Numerical Discretization Methods for the Extended Linear Quadratic Control Problem
Abstract
In this study, we introduce numerical methods for discretizing continuous-time linear-quadratic optimal control problems (LQ-OCPs). The discretization of continuous-time LQ-OCPs is formulated into differential equation systems, and we can obtain the discrete equivalent by solving these systems. We present the ordinary differential equation (ODE), matrix exponential, and a novel step-doubling method for the discretization of LQ-OCPs. Utilizing Euler-Maruyama discretization with a fine step, we reformulate the costs of continuous-time stochastic LQ-OCPs into a quadratic form, and show that the stochastic cost follows the distribution. In the numerical experiment, we test and compare the proposed numerical methods. The results ensure that the discrete-time LQ-OCP derived using the proposed numerical methods is equivalent to the original problem.
Cite
@article{arxiv.2404.09316,
title = {Numerical Discretization Methods for the Extended Linear Quadratic Control Problem},
author = {Zhanhao Zhang and Jan Lorenz Svensen and Morten Wahlgreen Kaysfeld and Anders Hilmar Damm Christensen and Steen Hørsholt and John Bagterp Jørgensen},
journal= {arXiv preprint arXiv:2404.09316},
year = {2024}
}
Comments
This paper (7 pages) has been accepted by the 22nd European Control Conference (ECC) in Stockholm, Sweden