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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 a powerful technique for model reduction of non-linear systems. It is based on a Galerkin type discretization with basis elements created from the dynamical system itself. In the context of optimal control this approach may suffer from the fact that the basis elements are computed from a reference trajectory containing features which are quite different from those of the optimally controlled trajectory. A method is proposed which avoids this problem of unmodelled dynamics in the proper orthogonal decomposition approach to optimal control. It is referred to as optimality system proper orthogonal decomposition (OS-POD).

Keywords

Optimal controlpartial differential equationsproper orthogonal decompositionmodel reduction.
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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