Boundary Observer for Space and Time Dependent Reaction-Advection-Diffusion Equations

TL;DR

This paper develops a boundary observer for reaction-advection-diffusion equations with space and time dependence, utilizing backstepping and a single boundary measurement, with proof of kernel equation existence.

Contribution

It introduces a novel boundary observer design for complex PDEs using backstepping, requiring only boundary measurements and establishing kernel equation solvability.

Findings

Successful design of boundary observer for reaction-advection-diffusion equations

Proof of existence of the observer kernel equation

Applicability to systems with space and time dependent parameters

Abstract

This paper presents boundary observer design for space and time dependent reaction-advection-diffusion equations using backstepping method. The method uses only a single measurement at the boundary of the systems. The existence of the observer kernel equation is proved using the method of successive approximation.