Finite-Time Trajectory Tracking Control of a Class of Nonlinear Discrete-Time Systems

This paper studies how to control the output of a class of nonlinear discrete-time systems, to completely track any given bounded reference trajectories in finite time. For this problem, we develop two kinds of constructive control methods for the total output case and the partial output case, respectively. For each case, the first kind of methods can design the time instant after which the complete trajectory tracking is accomplished, but cannot guarantee the monotonic decrease of the norm of the tracking error before that time instant; the other kind of methods not only can determine when the output trajectory coincides with the reference trajectory, but also can make the norm of the tracking error decrease monotonically before that time instant. For the partial output case, the proposed control methods can guarantee that the rest part of the system output is bounded for all the time. These control methods are feasible no matter whether the dynamic models of these systems are smooth or nonsmooth. Then, the simulation and experiment results prove the feasibility of the proposed methods.