Discrete ILQG method based on high-order exponential Runge–Kutta discretization

In this study, we employ the iterative Linear Quadratic Gaussian (ILQG) method, discretized based on the high-order exponential Runge–Kutta methods, to numerically solve stochastic optimal control problems. In the sense of weak convergence, we derive a mean-square third-order scheme with an additive noise, and provide corresponding order conditions. As the analysis of order conditions is local, the analysis is transformed into a $L^{\infty }$ error estimate of the discrete problem with control constraints. Finally, the global control law is approximated by computing the node control via the ILQG method. The numerical experiment further demonstrates the significant stability of ILQG in dealing with stochastic semilinear control problems. The proposed approach presents the advantages of simplicity and efficiency.