Robust stability of min-max MPC controllers for nonlinear systems with bounded uncertainties

Abstract

The closed loop formulation of the robust MPC has been shown to be a control technique capable of robustly stabilize uncertain nonlinear systems subject to constraints. Robust asymptotic stability of these controllers has been proved when the uncertainties are decaying. In this paper we extend the existing results to the case of uncertainties that decay with the state but do not tend to zero. This allows us to consider both plant uncertainties and external disturbances in a less conservative way. First, we provide some results on robust stability under the considered kind of uncertainties. Based on these, we prove robust stability of the min-max MPC. In the paper we show how the robust design of the local controller is translated to the min-max controller and how the persistent term of the uncertainties determines the convergence rate of the closed-loop system.