On Approximation of Backstepping Observers for Parabolic Systems with Robin Boundary Conditions

This paper presents an approach for the efficient numerical implementation of backstepping observers for a one dimensional reaction-diffusion-system with Robin boundary conditions. The associated observer gains are interpreted as unbounded operators. Approximating these observer gains together with the system equations the implementation of the observers as well as the whole design process can be considerably simplified. It is shown that for a complete modal observer approximation further simplifications are possible and that the observer can be finally realized without computing the backstepping-kernel.