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Numerical Discretization Methods for the Extended Linear Quadratic Control Problem by Zhang, Zhanhao; Svensen, Jan Lorenz; Kaysfeld, Morten Wahlgreen; Christensen, Anders Hilmar Damm; Hørsholt, Steen; Jørgensen, John Bagterp is a scholarly article available to read on EtoBox.

What is Numerical Discretization Methods for the Extended Linear Quadratic Control Problem about?

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 $\chi^2$ 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.

Author

Zhang, Zhanhao; Svensen, Jan Lorenz; Kaysfeld, Morten Wahlgreen; Christensen, Anders Hilmar Damm; Hørsholt, Steen; Jørgensen, John Bagterp

Published

2024

Language

EN