Type of Publication: | Dissertation |
Publication status: | Published |
URI (citable link): | http://nbn-resolving.de/urn:nbn:de:bsz:352-0-355213 |
Author: | Gubisch, Martin |
Year of publication: | 2016 |
Summary: |
In this thesis linear-quadratic optimal control problems for dynamical systems modeled by parabolic partial differential equations with control and state constraints are observed. Different model order reduction techniques basing on a spectral method called proper orthogonal decomposition are analyzed and both a-priori and a-posteriori error bounds are developed to quantify the arising model reduction errors efficiently. Iterative solution techniques for the coupled nonlinear optimality equations are proposed and an associated convergence analysis is provided. The theoretical findings are visualized by numerical tests which illustrate both the advantages and limits of the introduced model reduction strategies.
|
Examination date (for dissertations): | May 20, 2016 |
Dissertation note: | Doctoral dissertation, University of Konstanz |
Subject (DDC): | 510 Mathematics |
Keywords: | model order reduction, proper orthogonal decomposition, optimal control, partial differential equations, state constraints, a-posteriori error analysis |
Link to License: | In Copyright |
Bibliography of Konstanz: | Yes |
GUBISCH, Martin, 2016. Model order reduction techniques for the optimal control of parabolic partial differential equations with control and state constraints [Dissertation]. Konstanz: University of Konstanz
@phdthesis{Gubisch2016Model-35325, title={Model order reduction techniques for the optimal control of parabolic partial differential equations with control and state constraints}, year={2016}, author={Gubisch, Martin}, address={Konstanz}, school={Universität Konstanz} }
<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/123456789/35325"> <dc:rights>terms-of-use</dc:rights> <dc:date rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2016-09-19T06:10:39Z</dc:date> <foaf:homepage rdf:resource="http://localhost:8080/jspui"/> <dcterms:available rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2016-09-19T06:10:39Z</dcterms:available> <dspace:isPartOfCollection rdf:resource="https://kops.uni-konstanz.de/rdf/resource/123456789/39"/> <void:sparqlEndpoint rdf:resource="http://localhost/fuseki/dspace/sparql"/> <dcterms:issued>2016</dcterms:issued> <dc:contributor>Gubisch, Martin</dc:contributor> <bibo:uri rdf:resource="https://kops.uni-konstanz.de/handle/123456789/35325"/> <dspace:hasBitstream rdf:resource="https://kops.uni-konstanz.de/bitstream/123456789/35325/3/Gubisch_0-355213.pdf"/> <dcterms:title>Model order reduction techniques for the optimal control of parabolic partial differential equations with control and state constraints</dcterms:title> <dcterms:hasPart rdf:resource="https://kops.uni-konstanz.de/bitstream/123456789/35325/3/Gubisch_0-355213.pdf"/> <dc:creator>Gubisch, Martin</dc:creator> <dcterms:isPartOf rdf:resource="https://kops.uni-konstanz.de/rdf/resource/123456789/39"/> <dcterms:abstract xml:lang="eng">In this thesis linear-quadratic optimal control problems for dynamical systems modeled by parabolic partial differential equations with control and state constraints are observed. Different model order reduction techniques basing on a spectral method called proper orthogonal decomposition are analyzed and both a-priori and a-posteriori error bounds are developed to quantify the arising model reduction errors efficiently. Iterative solution techniques for the coupled nonlinear optimality equations are proposed and an associated convergence analysis is provided. The theoretical findings are visualized by numerical tests which illustrate both the advantages and limits of the introduced model reduction strategies.</dcterms:abstract> <dcterms:rights rdf:resource="https://rightsstatements.org/page/InC/1.0/"/> <dc:language>eng</dc:language> </rdf:Description> </rdf:RDF>
Gubisch_0-355213.pdf | 282 |