Finite-Dimensional Adaptive Observer Design for Reaction Diffusion Equation With Large Output Delay

The goal of this paper is to present a new finite-dimensional adaptive observer for some uncertain linear parabolic systems with delayed measurements. The observer is based on the modal decomposition approach and uses a classical persistent excitation condition. We prove that by using a finite-dimensional state predictor, we ensure exponential convergence of both states parameters estimation error for arbitrary long constant delay.