Finite-dimensional observer-based boundary stabilization of reaction-diffusion equations with a either Dirichlet or Neumann boundary measurement

TL;DR

This paper develops a method for boundary stabilization of reaction-diffusion equations using finite-dimensional observers, applicable with Dirichlet or Neumann boundary measurements, extending previous bounded operator assumptions.

Contribution

It demonstrates that finite-dimensional state-feedback and observers can be designed for reaction-diffusion PDEs with boundary measurements, regardless of boundedness assumptions.

Findings

Successful boundary stabilization with finite-dimensional observers.

Applicable to both Dirichlet and Neumann boundary measurements.

Extends previous methods beyond bounded operator assumptions.

Abstract

This paper investigates the output feedback boundary control of reaction-diffusion equations with either distributed or boundary measurement by means of a finite-dimensional observer. A constructive method dealing with the design of finite-dimensional observers for the feedback stabilization of reaction-diffusion equations was reported in a recent paper in the case where either the control or the observation operator is bounded and also satisfies certain regularity assumptions. In this paper, we go beyond by demonstrating that a finite-dimensional state-feedback combined with a finite-dimensional observer can always be successfully designed in order to achieve the Dirichlet boundary stabilization of reaction-diffusion PDEs with a either Dirichlet or Neumann boundary measurement.