Optimal Control for Controllable Stochastic Linear Systems

Abstract

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.

arXiv comment20 pages

References in corpus (1)

• Indefinite Stochastic Linear-Quadratic Optimal Control Problems with Random Coefficients: Closed-Loop Representation of Open-Loop Optimal Controls

Cited by in corpus (1)

• Linear-Quadratic Optimal Control for Backward Stochastic Differential Equations with Random Coefficients