Fixed-Time Fuzzy Control for Hamiltonian Systems via Event-Triggered Approach

This paper proposes new results on fixed-time fuzzy control for a class of Hamiltonian systems based on event-triggered scheme. A fuzzy system is utilized to approximate an unknown function in the considered Hamiltonian system. In terms of fixed-time stability criterions, a novel controller is presented to stabilize the resulting closed-loop system in fixed-time on a neighborhood of the origin. Moreover, in order to save resources, an event-triggered scheme is established to update the controller according to the trigger conditions. Taking advantage of Lyapunov stability theory, some sufficient conditions are presented to make the system states converge to the origin in a fixed time. At the same time, under the designed controller, there exists a positive lower bound between adjacent trigger times, which means that the Zeno phenomenon is avoided in the proposed event-triggered mechanism. The validity of the designed controller and event-triggered approach is also verified by a circuit system simulation example.