Balanced Stochastic Optimal Control of Uncertain Linear Systems with Constraints

Abstract

This paper addresses finite-time horizon optimal control for discrete-time dynamics with additional stochastic disturbances. In contrast to most existing approaches to this problem, we also minimize the uncertainty of future states arising from stochastic disturbances and from an uncertain initial state. Thus, the optimal control strategy balances the minimization of the expected distances to a reference signal, and the minimization of the uncertainty respectively. As opposed to prior work, the optimization is formulated subject to possible disturbance feedback policies. This enables to solve one semi-definite program over H steps, instead of solving H problems over one step, and the resulting reduced complexity allows one to use the scheme in online and predictive control. The proposed method is applicable to time-varying state constraints (in the sense of chance constraints) as well as time-invariant input constraints.