## POD-based augmented Lagrangian method for state constrained heat-convection phenomena

2018
##### Series
Konstanzer Schriften in Mathematik; 377
##### Publication type
Working Paper/Technical Report
Published
##### Abstract
We consider an optimal boundary control problem of the heat equation with convection with bilateral control and state constraints. The goal is to keep the temperature (state) within a desired range while the norm of the boundary controls is minimized. To numerically approximate the unique solution of the problem, a first-order augmented Lagrangian method is utilized. The gradient of the augmented Lagrangian is characterized by the solution of the adjoint equation. To decrease the computational time, we apply a reduced-order approach based on proper orthogonal decomposition (POD). To gain a sufficiently accurate approximation, we propose and compare different manners to compute the snapshots and thus the POD basis. Numerical tests compare the efficiency of the proposed strategies.
510 Mathematics
##### Keywords
Optimal control, model predictive control model reduction, augmented Lagrange method, heat equation
##### Cite This
ISO 690JEHLE, Jonas Siegfried, Luca MECHELLI, Stefan VOLKWEIN, 2018. POD-based augmented Lagrangian method for state constrained heat-convection phenomena
BibTex
@techreport{Jehle2018PODba-42857,
year={2018},
series={Konstanzer Schriften in Mathematik},
title={POD-based augmented Lagrangian method for state constrained heat-convection phenomena},
number={377},
author={Jehle, Jonas Siegfried and Mechelli, Luca and Volkwein, Stefan},
note={Konferenz: IUTAM Symposium 2018, 22. Mai 2018 - 25. Mai 2018, Stuttgart}
}

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#" >
<dc:language>eng</dc:language>
<dc:contributor>Mechelli, Luca</dc:contributor>
<dcterms:issued>2018</dcterms:issued>
<dc:creator>Volkwein, Stefan</dc:creator>
<dcterms:rights rdf:resource="https://rightsstatements.org/page/InC/1.0/"/>
<dcterms:hasPart rdf:resource="https://kops.uni-konstanz.de/bitstream/123456789/42857/3/Jehle_2-gh534968czve7.pdf"/>
<bibo:uri rdf:resource="https://kops.uni-konstanz.de/handle/123456789/42857"/>
<dc:creator>Mechelli, Luca</dc:creator>
<dcterms:abstract xml:lang="eng">We consider an optimal boundary control problem of the heat equation with convection with bilateral control and state constraints. The goal is to keep the temperature (state) within a desired range while the norm of the boundary controls is minimized. To numerically approximate the unique solution of the problem, a first-order augmented Lagrangian method is utilized. The gradient of the augmented Lagrangian is characterized by the solution of the adjoint equation. To decrease the computational time, we apply a reduced-order approach based on proper orthogonal decomposition (POD). To gain a sufficiently accurate approximation, we propose and compare different manners to compute the snapshots and thus the POD basis. Numerical tests compare the efficiency of the proposed strategies.</dcterms:abstract>
<dc:contributor>Volkwein, Stefan</dc:contributor>
<void:sparqlEndpoint rdf:resource="http://localhost/fuseki/dspace/sparql"/>
<dc:creator>Jehle, Jonas Siegfried</dc:creator>
<dcterms:available rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2018-07-16T06:57:19Z</dcterms:available>
<dc:date rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2018-07-16T06:57:19Z</dc:date>
<dspace:isPartOfCollection rdf:resource="https://kops.uni-konstanz.de/server/rdf/resource/123456789/39"/>
<dspace:hasBitstream rdf:resource="https://kops.uni-konstanz.de/bitstream/123456789/42857/3/Jehle_2-gh534968czve7.pdf"/>
<dcterms:title>POD-based augmented Lagrangian method for state constrained heat-convection phenomena</dcterms:title>
<foaf:homepage rdf:resource="http://localhost:8080/"/>
<dc:rights>terms-of-use</dc:rights>
<dc:contributor>Jehle, Jonas Siegfried</dc:contributor>
<dcterms:isPartOf rdf:resource="https://kops.uni-konstanz.de/server/rdf/resource/123456789/39"/>
</rdf:Description>
</rdf:RDF>

##### Comment on publication
Konferenz: IUTAM Symposium 2018, 22. Mai 2018 - 25. Mai 2018, Stuttgart
Yes