Active Fault Diagnosis for Uncertain LPV Systems: A Zonotopic Set-Membership Approach

Active fault diagnosis (AFD) techniques can improve fault diagnosis performance by designing a set of appropriate auxiliary inputs and injecting them into the system to stimulate fault characteristics. The AFD problem for uncertain linear parameter-varying (LPV) systems with bounded external disturbances is studied based on a set-membership approach in this paper. Based on zonotopes, a set-membership observer is designed to estimate system states to reduce the influence of external disturbances, which aims to reduce conservatism. A
$F_{W}$
-radius-based criterion is minimized to get the optimal observer gain matrix. Because of the system uncertainties, the generator matrices of the output sets will have elements associated with the auxiliary input. A method is proposed to eliminate the relationship between the auxiliary input and the generator matrices, and a mixed-integer quadratic program (MIQP) is constructed to get the auxiliary input. By solving the optimization problem, the auxiliary input is designed for the considered finite kinds of faults to achieve fault diagnosis. Finally, numerical simulations are presented to demonstrate the effectiveness of the proposed approach.
Note to Practitioners
—This paper studies the AFD problem for uncertain LPV systems. Most existing AFD methods are proposed for linear time-invariant systems. The uncertainty of the LPV systems makes the existing AFD methods no longer applicable. In addition, most of the existing AFD methods for uncertain LPV systems are based on the following framework: the auxiliary input is designed at the initial time and injected directly into the system. This framework does not adjust the auxiliary input according to the real-time output of the system during the diagnosis process, which leads to the conservatism of the method. To handle these challenges, this paper proposes an AFD method based on a set-membership approach. A set-membership observer is designed to estimate the system state set based on the system output information. Then the auxiliary input is recalculated according to the estimated system state by solving a MIQP problem at each step. Simulation results suggest that the proposed method is feasible, but it has a large computational burden when the system is complex. Our future work is mainly to reduce the computational complexity and the impact of auxiliary inputs on system performance.