Inherent Robustness Properties of Quasi-infinite Horizon MPC

We consider inherent robustness properties of model predictive control (MPC) for continuous-time nonlinear systems with input constraints and terminal constraints. We show that when the linear quadratic control law is chosen as the terminal control law, and the related Lyapunov matrix is chosen as the terminal penalty matrix, MPC with nominal prediction model and bounded disturbances has some degree of inherent robustness. We emphasize that the input constraint sets can be any compact set rather than convex sets, and our results do not rely on the continuity of the optimal cost functional or control law in the interior of the feasible region.