Optimal state estimation and fault diagnosis for a class of nonlinear systems

This study proposes a scheme for state estimation and, consequently, fault diagnosis in nonlinear systems. Initially, an optimal nonlinear observer is designed for nonlinear systems subject to an actuator or plant fault. By utilizing Lyapunov's direct method, the observer is proved to be optimal with respect to a performance function, including the magnitude of the observer gain and the convergence time. The observer gain is obtained by using approximation of Hamilton-Jacobi-Bellman (HJB) equation. The approximation is determined via an online trained neural network (NN). Next a class of affine nonlinear systems is considered which is subject to unknown disturbances in addition to fault signals. In this case, for each fault the original system is transformed to a new form in which the proposed optimal observer can be applied for state estimation and fault detection and isolation (FDI). Simulation results of a single-link flexible joint robot (SLFJR) electric drive system show the effectiveness of the proposed methodology.