Regional input-to-state stability of min-max model predictive control

The objective of this paper is, on the base of existing results, to provide a general framework for synthesizing min-max MPC schemes with an a priori robust stability guarantee for nonlinear constrained systems. Using regional input-to-state stability, it is proven that the standard min-max approach can only guarantee practical stability. This is due to the choice of the stage cost. In order to avoid this problem, two different solutions have been considered: the first one is based on a particular design of the stage cost of the performance index, while the second one is based on a dual-mode strategy. It is shown that under fairly mild assumptions both controllers guarantee input-to-state stability.