Active Fault Diagnosis for LPV Systems Based on Constrained Zonotopes

This paper investigates the active fault diagnosis problem for linear parameter-varying systems with bounded disturbances. Constrained zonotopes (CZs) are utilized to model the range of the system disturbances, in which case the system state and output can also be described by CZs. Different models are employed to describe different fault modes. The basic idea of the proposed method is to design proper auxiliary input and inject it into the system to ensure that the system's output is only within the theoretical output set of a certain system mode. The auxiliary input, which can guarantee fault diagnosis and has minimum energy, is calculated by solving a bilevel programming problem. By replacing the inner programming problem with its necessary and sufficient conditions, the original bilevel programming problem can be transformed into a single-level programming problem. Through variable substitution, linear relaxation, and complementary condition transformation, the obtained single-level programming problem can be transformed into a mixed integer quadratic programming problem. Furthermore, in order to reduce conservatism, an online updating scheme is proposed. The auxiliary input is redesigned at every moment and injected into the system by a selection mechanism. A numerical example is presented to demonstrate the effectiveness of the proposed approach.