Regulation of a reaction-diffusion equation with bounded observation

Abstract

This paper solves a regulation problem for a reaction-diffusion equation. More precisely, for a given bounded observation, we design a boundary controller so that the setpoint output of the equation converges to a prescribed reference signal. The control law is finite-dimensional and is obtained by coupling a pole-placement control law with an observer. The proofs are based on a Lyapunov function and relies on the properties of Sturm-Liouville operators.