  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.

Optimization and Control