  The optimal control problem for discrete-time systems with colored
multiplicative noise is discussed in this paper. The problem will be more
difficult to deal with than the case of white noise due to the correlation of
the adjoining state. By solving the forward and backward stochastic difference
equations (FBSDEs), the necessary and sufficient conditions for the solvability
of the optimal control problems in both delay-free and one-step input delay
case are given.
