Multilevel techniques for the solution of HJB minimum-time control problems
Multilevel techniques for the solution of HJB minimum-time control problems
Lade...
Datum
2018
Autor:innen
Herausgeber:innen
ISSN der Zeitschrift
eISSN
item.preview.dc.identifier.isbn
Bibliografische Daten
Verlag
Schriftenreihe
URI (zitierfähiger Link)
Internationale Patentnummer
Link zur Lizenz
EU-Projektnummer
Projekt
Open Access-Veröffentlichung
Sammlungen
Titel in einer weiteren Sprache
Publikationstyp
Working Paper/Technical Report
Publikationsstatus
Submitted
Erschienen 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)
510 Mathematik
Schlagwörter
Hamilton-Jacobi equation, minimum-time problem, value iteration, policy iteration, Anderson acceleration, multilevel acceleration methods, FAS
Konferenz
Rezension
undefined / . - undefined, undefined. - (undefined; undefined)
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>
Interner Vermerk
xmlui.Submission.submit.DescribeStep.inputForms.label.kops_note_fromSubmitter
Prüfungsdatum der Dissertation
Finanzierungsart
Kommentar zur Publikation
Allianzlizenz
Corresponding Authors der Uni Konstanz vorhanden
Internationale Co-Autor:innen
Universitätsbibliographie
Ja