Approximate Infinite-Horizon Optimal Control for Stochastic Systems

The policy of an optimal control problem for nonlinear stochastic systems can be characterized by a second-order partial differential equation for which solutions are not readily available. In this paper we provide a systematic method for obtaining approximate solutions for the infinite-horizon optimal control problem in the stochastic framework. The method is demonstrated on an illustrative numerical example in which the control effort is not weighted, showing that the technique is able to deal with one of the most striking features of stochastic optimal control.