Case study for stochastic systems: from pontryagin to receding horizon optimal control

The aim of this paper is to explore the implementation of receding horizon optimal control based on the Pontryagin´s maximum principle for the dynamical systems represented by stochastic differential equations. A brief review of stochastic Pontryagin´s maximum principle is given, and then the issues of solving forward-backward stochastic differential equations are addressed which leads to the possibility of implementing the receding horizon optimal controller for a class of stochastic systems. Numerical examples are demonstrated to show the outline of the presented design procedure.