Adaptive extended state observer-based distributed fault detection and estimation for an unstable wave equation

In this paper, we study the fault detection along with the estimation problem for an unstable wave equation based on an adaptive extended state observer (ESO) using only boundary measurements. A fault detection filter (FDF) is proposed in the first place to detect fault based on a naive observer. Once an alarm has been raised by the FDF, a fault estimation filter is activated for fault identification by incorporating an adaptive law into the naive observer. The fault estimator along with the adaptive state observer consists of an adaptive ESO motivated by the intuitive idea of ESO. Numerical simulations on a faulty wave equation are presented to validate the fault detection and estimation performance.