Switching Event-Triggered Fixed-Time Control for Uncertain High-Order Nonlinear Systems

This article investigates event-based fixed-time control problem for a class of uncertain high-order nonlinear systems. Different from existing event-triggered results, which can only achieve bounded or finite-time stability, this article studies on fixed-time stability, and unknown control coefficients are allowed in the system. To compensate uncertainties, an adaptive controller is designed with a switching parameter by utilizing adding a power integrator method. A logic switching rule is constructed based on fixed-time stability theorem to tune the switching parameter online. To save communication resources, a novel event-triggered mechanism is designed by introducing a $K_\infty$ class function and a pretrigger idea. This design enables the controller to update timely when all state variables reach zero, while avoiding redundant switching. In order to achieve coexistence of the two discrete conditions, a new fixed-time switching event-triggered mechanism is developed to determine the moments of triggering and switching reasonably. By applying the Lyapunov stability theory, it is strictly proved that all state variables reach origin in a fixed time. Finally, a simulation example is given to show the effectiveness of the proposed method.