Numerical Analysis of Optimality-System POD for Constrained Optimal Control

dc.contributor.authorGrimm, Eva
dc.contributor.authorGubisch, Martin
dc.contributor.authorVolkwein, Stefan
dc.date.accessioned2015-12-08T10:01:50Z
dc.date.available2015-12-08T10:01:50Z
dc.date.issued2015eng
dc.description.abstractIn this work linear-quadratic optimal control problems for parabolic equations with control and state constraints are considered. Utilizing a Lavrentiev regularization we obtain a linear-quadratic optimal control problem with mixed control-state constraints. For the numerical solution a Galerkin discretization is applied utilizing proper orthogonal decomposition (POD). Based on a perturbation method it is determined by a-posteriori error analysis how far the suboptimal control, computed on the basis of the POD method, is from the (unknown) exact one. POD basis updates are computed by optimality-system POD. Numerical examples illustrate the theoretical results for control and state constrained optimal control problems.eng
dc.description.versionpublishedeng
dc.identifier.doi10.1007/978-3-319-22997-3_18eng
dc.identifier.urihttps://kops.uni-konstanz.de/handle/123456789/32367
dc.language.isoengeng
dc.subject.ddc510eng
dc.titleNumerical Analysis of Optimality-System POD for Constrained Optimal Controleng
dc.typeINPROCEEDINGSeng
dspace.entity.typePublication
kops.citation.bibtex
@inproceedings{Grimm2015Numer-32367,
  year={2015},
  doi={10.1007/978-3-319-22997-3_18},
  title={Numerical Analysis of Optimality-System POD for Constrained Optimal Control},
  number={105},
  isbn={978-3-319-22996-6},
  issn={1439-7358},
  publisher={Springer},
  address={Cham [u.a.]},
  series={Lecture Notes in Computational Science and Engineering},
  booktitle={Recent Trends in Computational Engineering : CE2014 ; Optimization, Uncertainty, Parallel Algorithmus, Coupled and Complex Problems},
  pages={297--317},
  editor={Mehl, Miriam},
  author={Grimm, Eva and Gubisch, Martin and Volkwein, Stefan}
}
kops.citation.iso690GRIMM, Eva, Martin GUBISCH, Stefan VOLKWEIN, 2015. Numerical Analysis of Optimality-System POD for Constrained Optimal Control. 3rd International Workshop on Computational Engineering (CE 2014). Stuttgart, 6. Okt. 2014 - 10. Okt. 2014. In: MEHL, Miriam, ed. and others. Recent Trends in Computational Engineering : CE2014 ; Optimization, Uncertainty, Parallel Algorithmus, Coupled and Complex Problems. Cham [u.a.]: Springer, 2015, pp. 297-317. Lecture Notes in Computational Science and Engineering. 105. ISSN 1439-7358. eISSN 2197-7100. ISBN 978-3-319-22996-6. Available under: doi: 10.1007/978-3-319-22997-3_18deu
kops.citation.iso690GRIMM, Eva, Martin GUBISCH, Stefan VOLKWEIN, 2015. Numerical Analysis of Optimality-System POD for Constrained Optimal Control. 3rd International Workshop on Computational Engineering (CE 2014). Stuttgart, Oct 6, 2014 - Oct 10, 2014. In: MEHL, Miriam, ed. and others. Recent Trends in Computational Engineering : CE2014 ; Optimization, Uncertainty, Parallel Algorithmus, Coupled and Complex Problems. Cham [u.a.]: Springer, 2015, pp. 297-317. Lecture Notes in Computational Science and Engineering. 105. ISSN 1439-7358. eISSN 2197-7100. ISBN 978-3-319-22996-6. Available under: doi: 10.1007/978-3-319-22997-3_18eng
kops.citation.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/123456789/32367">
    <dc:creator>Grimm, Eva</dc:creator>
    <dc:date rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2015-12-08T10:01:50Z</dc:date>
    <dcterms:available rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2015-12-08T10:01:50Z</dcterms:available>
    <dc:creator>Gubisch, Martin</dc:creator>
    <bibo:uri rdf:resource="https://kops.uni-konstanz.de/handle/123456789/32367"/>
