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.
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Figure 11. Enlargements of Figure 9
Figure 12. Enlargements of Figure 10
Figure 13.
Solution to two-dimensional advection equation (8) at time
Figure 14.
Solution to two-dimensional advection equation (8) at time
Figure 22.
Solution to two-dimensional shallow water equations (12) at time
Figure 23.
Solution to two-dimensional shallow water equations (12) at time
Figure 25.
Solution to two-dimensional shallow water equations (12) at time
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