Performance output exponential tracking for a wave equation with a general boundary disturbance

In this paper, we consider performance output tracking for a wave equation with a general boundary disturbance. The control and the disturbance are unmatched. Different from the existing results, the hidden regularity, instead of the high gain or variable structure, is utilized in the adaptive servomechanism design. As a result, we are able to cope with more complicated and general disturbances. Moreover, the performance output can track the reference signal exponentially, and at the same time, all the states of the subsystems involved are uniformly bounded. More specially, the overall closed-loop system is exponentially stable when the disturbance and reference are disconnected to the system. The numerical simulations are presented to illustrate the effect of the proposed scheme.