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.

I. Introduction

Over the past three decades, time-optimal control has been extensively studied. Due to the better performances, such as faster convergence, better robustness and accuracy, researchers have paid great attention to finite-time stability (FTS) and fixed-time stability (FxTS) [1], [2], [3], [4], [5]. Compared with FTS, the upper bound of settling time of FxTS is related to system parameters rather than initial conditions, which is usually not available in practical systems. Furthermore, an introduction of prescribed-time stability (PTS) was proposed in [6], which triggered a wave of research [7], [8], [9]. In contrast with FxTS, although the settling time of PTS can be designed arbitrarily without any information required from systems, its controller can only function within a prescribed time, and hence is unable to resist subsequent disturbances. By comparison, FxTS has a better robustness, and the control effect is more enduring. On the whole, it is meaningful to develop further research on FxTS with these advantages.