Global disturbance rejection of the uncertain Duffing’s system

In this paper, we deal with the output feedback disturbance rejection problem of the Duffingpsilas system with all the parameters unknown. By treating the unknown sinusoidal external disturbance as a signal produced by an unknown exosystem, we can first formulate the problem as a global robust output regulation problem subject to an unknown exosystem. Then we apply the adaptive output regulation technique to construct an output feedback control law to solve the problem. Further, our adaptive control law contains a parameter update law for estimating the unknown frequency of the disturbance and it is shown that the estimated frequency converges to its real value.