Robust Output Regulation for a Wave Equation via Adaptive Internal Model.

This paper considers output regulation for a 1-d wave equation where the disturbances generated from an unknown finite-dimensional exosystem. By solving a Sylvester equation, the original system is decoupled into a PDE-ODE cascade system. An adaptive observer is adopted to estimate all possible unknown frequencies that have entered into a transformed system which has disturbance in tracking error only. By the estimates of the unknown frequencies, we are able to design a tracking error based feedback control to achieve output regulation for this PDEs where the tracking error is solely used and the asymptotic convergence is achieved.