Some properties of nonlinear model predictive control with guaranteed nominal stability

Abstract

In this note, we discuss the properties of model predictive control of nonlinear systems with input constraints. It shows that the prediction trajectory will not leave the terminal set once it enters into it, and the terminal state lies in a sublevel set of the terminal set if there exists a point of the prediction trajectory lying in the sublevel set. Furthermore, we show that the feasible set of the related optimization problem is a bounded set around the origin.