimal control. Thus, we consider a control- and state-reduced problem that admits the same minimizer as the solely state-reduced problem. Lower and upper a posteriori error bounds for the optimal control and a representation for the error in the optimal function value are provided. These bounds are used in an adaptive algorithm to solve the control problem. We prove its convergence and numerically demonstrate the advantage of combined control and state space reduction.</dcterms:abstract>
    <dc:contributor>Kartmann, Michael</dc:contributor>
    <dcterms:title>Optimality-Based Control Space Reduction for Infinite-Dimensional Control Spaces</dcterms:title>
    <dcterms:available rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2025-12-01T14:54:56Z</dcterms:available>
  </rdf:Description>
</rdf:RDF>

Interner Vermerk

xmlui.Submission.submit.DescribeStep.inputForms.label.kops_note_fromSubmitter

Kontakt
URL der Originalveröffentl.

Prüfdatum der URL

Prüfungsdatum der Dissertation

Finanzierungsart

Kommentar zur Publikation

Allianzlizenz
Corresponding Authors der Uni Konstanz vorhanden
Internationale Co-Autor:innen
Universitätsbibliographie
Ja
Begutachtet
Diese Publikation teilen