Adaptive sensor and actuator fault estimation for a class of uncertain Lipschitz nonlinear systems

This paper deals with state and fault estimations for a class of uncertain Lipschitz nonlinear systems. The proposed scheme combines a descriptor form observer and an adaptive sliding mode observer. The adaptive descriptor sliding approach is proposed to jointly estimate the state and reconstruct the sensor fault while rejecting the effect of uncertainties and Lipschitz nonlinearities. Using a Lyapunov analysis, the stability condition is analyzed and the observer gains are designed such that the reduced-order system is practically stable. Then, an adaptive super-twisting observer is derived to reconstruct the actuator faults. The main feature of the proposed adaptive scheme is that it does not overestimate the observer gains, which mitigates chattering in the presence of bounded uncertainties, actuator, and sensor faults with unknown boundaries. Simulation results for a robotic manipulator show the effectiveness of the proposed method.