Constrained robust model predictive control based on periodic invariance

The dual-mode strategy has been adopted in many constrained MPC methods. The size of stabilizable regions of states of MPC methods depends on the size of underlying feasible and positively invariant set and number of control moves. These results, however, could be conservative because the definition of positive invariance does not allow temporal leave of states from the set. in this paper, a concept of periodic invariance is introduced in which states are allowed to leave a set temporarily but return into the set in finite time steps. This approach is novel in the sense that a set of different state feedback gains can be used to steer the state back into the starting set. These facts make it possible for the periodically invariant sets to be considerably larger than ordinary invariant sets. The periodic invariance can be defined for systems with polyhedral model uncertainties. We derive computationally very efficient MPC methods based on these periodically invariant sets. Some numerical examples are given to show that the use of periodic invariance yields considerably larger stabilizable sets with better performance than the case of using ordinary invariance.