Distributed cooperative fault detection and isolation for uncertain multi-agent systems based on zonotope theory

In recent years, multi-agent system (MAS) have attracted extensive attention, but the study for MAS via zonotope theory is very few. This article considers the distributed cooperative fault detection (FD) and fault isolation (FI) problems for a MAS, in which every agent is assumed to be with disturbances in both the sate equation and output equation, by combining Luenberger-like observers and zonotope theory. To begin with, a robust H-infinity observer is constructed for each agent, and zonotope theory is applied on the error dynamic system of the H-infinity observer such that the boundary estimation of the system state can be computed iteratively when the MAS has no fault. After this, for distributed cooperative FD purpose, a residual is also constructed based on the H-infinity observer. Because the constructed residual contains disturbance, it cannot be used for FD directly. To overcome this drawback, the interval estimation of the residual is calculated by using zonotope method, and based on the residual interval estimate, a residual-based distributed cooperative FD strategy is presented. Moreover, the distributed cooperative FI scheme is discussed and an FI strategy is also developed by modifying the distributed cooperative FD scheme. Finally, a simulation example is presented to show the effectiveness and advantages of the proposed method.