Asymptotic Disturbance Rejection of the Duffing's System by Adaptive Output Feedback Control

This paper studies the output feedback disturbance rejection problem of the uncertain Duffing's system subject to a sinusoidal external disturbance with unknown frequency and amplitude. We first formulate the problem as a global robust output regulation problem subject to an uncertain exosystem which models the sinusoidal disturbance. Then, we apply the adaptive output regulation technique to construct an output feedback control law to solve the problem. Our adaptive control law contains a parameter update law for estimating the unknown frequency of the disturbance, and we will show that the estimated frequency converges to its real value.