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M2AN, Vol. 42, N°1, pp. 1-23
DOI: 10.1051/m2an:2007054
Proper orthogonal decomposition for optimality systems
Karl Kunisch and Stefan VolkweinKarl-Franzens-Universität Graz, Institut für Mathematik und Wissenschaftliches Rechnen, Heinrichstrasse 36, 8010 Graz, Austria. karl.kunisch@uni-graz.at; stefan.volkwein@uni-graz.at
(Received March 24, 2006. Published online 12 January 2008.)
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).
Mathematics Subject Classification. 35K20, 65Nxx, 90C20
Key words: Optimal control, partial differential equations, proper orthogonal decomposition, model reduction.
© EDP Sciences, SMAI 2008