Actuator and Sensor Fault Reconstructions for Uncertain Lipschitz Nonlinear Systems Based on H∞ Observers

This paper considers fault reconstruction problems for a class of uncertain Lipschitz nonlinear systems with actuator faults, sensor faults, and external disturbances. First, by extending the state vector, the original system is transformed into an augmented descriptor system before an H observer, which can decouple the disturbances, is developed. Since the sensor faults become parts of the extended state vector, the descriptor observer can provide not only state estimates but also the sensor fault reconstructions. Second, a second-order high-gain sliding mode observer is used to estimate the derivatives of the system outputs in a finite time. Third, using the estimates of the states and the output derivatives, an algebraic actuator fault reconstruction method is proposed. Finally, a simulation example is given to validate the proposed method.