The Finite-time State Estimation and Fault Reconstruction for Uncertain Linear Systems

To address a class of uncertain linear systems with external disturbances and actuator faults, we propose a method for estimating the finite-time state and reconstructing the actuator faults. First, by state and output equivalent transformations, we obtain a reduced-order decoupled system that can eliminate the influence of both actuator faults and disturbance information from the modeling uncertainty. Based on the above transformations, we present the finite-time estimator in which we employ a delay that can be set to be small enough for the purpose of estimating the states of reduced-order system in finite-time such that the purpose of finite-time state estimation can be realized for the original system. Second, we consider a high-gain sliding mode differentiator to exactly estimate the derivative of the output vector of the original system in finite time. Next, based on the estimates of both the state and output derivative of the original system, we propose an information reconstruction method that can simultaneously estimate actuator faults and uncertain information. Finally, we provide F-16 aircraft model subjects to actuator faults and validate the effectiveness of the proposed method.