Set-based Active Fault Diagnosis for Discrete-time Linear Descriptor Systems

Abstract

This paper focuses on designing a suitable input sequence for active fault diagnosis (AFD) of the discrete-time linear descriptor (DTLD) system. In order to successfully implement this objective, we propose to transform the descriptor system into a so-called equivalent slow-fast system. In this system form, the study of the slow subsystem is completely consistent with the normal linear system, while the system matrix of the fast subsystem is nilpotent. In this paper, the authors further propose to use the form of an augmented input sequence to describe the state of the fast subsystem, so that the design of an input sequence for the descriptor system can be completed by using the mixed integer quadratic programming (MIQP). Based on the established optimization objective function, this paper proposes a new optimization criterion, considering the smoothness of the input sequence and its energy, and adjusting the ratio of both of the specifications to obtain the optimal input sequence. At the end of this paper, a numerical example is used to illustrate the effectiveness of the proposed method and the new optimization criterion.