Robust fault reconstruction via learning observers in linear parameter‐varying systems subject to loss of actuator effectiveness

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In this study, the problem of robust fault reconstruction in polytopic linear parameter-varying systems, subject to loss of actuator effectiveness and external disturbances, is investigated using a learning observer (LO). A polytopic LO is proposed to achieve system state estimation and actuator fault reconstruction at the same time. The proposed LO is sensitive to incipient faults because no chattering is induced. Both constant and time-varying faults can be accurately reconstructed and detected. Moreover, simultaneous fault reconstruction and detection can be performed using a single LO because the reconstructed fault signal can be employed as a fault alarm. The stability and convergence of polytopic LO and the uniformly ultimately boundedness of the dynamic error system is proved using Lyapunov stability theory and H ∞ techniques. A systematic design of the LO is effectively solved using standard linear-matrix-inequality techniques. At last, simulation results on a satellite system for attitude control verify the effectiveness of the proposed fault-reconstruction approach.