A Dynamic Event-Triggered Fuzzy $H_{i}/H_{\infty}$ Optimization Approach to Fault Detection for T-S Fuzzy Systems

Abstract

This paper investigates the problem of dynamic event-triggered optimal fault detection (FD) for Takagi-Sugeno (T-S) fuzzy systems. Aiming at conserving limited communication resources, a dynamic event-triggering mechanism is implemented to transmit the system measurement to the remote fault detector. Based on it, a dynamic event-triggered T-S fuzzy fault detection filter (FDF) is constructed so that the generated residual is completely decoupled from the event-triggered transmission error. Subsequently, the design of T-S fuzzy FDF is formulated as an $H_{i}/H_{\infty}$ optimization problem such that an optimal tradeoff can be achieved between the robustness against unknown input and the sensitivity to fault. Different from existing linear matrix inequality-based event-triggered FD approaches for T-S fuzzy systems, the optimal solution is obtained by recursively computing the Riccati equations, allowing for the independent implementation of the event generator and the $H_{i}/H_{\infty}$-FDF. A three-phase induction motor system is employed to illustrate the effectiveness of the proposed method.