Descriptor sliding mode approach for fault/noise reconstruction and fault-tolerant control of nonlinear uncertain systems

The problem of fault/noise reconstruction and fault-tolerant control of Lipschitz nonlinear uncertain systems is investigated in this paper. A descriptor sliding mode approach is presented, where an auxiliary descriptor state vector consisting of system state vector, actuator fault vector, and virtual sensor fault vector is introduced to construct a new augmented descriptor system, based on which a novel descriptor sliding mode observer is designed for system state estimation and fault/noise reconstruction. Through LMI optimization the stability conditions of estimation error dynamics are established to facilitate the determination of the design parameters. In light of estimation information, a fault tolerant controller is designed to maintain system stability. It is shown that by utilizing the descriptor sliding mode approach, satisfactory fault reconstruction performance can be obtained, and the reachablity of the sliding mode surfaces can be achieved in both descriptor error space and estimation state space. A numerical simulation example is presented to validate the effectiveness and benefits of the proposed approach.