Numerical Discretization Methods for the Extended Linear Quadratic Control Problem
<|reference_start|>Numerical Discretization Methods for the Extended Linear Quadratic Control Problem: 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.<|reference_end|>
@article{zhang2024numerical,
    title={Numerical Discretization Methods for the Extended Linear Quadratic
  Control Problem},
    author={Zhanhao Zhang, Jan Lorenz Svensen, Morten Wahlgreen Kaysfeld, Anders
  Hilmar Damm Christensen, Steen H{o}rsholt, John Bagterp J{o}rgensen},
    journal={arXiv preprint arXiv:2404.09316},
    year={2024},
    archivePrefix={arXiv},
    eprint={2404.09316},
    primaryClass={eess.SY cs.SY}
}