# Proper orthogonal decomposition for optimality systems

ESAIM: Mathematical Modelling and Numerical Analysis (2008)

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

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topKunisch, 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 -

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## Citations in EuDML Documents

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

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