Boundary Observer Design for a Wave PDE with Parameter Uncertainty

Abstract

This paper focuses on developing a boundary observer for a wave PDE with parameter uncertainty. This problem is a collocated case where the sensors and the actuators are located at the same boundary. The objective is to design an observer for opposite boundary as well as unknown system parameters. The problem is reformulated as the observer design problem for linear system with simultaneous delays and uncertainties in input and output channels. We represent the delay as a transport PDE and develop adaptive observer for ODE-PDE cascade system. The exponential convergence of the proposed observer is proven under an ad-hoc persistent excitation condition. The performance of the observer is demonstrated in a numerical simulation.