Enlarging the domain of attraction of MPC controller using invariant sets

Abstract

This paper presents a method for enlarging the domain of attraction of nonlinear model predictive control (MPC). The useful way of guaranteeing stability of nonlinear MPC is to add a terminal constraint and a terminal cost in the optimization problem. The terminal constraint is a positively invariant set for the system and the terminal cost is an associated Lyapunov function. The domain of attraction of the controller depends on the size of the terminal region and the prediction horizon. By increasing the prediction horizon, the domain of attraction is enlarged but at expense of a greater computational burden. A strategy to enlarge the domain of attraction of MPC without increasing the prediction horizon is presented. The terminal constraint is replaced by a contractive terminal constraint which is given by a sequence of control invariant sets for the system. This strategy guarantees closed loop stability under the same assumptions.