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Proper orthogonal decomposition for optimality systems

Published online by Cambridge University Press:  12 January 2008

Karl Kunisch  and
Stefan Volkwein
Karl Kunisch
Affiliation:
Karl-Franzens-Universität Graz, Institut für Mathematik und Wissenschaftliches Rechnen, Heinrichstrasse 36, 8010 Graz, Austria. karl.kunisch@uni-graz.at; stefan.volkwein@uni-graz.at
Stefan Volkwein
Affiliation:
Karl-Franzens-Universität Graz, Institut für Mathematik und Wissenschaftliches Rechnen, Heinrichstrasse 36, 8010 Graz, Austria. karl.kunisch@uni-graz.at; stefan.volkwein@uni-graz.at
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Abstract

Proper orthogonal decomposition (POD) is apowerful technique for model reduction of non-linear systems. Itis based on a Galerkin type discretization with basis elementscreated from the dynamical system itself. In the context ofoptimal control this approach may suffer from the fact that thebasis elements are computed from a reference trajectory containingfeatures which are quite different from those of the optimallycontrolled trajectory. A method is proposed which avoids thisproblem of unmodelled dynamics in the proper orthogonaldecomposition approach to optimal control. It is referred to asoptimality system proper orthogonal decomposition (OS-POD).

Keywords

Optimal controlpartial differential equationsproper orthogonal decompositionmodel reduction.

Information

Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 42 , Issue 1 , January 2008 , pp. 1 - 23
Copyright
© EDP Sciences, SMAI, 2008

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