Solving stochastic nonlinear optimal control problem using successive approximations method

In this paper, we introduce a systematic method to solve Hamilton Jacobbi Bellman partial differential equation (HJB) arising from stochastic nonlinear optimal control problems. The solution of this HJB is rarely reached using analytical methods, however, this can be done using numerical methods. In this paper, the introduced method can be considered as an extension of the successive approximations method used to solve deterministic nonlinear optimal control problems. The proposed method gives a closed loop feed back control law which is also a difficult target to reach in these kinds of problems