Fourier-splitting method for solving hyperbolic LQR problems

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.

Año de publicación:

2018

Keywords:

• Hyperbolic LQR problem
• Fourier method
• Optimal feedback control
• Operator splitting method
• Numerical solution

Fuente:

scopus