A novel zonotopic Kalman filter-based actuator fault detection for time delay systems

This paper addresses the problems of state estimation and actuator fault diagnosis in linear discrete time delay systems with actuator faults, and a zonotopic Kalman filter-based actuator fault detection (Z-KF-AFD) algorithm is proposed. First, the relationship between faults and states is calculated by approximating small-range noise. Next, by wrapping non-zero initial states with delays and zero initial faults within a zonotopic set, the zonotopic Kalman filter (ZKF) is iteratively derived to establish the association between current and delayed data. The optimal observer estimator gain for the optimal ZKF is then designed by minimizing the size of the zonotopic set. Subsequently, the fault zonotopic set, which links the state at the current time to the delayed state, is separated. Fault detection is achieved by determining whether zero lies within the bounds of the estimated fault zonotope. Finally, the feasibility of the proposed algorithm is validated through fault diagnosis examples involving a numerical system and a bidirectional DC-DC converter system.