Robust sensor fault estimation and fault-tolerant control for uncertain Lipschitz nonlinear systems

This paper investigates the problem of fault estimation and fault tolerant control for a class of Lipschitz nonlinear systems, which are subjected simultaneously to sensor faults and uncertainties. By taking the sensor faults as auxiliary states, an augmented system is constructed. For this system, an unknown input observer (UIO) with ℋ∞ performance criterion is first developed to simultaneously estimate states and sensor faults. By using the state estimates obtained from the observer, a state-feedback controller is designed to compensate the effects of faults and to make the fault-tolerant control system asymptotically stable with the prescribed ℋ∞ performance. Based on linear matrix inequality (LMI) technique, algorithms are presented to compute the observer design matrices and controller gain. The effectiveness of the proposed observer and controller are illustrated by considering an example of a satellite control system. The results of the simulation demonstrate that the proposed schemes can successfully estimate sensor faults and guarantee the asymptotic stability of the resulting closed-loop system in the presence of uncertainties and sensor faults.