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

Cheng He,Jian Wu,Zhang Zhe,Jiyang Dai,Tianchi Tong

doi:10.1109/access.2020.2972353

Cheng He, Jian Wu + Show 3 more

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https://doi.org/10.1109/access.2020.2972353

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Abstract

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 f̂ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</sub> (Z <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</sub> ). 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 yd. 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.

Highlights

Compared with general nonlinear systems such as lowertriangular systems or strict feedback nonlinear systems, the nonlinear pure-feedback system [1]–[3] is a more general system better reflecting actual situations
Neural networks have been widely applied in machine learning, image processing, nonlinear systems, and other fields since the first neural network model [4] based on single neuron construction was proposed in the 1940s
DESIGN OF FIXED-TIME CONTROLLER fixed-time adaptive neural tracking control for a class of unknown nonlinear pure-feedback systems is designed on the basis of backstepping

Summary

Introduction

Compared with general nonlinear systems such as lowertriangular systems or strict feedback nonlinear systems, the nonlinear pure-feedback system [1]–[3] is a more general system better reflecting actual situations. It has attracted considerable attention and been a focus of extensive research in recent years. Neural networks have been widely applied in machine learning, image processing, nonlinear systems, and other fields since the first neural network model [4] based on single neuron construction was proposed in the 1940s. The research and application of BP neural networks and RBF neural networks have significantly promoted the development of nonlinear systems. Backstepping adaptive control and neural network adaptive control have been rapidly developed and

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