Actuator fault detection and estimation for linear hyperbolic PDEs with Fredholm integrals

This paper considers the actuator detection and estimation problem for a class of linear first-order hyperbolic partial integral differential equation (PIDE) systems. Based on the fault detectability analysis, a Luenberger-type observer is employed to achieve fault detection. However, in the case of actuator fault occurrence, modified Luenberger-type observers are developed such that actuator fault estimation is achieved in the presence of actuator fault while the system state estimation is realized. In comparison to the existing filter-based methods for distributed parameter systems, in proposed method in this manuscript, it is not necessary to transform the plant into the observer canonical form. The advantage of the proposed method is its flexible extension to other linear distributed parameter systems including all Riesz-spectral systems, as well as higher order nonspectral hyperbolic PDE systems. In particular, the proposed method is applicable to stable or unstable plants since the corresponding observation error systems are always stable, and therefore faults as well as plant state can be adequately estimated. Finally, an illustrative example is present to verify theoretical results.