A model predictive control approach to trajectory tracking problems via time-varying level sets of Lyapunov functions

We discuss a model predictive control approach to trajectory tracking problems of constrained nonlinear continuous time systems, where the reference trajectory is a priori known and asymptotically constant. The proposed NMPC scheme is able to explicitly consider input and state constraints while guaranteeing recursive feasibility. To handle the time-varying nature of the tracking problem we advocate the use of time-varying level sets of Lyapunov functions as terminal regions. We prove a necessary and sufficient condition for positive invariance of these sets and show how these sets can be efficiently computed, if a quadratic Lyapunov function is available. As an example we consider a nonlinear CSTR reactor.