This is not the latest version of this item. The latest version can be found here.
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
Date
2015
Authors
Alla, Alessandro
Falcone, Maurizio
Volkwein, Stefan
Editors
Journal ISSN
Electronic ISSN
ISBN
Bibliographical data
Publisher
Series
Konstanzer Schriften in Mathematik; 339
URI (citable link)
International patent number
Link to the license
EU project number
Project
Open Access publication
Collections
Title in another language
Publication type
Working Paper/Technical Report
Publication status
Published in
Abstract
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.
Summary in another language
Subject (DDC)
510 Mathematics
Keywords
Optimal control, nonlinear dynamical systems, Hamilton-Jacobi Bellman equation, proper orthogonal decomposition, error analysis
Conference
Review
undefined / . - undefined, undefined. - (undefined; undefined)
Cite This
ISO 690
BibTex
RDF
Internal note
xmlui.Submission.submit.DescribeStep.inputForms.label.kops_note_fromSubmitter
Examination date of dissertation
Method of financing
Comment on publication
Der Preprint ist bei der Zeitschrift SIAM Journal on Control and Optimization am 13. September 2015 eingereicht worden.
Alliance license
Corresponding Authors der Uni Konstanz vorhanden
International Co-Authors
Bibliography of Konstanz
Yes