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Volume 7 Issue 2
Mar.  2020

IEEE/CAA Journal of Automatica Sinica

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Hamed Kazemi and Alireza Yazdizadeh, "Optimal State Estimation and Fault Diagnosis for a Class of Nonlinear Systems," IEEE/CAA J. Autom. Sinica, vol. 7, no. 2, pp. 517-526, Mar. 2020. doi: 10.1109/JAS.2020.1003051
Citation: Hamed Kazemi and Alireza Yazdizadeh, "Optimal State Estimation and Fault Diagnosis for a Class of Nonlinear Systems," IEEE/CAA J. Autom. Sinica, vol. 7, no. 2, pp. 517-526, Mar. 2020. doi: 10.1109/JAS.2020.1003051

Optimal State Estimation and Fault Diagnosis for a Class of Nonlinear Systems

doi: 10.1109/JAS.2020.1003051
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  • 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.

     

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    Highlights

    • This study proposes an optimal nonlinear observer for state estimation and fault diagnosis of 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).
    • A class of affine nonlinear systems is considered which is subject to unknown disturbances in addition to fault signals. In this case, we transform the system to a form in which there is a subsystem that includes the fault signal and omits disturbances. Then, by utilizing the proposed observer, the subsystem states and corresponding fault signal can be estimated and diagnosed, respectively.
    • The transformation is done via an existing coordinate transformation based on the concept of observability co-distribution in differential geometry under appropriate technical hypotheses. For each fault of the original system, the fault detection procedure can be repeated. Thus, a bank of FDI observers is introduced for this class of systems.
    • Simulation results of a single-link flexible joint robot (SLFJR) electric drive system show the effectiveness of the proposed methodology.

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