Online fault detection and diagnosis for a class of positive real infinite dimensional systems

We consider a class of positive real infinite dimensional systems that at some unknown time instance may exhibit component failures. The goal of this work is twofold, namely to estimate the state using only input and output signals of the infinite dimensional system under supervision, and to generate a residual signal which may subsequently be used for the detection and isolation of the component failure. Lyapunov redesign methods that were successfully utilized in finite dimensional systems, are extended and applied to this class of systems and are used to derive adaptation laws for the online approximator of the component failure. Examples that illustrate the applicability of this approach to a parabolic partial differential equation and a delay system are included along with some numerical results.