Proper orthogonal decomposition for optimality systems
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 42 (2008) no. 1, pp. 1-23.

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).

DOI : https://doi.org/10.1051/m2an:2007054
Classification : 35K20,  65Nxx,  90C20
Mots clés : optimal control, partial differential equations, proper orthogonal decomposition, model reduction
@article{M2AN_2008__42_1_1_0,
     author = {Kunisch, Karl and Volkwein, Stefan},
     title = {Proper orthogonal decomposition for optimality systems},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     pages = {1--23},
     publisher = {EDP-Sciences},
     volume = {42},
     number = {1},
     year = {2008},
     doi = {10.1051/m2an:2007054},
     zbl = {1141.65050},
     mrnumber = {2387420},
     language = {en},
     url = {http://www.numdam.org/articles/10.1051/m2an:2007054/}
}
Kunisch, Karl; Volkwein, Stefan. Proper orthogonal decomposition for optimality systems. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 42 (2008) no. 1, pp. 1-23. doi : 10.1051/m2an:2007054. http://www.numdam.org/articles/10.1051/m2an:2007054/

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