Inherently robust suboptimal nonlinear MPC: Theory and application

We discuss inherent robust stability properties of discrete-time nonlinear systems controlled by Model Predictive Control (MPC) algorithms that do not necessarily attain the global minimum of the optimization problem solved at each sample time. For these implementable suboptimal MPC algorithms, we prove nominal exponential stability of the origin of the closed-loop system. The stability property is robust with respect to (sufficiently small but otherwise arbitrary) process disturbances and state measurement/estimation errors. When (hard) state constraints appear in the control problem, our result requires a (local) continuity assumption of the feasible input space. If (hard) state constraints are not present, robustness of stability can be proved under standard assumptions. We show an example to illustrate the main ideas behind these results.