Input Constraint Sets for Robust Regulation of Linear Systems

In robust control under state constraints the set of admissible inputs is usually considered as given, under the assumption that the actuators have been already designed. However, if the input set is too small any controller will fail in stabilizing the closed-loop system while satisfying all prescribed constraints for some initial states of interest, or vice versa the chosen actuators may be over-sized. To handle this issue, in this paper we address the problem of computing the smallest input constraint set such that the closed-loop system is stabilizable from a prescribed set of initial states while respecting all constraints. We focus our attention on linear systems with additive disturbances, and develop the algorithm based on recursive feasibility of robust model predictive control. We demonstrate the results using numerical examples, in which we consider different metrics for the input constraint set selection.