Low complexity parameterized approximations of reachable sets for LTI systems

A low complexity method is proposed, suitable for online (i.e. real-time) implementation, for the computation an outer approximation of the reachable set for a stable linear discrete-time system, subject to external disturbances. The set, within which the disturbances are known to lie is bounded, but time-variant. An ¿optimal¿ outer approximation for the reachable set, the computation of which is of bounded time-space complexity, is proposed. The salient properties of the proposed approximation are established, and efficient online implementation methods, based on multi-parametric linear programming, are proposed. The theoretical results are illustrated with a simulation example. Some remarks are made regarding the applicability of our results in communication constrained robust model predictive control, and future research directions.