# Finite-Dimensional Controllers for Robust Regulation of Boundary Control Systems

## TL;DR

This paper develops finite-dimensional controllers for robust output regulation of boundary control systems, applying the approach to PDE models like parabolic and beam equations with damping, supported by numerical Finite Element simulations.

## Contribution

It introduces a novel controller design method based on extended systems and static differential equations for boundary control PDEs, including specific applications and numerical validation.

## Key findings

- Finite-dimensional controllers achieve robust regulation.
- Effective control for high-dimensional PDEs demonstrated.
- Numerical results confirm theoretical predictions.

## Abstract

We study the robust output regulation of linear boundary control systems by constructing extended systems. The extended systems are established based on solving static differential equations under two new conditions. We first consider the abstract setting and present finite-dimensional reduced order controllers. The controller design is then used for particular PDE models: high-dimensional parabolic equations and beam equations with Kelvin-Voigt damping. Numerical examples will be presented using Finite Element Method.