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.

Automated summary

This paper considers output regulation for a 1-d wave equation with disturbances generated from an unknown finite-dimensional exosystem. By decoupling the original system into a PDE-ODE cascade system through solving a Sylvester equation, an adaptive observer is utilized to estimate all possible unknown frequencies that affect a transformed system with disturbance only in the tracking error. Based on the estimates of the unknown frequencies, a tracking error based feedback control is designed to achieve output regulation for this PDE, using only the tracking error and achieving asymptotic convergence.