Fixed-Time Adaptive Neural Tracking Control for a Class of Uncertain Nonlinear Pure-Feedback Systems

This paper presents fixed-time adaptive neural tracking control for a class of uncertain nonlinear pure-feedback systems. To overcome the design difficulty arising from the nonaffine structure of nonlinear pure-feedback systems, the mean value theorem is introduced to separate the nonaffine appearance of nonlinear pure-feedback systems. Radial basis function (RBF) neural networks are employed to approximate designed unknown functions
${{\hat {f}}_{i}}({Z_{i}})$
. By combining RBFs and Lyapunov functions, a novel fixed-time controller is designed, and semiglobal uniform ultimate boundedness of all signals in the closed-loop control system is guaranteed in a fixed time. Sufficient conditions are given to ensure that the system has semiglobal fixed-time stability. The main purpose of this paper is to design a controller for an unknown nonlinear pure-feedback system so that the system output
$y$
can track the reference signal
${y_{d}}$
. The simulation experiments indicate that the selection of sufficient design parameters makes the tracking error converge on a domain of the origin. Compared with the existing finite-time control and fixed-time control, the proposed fixed-time control scheme reduces the size of the tracking error.