Adaptive neural network backstepping control for a class of uncertain fractional-order chaotic systems with unknown backlash-like hysteresis

Yimin Wu,Hui Lv

doi:10.1063/1.4960110

Abstract

In this paper, we consider the control problem of a class of uncertain fractional-order chaotic systems preceded by unknown backlash-like hysteresis nonlinearities based on backstepping control algorithm. We model the hysteresis by using a differential equation. Based on the fractional Lyapunov stability criterion and the backstepping algorithm procedures, an adaptive neural network controller is driven. No knowledge of the upper bound of the disturbance and system uncertainty is required in our controller, and the asymptotical convergence of the tracking error can be guaranteed. Finally, we give two simulation examples to confirm our theoretical results.

Highlights

In the last three decades, fractional-order calculus has received more and more attention from researchers due to its interesting properties and some potential applications.1–11 a large number of systems can be described by using fractional-order differential equations because they have some unusual properties
We consider the control problem of a class of uncertain fractionalorder chaotic systems preceded by unknown backlash-like hysteresis nonlinearities based on backstepping control algorithm
We model the hysteresis by using a differential equation

Summary

Introduction

In the last three decades, fractional-order calculus has received more and more attention from researchers due to its interesting properties and some potential applications. a large number of systems can be described by using fractional-order differential equations because they have some unusual properties. In the last three decades, fractional-order calculus has received more and more attention from researchers due to its interesting properties and some potential applications.. A large number of systems can be described by using fractional-order differential equations because they have some unusual properties. Fractional calculus has been utilized to establish the system models in many fields, for instance, biophysics, blood flow phenomena, physics, engineering, aerodynamics, biology, control theory, electron-analytical chemistry.. Applications of fractional-order differential equations to different areas are investigated by many researchers, and some basic results have been achieved; see, Refs. Neural network based control is an effective method in controlling uncertain integer-order nonlinear systems.. In most of above literatures, the quadratic Lyapunov functions Fractional calculus has been utilized to establish the system models in many fields, for instance, biophysics, blood flow phenomena, physics, engineering, aerodynamics, biology, control theory, electron-analytical chemistry. Applications of fractional-order differential equations to different areas are investigated by many researchers, and some basic results have been achieved; see, Refs. 2, 14, and 15.

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