Optimal control of stochastic systems: a numerical study of the stochastic linear quadratic regulator framework

Optimal control of stochastic linear systems is fundamental in control theory, with applications in robotics, finance, and engineering. The Stochastic Linear Quadratic Regulator (SLQR) derives optimal feedback laws via the Riccati equation but requires numerical discretization of the resulting stochastic dynamics. Despite extensive studies on numerical methods for stochastic differential equations, their performance within the SLQR framework remains insufficiently explored. This study compares two predictor–corrector schemes of different orders: the Order 1.0 Predictor-Corrector (PC) method and the Order 2.0 Weak PC method. A one-dimensional linear quadratic problem with a closed-form solution enables precise error evaluation against the analytical trajectory. Convergence analysis across varying time step sizes shows that the Order 2.0 Weak PC method achieves consistently higher accuracy, particularly for fine discretizations, underscoring the importance of higher-order schemes in stochastic optimal control.