Numerical Discretization Methods for the Discounted Linear Quadratic Control Problem
Abstract
This study focuses on the numerical discretization methods for the continuous-time discounted linear-quadratic optimal control problem (LQ-OCP) with time delays. By assuming piecewise constant inputs, we formulate the discrete system matrices of the discounted LQ-OCPs into systems of differential equations. Subsequently, we derive the discrete-time equivalent of the discounted LQ-OCP by solving these systems. This paper presents three numerical methods for solving the proposed differential equations systems: the fixed-time-step ordinary differential equation (ODE) method, the step-doubling method, and the matrix exponential method. Our numerical experiment demonstrates that all three methods accurately solve the differential equation systems. Interestingly, the step-doubling method emerges as the fastest among them while maintaining the same level of accuracy as the fixed-time-step ODE method.
Cite
@article{arxiv.2407.18769,
title = {Numerical Discretization Methods for the Discounted Linear Quadratic Control Problem},
author = {Zhanhao Zhang and Steen Hørsholt and John Bagterp Jørgensen},
journal= {arXiv preprint arXiv:2407.18769},
year = {2024}
}