Discrete-time Non-smooth Nonlinear MPC: Stability and Robustness

This paper considers discrete-time nonlinear, possibly discontinuous, systems in closed-loop with Model Predictive Controllers (MPC). The aim of the paper is to provide a priori sufficient conditions for asymptotic stability in the Lyapunov sense and robust stability, while allowing for both the system dynamics and the value function of the MPC cost to be discontinuous functions of the state. The motivation for this work lies in the recent development of MPC for hybrid systems, which are inherently discontinuous and nonlinear. For a particular class of discontinuous piecewise affine systems, a new MPC set-up based on infinity norms is proposed, which is proven to be robust to bounded additive disturbances. This robust stability result does not require continuity of the system dynamics nor of the MPC value function.