POD basis updates for nonlinear PDE control

Type of Publication: Journal article
Publication status: Published
Author: Gräßle, Carmen; Gubisch, Martin; Metzdorf, Simone; Rogg, Sabrina; Volkwein, Stefan
Year of publication: 2017
Published in: at - Automatisierungstechnik ; 65 (2017), 5. - pp. 298-307. - ISSN 0340-434X. - eISSN 2196-677X
DOI (citable link): https://dx.doi.org/10.1515/auto-2016-0100
Title in another language: POD Basis Updates zur Steuerung nichtlinearer partieller Differentialgleichungen
Summary:
In the present paper a semilinear boundary control problem is considered. For its numerical solution proper orthogonal decomposition (POD) is applied. POD is based on a Galerkin type discretization with basis elements created from the evolution problem itself. In the context of optimal control this approach may suffer from the fact that the basis elements are computed from a reference trajectory containing features which are quite different from those of the optimally controlled trajectory. Therefore, different POD basis update strategies which avoids this problem of unmodelled dynamics are com- pared numerically.
Summary in another language:
Im vorliegenden Paper wird ein semilineares Randsteuerungsproblem betrachtet. Für die numerische Lösung wird Proper Orthogonal Decomposition (POD) verwendet. POD basiert auf einer Galerkin Diskretisierung, bei der die Basiselemente mithilfe des zeitabhängigen Problems erzeugt werden. Bezogen auf das Problem der optimalen Steuerung kann dieser Ansatz jedoch dazu führen, dass die Basiselemente aus einer Referenz-Trajektorie berechnet werden, deren Eigenschaften sich wesentlich von der optimalen Lösung unterscheiden. Deshalb werden hier unterschiedliche POD Basis Update Strategien numerisch verglichen, welche dieses Problem der unmodellierten Dynamik vermeiden.
Subject (DDC): 510 Mathematics
Keywords: Optmal control, reduced-order modeling, proper orthogonal decomposition, nonlinear optimization
Bibliography of Konstanz: Yes

Cite This

Files in this item

Files Size Format View

There are no files associated with this item.

GRÄSSLE, Carmen, Martin GUBISCH, Simone METZDORF, Sabrina ROGG, Stefan VOLKWEIN, 2017. POD basis updates for nonlinear PDE control. In: at - Automatisierungstechnik. 65(5), pp. 298-307. ISSN 0340-434X. eISSN 2196-677X. Available under: doi: 10.1515/auto-2016-0100

@article{Grale2017basis-34979, title={POD basis updates for nonlinear PDE control}, year={2017}, doi={10.1515/auto-2016-0100}, number={5}, volume={65}, issn={0340-434X}, journal={at - Automatisierungstechnik}, pages={298--307}, author={Gräßle, Carmen and Gubisch, Martin and Metzdorf, Simone and Rogg, Sabrina and Volkwein, Stefan} }

<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/rdf/resource/123456789/34979"> <dc:creator>Volkwein, Stefan</dc:creator> <dc:creator>Gubisch, Martin</dc:creator> <foaf:homepage rdf:resource="http://localhost:8080/jspui"/> <void:sparqlEndpoint rdf:resource="http://localhost/fuseki/dspace/sparql"/> <dc:language>eng</dc:language> <dcterms:abstract xml:lang="eng">In the present paper a semilinear boundary control problem is considered. For its numerical solution proper orthogonal decomposition (POD) is applied. POD is based on a Galerkin type discretization with basis elements created from the evolution problem itself. In the context of optimal control this approach may suffer from the fact that the basis elements are computed from a reference trajectory containing features which are quite different from those of the optimally controlled trajectory. Therefore, different POD basis update strategies which avoids this problem of unmodelled dynamics are com- pared numerically.</dcterms:abstract> <dcterms:isPartOf rdf:resource="https://kops.uni-konstanz.de/rdf/resource/123456789/39"/> <dcterms:available rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2016-08-08T12:49:08Z</dcterms:available> <dspace:isPartOfCollection rdf:resource="https://kops.uni-konstanz.de/rdf/resource/123456789/39"/> <dc:creator>Gräßle, Carmen</dc:creator> <dc:contributor>Gräßle, Carmen</dc:contributor> <dc:contributor>Volkwein, Stefan</dc:contributor> <bibo:uri rdf:resource="https://kops.uni-konstanz.de/handle/123456789/34979"/> <dc:contributor>Gubisch, Martin</dc:contributor> <dcterms:issued>2017</dcterms:issued> <dc:contributor>Rogg, Sabrina</dc:contributor> <dc:contributor>Metzdorf, Simone</dc:contributor> <dc:creator>Rogg, Sabrina</dc:creator> <dc:date rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2016-08-08T12:49:08Z</dc:date> <dc:creator>Metzdorf, Simone</dc:creator> <dcterms:title>POD basis updates for nonlinear PDE control</dcterms:title> <dcterms:alternative>POD Basis Updates zur Steuerung nichtlinearer partieller Differentialgleichungen</dcterms:alternative> </rdf:Description> </rdf:RDF>

This item appears in the following Collection(s)

Search KOPS


Browse

My Account