Adaptive output regulation for a one-dimensional wave system with variable coefficients subject to unknown biased harmonic disturbances

Abstract In this work, we consider the output tracking problem of a hybrid wave-ODE system subject to unknown external disturbances in all possible channels. Both the disturbances and the reference signal are of unknown harmonic type. The performance output is noncollocated with the control input. We first construct an undisturbed auxiliary system and a proper internal model dynamic to restructure the tracking error. Then, we propose an error-based feedback controller to achieve output tracking by utilizing an invertible transform and an adaptive frequency estimation method. The well-posedness and stability of the closed-loop system is established by exploiting the principles of semigroup theory. Finally, these theoretical results are illustrated with numerical simulations.