Robust output regulation of 1-d wave equation

In the last a few years, there have been a couple of works addressing output regulation for 1-d linear wave equations without robustness. The aim of this paper is to provide, under the guidance of the internal model principle, a united way to achieve more profound results including fast convergence, no man-made assumption, simple control design and particularly robustness. Different from existing works where disturbance appears only in one channel, we allow disturbances in all possible channels. Our approach is an observer based control approach which is designed only for a nominal system yet also has the power to guarantee output regulation for original uncertain PDE system. Simulation examples are presented to show the effectiveness of the proposed control. (C) 2021 Elsevier Ltd. All rights reserved.

Automated summary

This paper presents a unified approach based on the internal model principle to achieve output regulation for 1-d linear wave equations, with features such as fast convergence, no man-made assumption, simple control design, and robustness. By allowing disturbances in all possible channels and using an observer-based control approach, the proposed method can ensure output regulation for the original uncertain PDE system.