Optimal Control of Fractional-order Switching Stochastic Systems

In this paper, we consider an optimal control problem for a switching fractional-order stochastic system. First, to ensure the existence and uniqueness of mild solution of a class of stochastic system of fractional order, a set of sufficient conditions is constructed via contraction mapping principle. Moreover, the fractional-order stochastic switching system is embedded into a large family of systems and it is shown that the set trajectories of the fractional-order switching stochastic system is dense in the set of trajectories of the embedded system. Finally, the existence of fractional optimal controls for the switched optimal control problem is investigated if we limit the number of switches.