Fixed-Time Stabilization of a Class of Strict-Feedback Nonlinear Systems via Dynamic Gain Feedback Control

This paper presents a novel fixed-time stabilization control (FSC) method for a class of strict-feedback nonlinear systems involving unmodelled system dynamics. The key feature of the proposed method is the design of two dynamic parameters. Specifically, a set of auxiliary variables is first introduced through state transformation. These variables combine the original system states and the two introduced dynamic parameters, facilitating the closed-loop system stability analyses. Then, the two dynamic parameters are delicately designed by utilizing the Lyapunov method, ensuring that all the closed-loop system states are globally fixed-time stable. Compared with existing results, the “explosion of complexity” problem of backstepping control is avoided. Moreover, the two designed dynamic parameters are dependent on system states rather than a time-varying function, thus the proposed controller is still valid beyond the given fixed-time convergence instant. The effectiveness of the proposed method is demonstrated through two practical systems.