Adaptive Fixed-Time Control for Uncertain Nonlinear Cascade Systems by Dynamic Feedback

This article concerns with the adaptive fixed-time control problem for classes of nonlinear cascade systems with parametric uncertainty. The majority of existing finite/fixed-time control strategies for uncertain nonlinear systems can only make system states approach to the neighborhood of origin over a finite/fixed time. Different from these results, we put forward a time-varying gain-based control algorithm to ensure that all system states return to the origin in a fixed time. With the help of the backstepping method, a time-varying adaptive controller is designed for a high-order nonlinear systems subject to uncertain parameters. Through constructing appropriate dynamic gain-based Lyapunov functions and utilizing our proposed stability criterion, it is proved that all states of the uncertain system can be adjusted to the origin in a fixed-time interval. Moreover, the settling time is not depend on the initial conditions of system and can be preset according to the actual requirements. Finally, the simulation results are provided to illustrate the effectiveness of the developed dynamic time-varying feedback control algorithm.