Monte Carlo Methods for Controller Approximation and Stabilization in Nonlinear Stochastic Optimal Control

© 2015 An approximation method for receding horizon optimal control, in nonlinear stochastic systems, is considered in this work. This approximation method is based on Monte Carlo simulation and derived via the Feynman-Kac formula, which gives a stochastic interpretation for the solution of a Hamilton-Jacobi-Bellman equation associated with the true optimal controller. It is shown that this controller approximation method practically stabilises the system over an infinite horizon and thus the controller approximation errors do not accumulate or lead to instability over time