Switching Event-Triggered Fixed-Time Control for Uncertain High-Order Nonlinear Systems
Changchun Hua, Wei Tian, Qidong Li
Abstract
This paper 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 paper 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. And 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 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$K_\infty$</tex-math></inline-formula> class function and a pre-trigger 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.