Publikation: Multilevel techniques for the solution of HJB minimum-time control problems
Dateien
Datum
Autor:innen
Herausgeber:innen
ISSN der Zeitschrift
Electronic ISSN
ISBN
Bibliografische Daten
Verlag
Schriftenreihe
Auflagebezeichnung
URI (zitierfähiger Link)
Internationale Patentnummer
Link zur Lizenz
Angaben zur Forschungsförderung
Projekt
Open Access-Veröffentlichung
Sammlungen
Core Facility der Universität Konstanz
Titel in einer weiteren Sprache
Publikationstyp
Publikationsstatus
Wird erscheinen in
Zusammenfassung
The approximation of feedback control via the Dynamic Programming approach is a challenging problem. The computation of the feedback requires the knowledge of the value function, which can be characterized as the unique viscosity solution of a nonlinear Hamilton-Jacobi-Bellman (HJB) equation. The major obstacle is that the numerical methods known in literature strongly suffer when the dimension of the discretized problem becomes large. This is a strong limitation to the application of classical numerical schemes for the solution of the HJB equation in real applications. To tackle this problem, a new multi-level numerical framework is proposed. Numerical evidences show that classical methods have good smoothing properties, which allow one to use them as smoothers in a multilevel strategy. Moreover, a new smoother iterative scheme based on the Anderson acceleration of the classical value function iteration is introduced. The effectiveness of our new framework is proved by several numerical experiments focusing on minimum-time control problems.
Zusammenfassung in einer weiteren Sprache
Fachgebiet (DDC)
Schlagwörter
Konferenz
Rezension
Zitieren
ISO 690
CIARAMELLA, Gabriele, Giulia FABRINI, 2018. Multilevel techniques for the solution of HJB minimum-time control problemsBibTex
@techreport{Ciaramella2018Multi-44827,
year={2018},
title={Multilevel techniques for the solution of HJB minimum-time control problems},
author={Ciaramella, Gabriele and Fabrini, Giulia}
}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/123456789/44827">
<dcterms:title>Multilevel techniques for the solution of HJB minimum-time control problems</dcterms:title>
<dc:language>eng</dc:language>
<dspace:isPartOfCollection rdf:resource="https://kops.uni-konstanz.de/server/rdf/resource/123456789/39"/>
<dcterms:hasPart rdf:resource="https://kops.uni-konstanz.de/bitstream/123456789/44827/3/Ciaramella_2-11gwqah6olyg0.pdf"/>
<dcterms:available rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2019-02-04T14:26:55Z</dcterms:available>
<dspace:hasBitstream rdf:resource="https://kops.uni-konstanz.de/bitstream/123456789/44827/3/Ciaramella_2-11gwqah6olyg0.pdf"/>
<dcterms:isPartOf rdf:resource="https://kops.uni-konstanz.de/server/rdf/resource/123456789/39"/>
<dcterms:rights rdf:resource="https://rightsstatements.org/page/InC/1.0/"/>
<dc:contributor>Ciaramella, Gabriele</dc:contributor>
<dc:date rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2019-02-04T14:26:55Z</dc:date>
<foaf:homepage rdf:resource="http://localhost:8080/"/>
<dc:rights>terms-of-use</dc:rights>
<dc:contributor>Fabrini, Giulia</dc:contributor>
<dcterms:issued>2018</dcterms:issued>
<dc:creator>Fabrini, Giulia</dc:creator>
<bibo:uri rdf:resource="https://kops.uni-konstanz.de/handle/123456789/44827"/>
<dc:creator>Ciaramella, Gabriele</dc:creator>
<dcterms:abstract xml:lang="eng">The approximation of feedback control via the Dynamic Programming approach is a challenging problem. The computation of the feedback requires the knowledge of the value function, which can be characterized as the unique viscosity solution of a nonlinear Hamilton-Jacobi-Bellman (HJB) equation. The major obstacle is that the numerical methods known in literature strongly suffer when the dimension of the discretized problem becomes large. This is a strong limitation to the application of classical numerical schemes for the solution of the HJB equation in real applications. To tackle this problem, a new multi-level numerical framework is proposed. Numerical evidences show that classical methods have good smoothing properties, which allow one to use them as smoothers in a multilevel strategy. Moreover, a new smoother iterative scheme based on the Anderson acceleration of the classical value function iteration is introduced. The effectiveness of our new framework is proved by several numerical experiments focusing on minimum-time control problems.</dcterms:abstract>
<void:sparqlEndpoint rdf:resource="http://localhost/fuseki/dspace/sparql"/>
</rdf:Description>
</rdf:RDF>
