  In this paper, we study the optimal control problem for system driven by
mixed fractional Brownian motion (including a fractional Brownian motion with
Hurst parameter $H>1/2$ and the underlying standard Brownian motion). By using
Malliavin calculus, we obtain the necessary condition the optimal control
should satisfy. Through martingale representation theorem and the properties of
the transforms operator, we give out the adjoint backward stochastic
differential equation in a natural way. As a straightforward consequence, the
maximum principle for control system driven by fractional Brownian motion and
an independent Brownian motion is also deduced, which is different to the
underlying case. As an application, the linear quadratic case is investigated
to illustrate the main results.
