Optimality system POD and a-posteriori error analysis for linear-quadratic problems

Thumbnail Image
Date
2011
Editors
Contact
Journal ISSN
Electronic ISSN
ISBN
Bibliographical data
Publisher
Series
Konstanzer Schriften in Mathematik; 291
URI (citable link)
DOI (citable link)
ArXiv-ID
International patent number
Link to the license
EU project number
Project
Open Access publication
Restricted until
Title in another language
Research Projects
Organizational Units
Journal Issue
Publication type
Working Paper/Technical Report
Publication status
Published in
Abstract
In this paper an abstract linear-quadratic optimal control problem governed by an evolution equation is considered. To solve this problem numerically a reduced-order approach based on proper orthogonal decomposition (POD) is applied. The error between the POD suboptimal control and the optimal control of the original problem is controlled by an a-posteriori error analysis. However, if the POD basis has bad approximation properties, a huge number of POD basis function is required to solve the reduced-order problem with the desired accuracy. To overcome this problem optimality system POD (OS-POD) is utilized, where the POD basis is chosen with respect to the optimization criteria.
Summary in another language
Subject (DDC)
510 Mathematics
Keywords
Optimal control,model reduction,proper orthogonal decomposition,a-posteriori error estimates,optimality system POD
Conference
Review
undefined / . - undefined, undefined. - (undefined; undefined)
Cite This
ISO 690VOLKWEIN, Stefan, 2011. Optimality system POD and a-posteriori error analysis for linear-quadratic problems
BibTex
@techreport{Volkwein2011Optim-15360,
  year={2011},
  series={Konstanzer Schriften in Mathematik},
  title={Optimality system POD and a-posteriori error analysis for linear-quadratic problems},
  number={291},
  author={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/123456789/15360">
    <void:sparqlEndpoint rdf:resource="http://localhost/fuseki/dspace/sparql"/>
    <dspace:hasBitstream rdf:resource="https://kops.uni-konstanz.de/bitstream/123456789/15360/1/Volkwein_Optimality.pdf"/>
    <dc:date rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2011-11-24T09:11:50Z</dc:date>
    <dcterms:available rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2011-11-24T09:11:50Z</dcterms:available>
    <dc:contributor>Volkwein, Stefan</dc:contributor>
    <foaf:homepage rdf:resource="http://localhost:8080/"/>
    <bibo:uri rdf:resource="http://kops.uni-konstanz.de/handle/123456789/15360"/>
    <dcterms:hasPart rdf:resource="https://kops.uni-konstanz.de/bitstream/123456789/15360/1/Volkwein_Optimality.pdf"/>
    <dc:rights>terms-of-use</dc:rights>
    <dcterms:isPartOf rdf:resource="https://kops.uni-konstanz.de/server/rdf/resource/123456789/39"/>
    <dc:language>eng</dc:language>
    <dcterms:rights rdf:resource="https://rightsstatements.org/page/InC/1.0/"/>
    <dc:creator>Volkwein, Stefan</dc:creator>
    <dcterms:issued>2011</dcterms:issued>
    <dcterms:abstract xml:lang="eng">In this paper an abstract linear-quadratic optimal control problem governed by an evolution equation is considered. To solve this problem numerically a reduced-order approach based on proper orthogonal decomposition (POD) is applied. The error between the POD suboptimal control and the optimal control of the original problem is controlled by an a-posteriori error analysis. However, if the POD basis has bad approximation properties, a huge number of POD basis function is required to solve the reduced-order problem with the desired accuracy. To overcome this problem optimality system POD (OS-POD) is utilized, where the POD basis is chosen with respect to the optimization criteria.</dcterms:abstract>
    <dcterms:title>Optimality system POD and a-posteriori error analysis for linear-quadratic problems</dcterms:title>
    <dspace:isPartOfCollection rdf:resource="https://kops.uni-konstanz.de/server/rdf/resource/123456789/39"/>
  </rdf:Description>
</rdf:RDF>
Internal note
xmlui.Submission.submit.DescribeStep.inputForms.label.kops_note_fromSubmitter
Contact
URL of original publication
Test date of URL
Examination date of dissertation
Method of financing
Comment on publication
Alliance license
Corresponding Authors der Uni Konstanz vorhanden
International Co-Authors
Bibliography of Konstanz
Yes
Refereed