Simultaneous robust actuator and sensor fault estimation for uncertain non-linear Lipschitz systems

The present study proposes two schemes for simultaneously estimating actuator and sensor faults for a class of uncertain non-linear systems. In the first scheme, two sliding mode observers (SMOs) are designed to estimate actuator and sensor faults, respectively, under the assumption that the matching condition holds. In the second scheme, the assumption of matching condition is relaxed and an adaptive observer has been designed to estimate the sensor fault instead of using an SMO. The effects of the system uncertainties on the estimation errors of states and faults are reduced by integrating a prescribed ℋ_∞ disturbance attenuation level into the proposed schemes. The sufficient condition for the existence of the proposed observers with ℋ_∞ tracking performance is derived and expressed as a linear matrix inequality optimisation problem such that the ℒ₂ gain between the estimation errors and system uncertainties is minimised. Finally, a simulation study is presented to illustrate the effectiveness of the proposed schemes.