Proper orthogonal decomposition for optimality systems

Karl Kunisch; Stefan Volkwein

ESAIM: Mathematical Modelling and Numerical Analysis (2008)

  • Volume: 42, Issue: 1, page 1-23
  • ISSN: 0764-583X

Abstract

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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).

How to cite

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Kunisch, Karl, and Volkwein, Stefan. "Proper orthogonal decomposition for optimality systems." ESAIM: Mathematical Modelling and Numerical Analysis 42.1 (2008): 1-23. <http://eudml.org/doc/250374>.

@article{Kunisch2008,
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). },
author = {Kunisch, Karl, Volkwein, Stefan},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Optimal control; partial differential equations; proper orthogonal decomposition; model reduction.; optimal control; model reduction; numerical examples},
language = {eng},
month = {1},
number = {1},
pages = {1-23},
publisher = {EDP Sciences},
title = {Proper orthogonal decomposition for optimality systems},
url = {http://eudml.org/doc/250374},
volume = {42},
year = {2008},
}

TY - JOUR
AU - Kunisch, Karl
AU - Volkwein, Stefan
TI - Proper orthogonal decomposition for optimality systems
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2008/1//
PB - EDP Sciences
VL - 42
IS - 1
SP - 1
EP - 23
AB - 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).
LA - eng
KW - Optimal control; partial differential equations; proper orthogonal decomposition; model reduction.; optimal control; model reduction; numerical examples
UR - http://eudml.org/doc/250374
ER -

References

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Citations in EuDML Documents

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  1. Martin Kahlbacher, Stefan Volkwein, POD a-posteriori error based inexact SQP method for bilinear elliptic optimal control problems
  2. Martin Kahlbacher, Stefan Volkwein, POD error based inexact SQP method for bilinear elliptic optimal control problems
  3. Dominique Chapelle, Asven Gariah, Jacques Sainte-Marie, Galerkin approximation with proper orthogonal decomposition : new error estimates and illustrative examples
  4. Dominique Chapelle, Asven Gariah, Jacques Sainte-Marie, Galerkin approximation with proper orthogonal decomposition : new error estimates and illustrative examples
  5. Dominique Chapelle, Asven Gariah, Jacques Sainte-Marie, Galerkin approximation with proper orthogonal decomposition : new error estimates and illustrative examples

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