  This paper is concerned with a constrained stochastic linear-quadratic
optimal control problem, in which the terminal state is fixed and the initial
state is constrained to lie in a stochastic linear manifold. The
controllability of stochastic linear systems is studied. Then the optimal
control is explicitly obtained by considering a parameterized unconstrained
backward LQ problem and an optimal parameter selection problem. A notable
feature of our results is that, instead of solving an equation involving
derivatives with respect to the parameter, the optimal parameter is
characterized by an algebraic equation.
