Constrained robust model predictive control based on periodic invariance

In this paper, a receding-horizon control method for input/state constrained systems with polyhedral uncertainties is proposed. The dual-mode prediction strategy is adopted to deal with the constraints and periodically-invariant sets are used to derive a target invariant set of the dual-mode prediction strategy. The proposed control method is shown to have novel characteristics earlier approaches do not have i.e.: (i) the convex-hull of all the periodically invariant sets are invariant in the sense that there are feasible feedback gains guaranteeing invariance for any elements of the convex-hull and it provides larger target sets than other methods based on ordinary invariant sets. (ii) A particular convex-hull of periodically invariant sets, that is computable off-line, can be used as an invariant target set. In this case the number of on-line variables is only equal to the period of invariance and thus the proposed algorithm is computationally very efficient. These on-line variables provide interpolation between different feedback gains to yield best performance.