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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 a matrix equation.

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