Optimal Control for Controllable Stochastic Linear Systems

TL;DR

This paper investigates the controllability and optimal control of constrained stochastic linear systems, providing explicit solutions by characterizing optimal parameters through algebraic equations.

Contribution

It introduces a novel approach to solve constrained stochastic LQ problems by explicitly characterizing optimal parameters via algebraic equations, avoiding derivative-based equations.

Findings

Explicit optimal control solutions for constrained stochastic LQ problems

Characterization of optimal parameters through algebraic equations

Enhanced understanding of controllability in 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.