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Fourier-Splitting Method for Solving Hyperbolic LQR Problems

Csomós, Petra and Mena, Hermann (2017) Fourier-Splitting Method for Solving Hyperbolic LQR Problems. Numerical Algebra, Control and Optimization (NACO). ISSN 2155-3289 (In Press)

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Abstract

We consider the numerical approximation to linear quadratic regulator problems for hyperbolic partial differential equations where the dynamics is driven by a strongly continuous semigroup. The optimal control is given in feedback form in terms of Riccati operator equations. The computational cost relies on solving the associated Riccati equation and computing the optimal state. In this paper we propose a novel approach based on operator splitting idea combined with Fourier’s method to efficiently compute the optimal state. The Fourier’s method allows to accurately approximate the exact flow making our approach computational efficient. Numerical experiments in one and two dimensions show the performance of the proposed method.

Item Type: Article
Subjects: Q Science / természettudomány > QA Mathematics / matematika > QA74 Analysis / analízis
Depositing User: Dr. Petra Csomós
Date Deposited: 19 Dec 2017 08:34
Last Modified: 01 Dec 2018 00:15
URI: http://real.mtak.hu/id/eprint/71217

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