Stability of infinite horizon MPC with incremental input constraints

In this paper we discuss the asymptotic stability of infinite horizon model predictive control (MPC) with incremental constraints. First, we discuss the properties of optimal cost function of the optimization problem. It shows that the optimal cost function is positive definite, continuous at the equilibrium and monotonic decreasing along the prediction trajectory. We choose the optimal cost function as a candidate Lyapuonv function and prove the asymptotic stability of nonlinear systems under control. We highlight that the optimal cost function is not necessarily continuous except for the equilibrium.