# Boundary control of partial differential equations using frequency domain optimization techniques

## TL;DR

This paper introduces a frequency domain $H_$-control method for boundary control of PDEs, ensuring practical controller implementation and demonstrating effectiveness on reaction-diffusion and wave equations.

## Contribution

The paper develops a novel frequency domain $H_$-control approach for boundary PDE control with practical, simple controllers, applicable to parabolic and hyperbolic systems.

## Key findings

- Effective control of reaction-diffusion with input delay
- Successful boundary anti-damping control of wave equation
- Controllers are physically implementable and structurally simple

## Abstract

We present a frequency domain based $H_\infty$-control strategy to solve boundary control problems for systems governed by parabolic or hyperbolic partial differential equation, where controllers are constrained to be physically implementable and of simple structure suited for practical applications. The efficiency of our technique is demonstrated by controlling a reaction-diffusion equation with input delay, and a wave equation with boundary anti-damping.