An Hi/H∞ optimisation approach to distributed event-triggered fault detection over wireless sensor networks

This paper is concerned with the problem of distributed event-triggered fault detection (FD) for linear discrete time-varying systems over resource-constrained wireless sensor networks. To reduce unnecessary communication frequency of sensor measurements and thus communication resource expenditure, an event-triggered communication mechanism is employed to determine whether or not each sensor's measurement should be broadcast to the distributed fault detection filter (FDF) over the wireless network at each time step. Then, an $ H_{i}/H_{\infty } $ Hi/H∞ optimisation approach is proposed to achieve distributed event-triggered fault detection for the concerned system. Specifically, a set of distributed event-triggered FDFs is constructed based on the event-triggered measurement information from each sensor node and its adjacent nodes. Different from the existing distributed event-triggered FD schemes, the major contributions of this paper are twofold. First, the proposed FDF for each sensor node can be designed individually and the residual signal on each node is completely decoupled from the event-triggered transmission error. Second, the design of distributed event-triggered FDFs is formulated as an $ H_{i}/H_{\infty } $ Hi/H∞ optimisation problem and an optimal solution can be obtained by recursively computing some Riccati recursions. Finally, a numerical example is given to illustrate the effectiveness of the proposed method.