An unknown input observer for a class of diffusion-convection-reaction systems

Abstract In this paper the problem of observer design for a class of 1D scalar semi-linear parabolic distributed parameter systems with unknown boundary input is addressed. An unknown input observer is proposed in which the measurement information is imposed directly at the measurement point in form of an algebraic constraint, similar to the reduced order observer in a finite-dimensional set-up. Sufficient conditions for strong state detectability of the system and exponential convergence of the observer are drawn in terms of measurement locations and system parameters. The approach is illustrated with two case studies: (i) an unstable heat equation, and (ii) a diffusion-convection-reaction system with multiple steady-state attractor profiles.