Numerical Analysis of Optimality-System POD for Constrained Optimal Control
| Type of Publication: | Contribution to a conference collection |
| Publication status: | Published |
| Author: | Grimm, Eva; Gubisch, Martin; Volkwein, Stefan |
| Year of publication: | 2015 |
| Conference: | 3rd International Workshop on Computational Engineering (CE 2014), Oct 6, 2014 - Oct 10, 2014, Stuttgart |
| Published in: | Recent Trends in Computational Engineering : CE2014 ; Optimization, Uncertainty, Parallel Algorithmus, Coupled and Complex Problems / Mehl, Miriam et al. (ed.). - Cham [u.a.] : Springer, 2015. - (Lecture Notes in Computational Science and Engineering ; 105). - pp. 297-317. - ISSN 1439-7358. - eISSN 2197-7100. - ISBN 978-3-319-22996-6 |
| DOI (citable link): | https://dx.doi.org/10.1007/978-3-319-22997-3_18 |
| Summary: |
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.
|
| Subject (DDC): | 510 Mathematics |
| Bibliography of Konstanz: | Yes |
Cite This
Files in this item
| Files | Size | Format | View |
|---|---|---|---|
|
There are no files associated with this item. |
|||
GRIMM, 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, pp. 297-317. ISSN 1439-7358. eISSN 2197-7100. ISBN 978-3-319-22996-6. Available under: doi: 10.1007/978-3-319-22997-3_18
@inproceedings{Grimm2015Numer-32367, title={Numerical Analysis of Optimality-System POD for Constrained Optimal Control}, year={2015}, doi={10.1007/978-3-319-22997-3_18}, number={105}, isbn={978-3-319-22996-6}, issn={1439-7358}, address={Cham [u.a.]}, publisher={Springer}, 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} }
<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/123456789/32367"> <dc:creator>Volkwein, Stefan</dc:creator> <void:sparqlEndpoint rdf:resource="http://localhost/fuseki/dspace/sparql"/> <dc:contributor>Grimm, Eva</dc:contributor> <dc:date rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2015-12-08T10:01:50Z</dc:date> <foaf:homepage rdf:resource="http://localhost:8080/jspui"/> <dc:creator>Gubisch, Martin</dc:creator> <dcterms:isPartOf rdf:resource="https://kops.uni-konstanz.de/rdf/resource/123456789/39"/> <dspace:isPartOfCollection rdf:resource="https://kops.uni-konstanz.de/rdf/resource/123456789/39"/> <dc:language>eng</dc:language> <dcterms:title>Numerical Analysis of Optimality-System POD for Constrained Optimal Control</dcterms:title> <dcterms:available rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2015-12-08T10:01:50Z</dcterms:available> <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> <dcterms:issued>2015</dcterms:issued> <dc:contributor>Gubisch, Martin</dc:contributor> <dc:creator>Grimm, Eva</dc:creator> <bibo:uri rdf:resource="https://kops.uni-konstanz.de/handle/123456789/32367"/> <dc:contributor>Volkwein, Stefan</dc:contributor> </rdf:Description> </rdf:RDF>
This item appears in the following Collection(s)
Search KOPS
Browse
My Account
