Performance output tracking for a wave equation subject to unmatched general boundary harmonic disturbance

In this paper, we consider performance output reference tracking for a wave equation with general harmonic disturbance at one end and the control at the other end. We first design a state reference system determined completely by the measured output and the reference signal where the parameter update law is presented. An adaptive servomechanism output feedback control is then designed. It is shown that the closed-loop system is well-posed. Three control objectives are achieved: (a) the performance output is tracking the reference signal; (b) all the internal-loops are bounded; (c) when the disturbance and reference are disconnected, the closed-loop is exponentially stable. Finally, the state of system is shown to be tracking the reference state and the updated parameters are convergent to their true values.