An Extended Hi/H∞ Optimization Approach to Dynamic Event-Triggered Fault Detection for a Class of Nonlinear Systems

This article investigates the problem of dynamic event-triggered fault detection (FD) for a class of nonlinear systems. Under the dynamic event-triggered strategy, an observer-based nonlinear fault detection filter (FDF) is developed as a residual generator through the processes of time-update and event-update. Different from the existing schemes of nonlinear event-triggered FD, the generated residual signal is fully decoupled from the event-triggered transmission error, which allows an independent development of the residual generator and the dynamic event detector. Moreover, the design of event-triggered FDF is formulated as an $H_{i}/H_{\infty }$ optimization problem so that an optimal tradeoff can be achieved between the robustness of residual against unknown input and the sensitivity to fault. Based on Taylor series expansion and first-order linearization, the existing conditions of the dynamic event-triggered FDF and a feasible solution of the $H_{i}/H_{\infty }$ optimization problem are given in terms of Riccati recursions. Finally, a three-tank system is considered to illustrate the validity of our proposed approach.