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Error analysis for POD approximations of infinite horizon problems via the dynamic programming approach

Error analysis for POD approximations of infinite horizon problems via the dynamic programming approach

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ALLA, Alessandro, Maurizio FALCONE, Stefan VOLKWEIN, 2015. Error analysis for POD approximations of infinite horizon problems via the dynamic programming approach

@techreport{Alla2015Error-31958, series={Konstanzer Schriften in Mathematik}, title={Error analysis for POD approximations of infinite horizon problems via the dynamic programming approach}, year={2015}, number={339}, author={Alla, Alessandro and Falcone, Maurizio and Volkwein, Stefan}, note={Der Preprint ist bei der Zeitschrift SIAM Journal on Control and Optimization am 13. September 2015 eingereicht worden.} }

<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:bibo="http://purl.org/ontology/bibo/" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:dcterms="http://purl.org/dc/terms/" xmlns:xsd="http://www.w3.org/2001/XMLSchema#" > <rdf:Description rdf:about="https://kops.uni-konstanz.de/rdf/resource/123456789/31958"> <dcterms:abstract xml:lang="eng">In this paper infinite horizon optimal control problems for nonlinear high-dimensional dynamical systems are studied. Nonlinear feedback laws can be computed via the value function characterized as the unique viscosity solution to the corresponding Hamilton-Jacobi-Bellman (HJB) equation which stems from the dynamic programming approach. However, the bottleneck is mainly due to the curse of dimensionality and HJB equations are only solvable in a relatively small dimension. Therefore, a reduced-order model is derived for the dynamical system and for this purpose the method of proper orthogonal decomposition (POD) is used. The resulting errors in the HJB equations are estimated by an a-priori error analysis, which suggests a new sampling strategy for the POD method. Numerical experiments illustrates the theoretical findings.</dcterms:abstract> <dc:language>eng</dc:language> <dcterms:available rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2015-10-16T09:52:56Z</dcterms:available> <dc:date rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2015-10-16T09:52:56Z</dc:date> <dc:creator>Falcone, Maurizio</dc:creator> <dc:creator>Alla, Alessandro</dc:creator> <dcterms:title>Error analysis for POD approximations of infinite horizon problems via the dynamic programming approach</dcterms:title> <dcterms:rights rdf:resource="http://nbn-resolving.de/urn:nbn:de:bsz:352-20150914100631302-4485392-8"/> <dc:contributor>Falcone, Maurizio</dc:contributor> <dc:contributor>Volkwein, Stefan</dc:contributor> <bibo:uri rdf:resource="http://kops.uni-konstanz.de/handle/123456789/31958"/> <dc:contributor>Alla, Alessandro</dc:contributor> <dcterms:issued>2015</dcterms:issued> <dc:creator>Volkwein, Stefan</dc:creator> </rdf:Description> </rdf:RDF>

Dateiabrufe seit 16.10.2015 (Informationen über die Zugriffsstatistik)

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