Dynamic Event-Based Hierarchical Fuzzy Prescribed Performance Control for Underactuated Systems with Uncertain Dead Zone

In this article, an event-based hierarchical fuzzy prescribed performance control strategy is proposed for a class of underactuated systems with input dead zones. It is worth noting that the slope of the input dead zone is uncertain (time-varying/fuzzy). Therefore, a suitable hierarchical fuzzy logic system (HFLS) is designed to compensate for uncertain dead zones while significantly reducing the number of fuzzy rules. In addition, a dynamic event-based mechanism (DEBM) is proposed, which not only determines when to update the control law of the upper-level fuzzy system, but also when to update the parameters of the lower-level fuzzy controller. Moreover, this strategy can better tolerate interference while achieving the specified transient and steady-state performance of the system, and greatly save computing/communication resources. Furthermore, a Lyapunov function is designed to prove the stability of the system and eliminate the Zeno phenomenon. Finally, simulations are conducted using a quadcopter under two uncertain dead zone conditions to verify the effectiveness of the method.