  In this paper we study stochastic optimal control problems of general fully
coupled forward-backward stochastic differential equations (FBSDEs). In Li and
Wei [8] the authors studied two cases of diffusion coefficients $\sigma$ of
FSDEs, in one case when $\sigma$\ depends on the control and does not depend on
the second component of the solution $(Y, Z)$ of the BSDE, and in the other
case $\sigma$ depends on $Z$ and doesn't depend on the control. Here we study
the general case when $\sigma$ depends on both $Z$ and the control at the same
time. The recursive cost functionals are defined by controlled general fully
coupled FBSDEs, then the value functions are given by taking the essential
supremum of the cost functionals over all admissible controls. We give the
formulation of related generalized Hamilton-Jacobi-Bellman (HJB) equations, and
prove the value function is its viscosity solution.
