| Issue |
ESAIM: M2AN
Volume 42, Number 1, January-February 2008
|
|
|---|---|---|
| Page(s) | 1 - 23 | |
| DOI | https://doi.org/10.1051/m2an:2007054 | |
| Published online | 12 January 2008 | |
Proper orthogonal decomposition for optimality systems
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
Received:
24
March
2006
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
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