    <dcterms:abstract xml:lang="eng">In this work linear-quadratic optimal control problems for parabolic equations with control and state constraints are considered. Utilizing a Lavrentiev regularization we obtain a linear-quadratic optimal control problem with mixed control-state constraints. For the numerical solution a Galerkin discretization is applied utilizing proper orthogonal decomposition (POD). Based on a perturbation method it is determined by a-posteriori error analysis how far the suboptimal control, computed on the basis of the POD method, is from the (unknown) exact one. POD basis updates are computed by optimality-system POD. Numerical examples illustrate the theoretical results for control and state constrained optimal control problems.</dcterms:abstract>
    <dspace:isPartOfCollection rdf:resource="https://kops.uni-konstanz.de/server/rdf/resource/123456789/39"/>
    <void:sparqlEndpoint rdf:resource="http://localhost/fuseki/dspace/sparql"/>
    <foaf:homepage rdf:resource="http://localhost:8080/"/>
    <dc:creator>Volkwein, Stefan</dc:creator>
    <dc:contributor>Grimm, Eva</dc:contributor>
    <dc:contributor>Gubisch, Martin</dc:contributor>
    <dcterms:title>Numerical Analysis of Optimality-System POD for Constrained Optimal Control</dcterms:title>
    <dc:contributor>Volkwein, Stefan</dc:contributor>
    <dcterms:issued>2015</dcterms:issued>
    <dc:language>eng</dc:language>
    <dcterms:isPartOf rdf:resource="https://kops.uni-konstanz.de/server/rdf/resource/123456789/39"/>
  </rdf:Description>
</rdf:RDF>
kops.conferencefield3rd International Workshop on Computational Engineering (CE 2014), 6. Okt. 2014 - 10. Okt. 2014, Stuttgartdeu
kops.date.conferenceEnd2014-10-10eng
kops.date.conferenceStart2014-10-06eng
kops.flag.knbibliographytrue
kops.location.conferenceStuttgarteng
kops.sourcefieldMEHL, Miriam, ed. and others. <i>Recent Trends in Computational Engineering : CE2014 ; Optimization, Uncertainty, Parallel Algorithmus, Coupled and Complex Problems</i>. Cham [u.a.]: Springer, 2015, pp. 297-317. Lecture Notes in Computational Science and Engineering. 105. ISSN 1439-7358. eISSN 2197-7100. ISBN 978-3-319-22996-6. Available under: doi: 10.1007/978-3-319-22997-3_18deu
kops.sourcefield.plainMEHL, Miriam, ed. and others. Recent Trends in Computational Engineering : CE2014 ; Optimization, Uncertainty, Parallel Algorithmus, Coupled and Complex Problems. Cham [u.a.]: Springer, 2015, pp. 297-317. Lecture Notes in Computational Science and Engineering. 105. ISSN 1439-7358. eISSN 2197-7100. ISBN 978-3-319-22996-6. Available under: doi: 10.1007/978-3-319-22997-3_18deu
kops.sourcefield.plainMEHL, Miriam, ed. and others. Recent Trends in Computational Engineering : CE2014 ; Optimization, Uncertainty, Parallel Algorithmus, Coupled and Complex Problems. Cham [u.a.]: Springer, 2015, pp. 297-317. Lecture Notes in Computational Science and Engineering. 105. ISSN 1439-7358. eISSN 2197-7100. ISBN 978-3-319-22996-6. Available under: doi: 10.1007/978-3-319-22997-3_18eng
kops.title.conference3rd International Workshop on Computational Engineering (CE 2014)eng
relation.isAuthorOfPublication86bea439-a257-4a07-82a8-bf53b4651c92
relation.isAuthorOfPublicatione9bc68c9-e2ac-40a9-b319-9d8deb7f8ca5
relation.isAuthorOfPublication1331ea51-1e11-44de-851e-280a04907915
relation.isAuthorOfPublication.latestForDiscovery86bea439-a257-4a07-82a8-bf53b4651c92
source.bibliographicInfo.fromPage297eng
source.bibliographicInfo.seriesNumber105eng
source.bibliographicInfo.toPage317eng
source.contributor.editorMehl, Miriam
source.flag.etalEditortrueeng
source.identifier.eissn2197-7100eng
source.identifier.isbn978-3-319-22996-6eng
source.identifier.issn1439-7358eng
source.publisherSpringereng
source.publisher.locationCham [u.a.]eng
source.relation.ispartofseriesLecture Notes in Computational Science and Engineeringeng
source.titleRecent Trends in Computational Engineering : CE2014 ; Optimization, Uncertainty, Parallel Algorithmus, Coupled and Complex Problemseng

Dateien