Probabilistic Control of Uncertain Linear Systems Using Stochastic Reachability

This paper proposes an approach to algorithmically synthesize control strategies for set-to-set transitions of discrete-time uncertain systems based on reachable set computations in a stochastic setting. For given Gaussian distributions of the initial states and disturbances, state sets wich are reachable to a chosen confidence level under the effect of time-variant control laws are computed by using principles of the ellipsoidal calculus. The proposed algorithm iterates over LMI-constrained semi-definite programming problems to compute probabilistically stabilizing controllers, while ellipsoidal input constraints are considered. An example for illustration is included.