Optimal Control for Fractional Stochastic Differential Systems via Adaptive Dynamic Programming

This paper is concerned with the implementation of optimal control for the fractional stochastic differential systems. Firstly, the fractional stochastic differential systems have been discretized into an approximate integer order system by the Euler-Maruyama method. Secondly, an adaptive dynamic programming algorithm for the discretized system is derived from Bellman's optimality principle, which has been implemented via neural networks with actor-critic structure. Finally, a numerical example is presented to show the feasibility and effectiveness of our scheme.