Finite-time observer–based robust fault estimation for nonlinear systems

This article investigates the finite-time fault-estimation problem for a class of Lipschitz nonlinear systems with actuator faults and unknown input disturbances. Specifically, the original system is preliminarily decoupled into two reduced-order subsystems using a linear nonsingular transformation. A novel finite-time observer is proposed to estimate actuator faults in finite time. Subsequently, the proposed finite-time observer is extended to nonlinear systems with unknown input disturbances to investigate the robust fault-estimation problem. The actuator fault and unknown input disturbance are estimated simultaneously using two finite-time observations. Furthermore, a fault-estimation scheme is designed based on finite-time observers. The finite-time stability of the observers is then analysed using the Moreno–Lyapunov function method. The analytical proofs presented herein demonstrate that estimation errors can converge to a region of zero in finite time. Finally, the effectiveness of the developed finite-time observers and fault-estimation scheme was validated through simulations of a sample single-link flexible-joint robot.