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分数阶Brussel系统混沌同步的三种控制方案

1. 郑州航空工业管理学院数学学院, 河南 郑州 450015
• 发布日期:2020-08-13
• 作者简介:程春蕊(1980— ),女,山东曹县人,讲师,理学硕士,主要研究方向为分数阶混沌系统. E-mail:chengzi0911@163.com
• 基金资助:
国家自然科学基金项目(NSFC1501525)

Three control schemes of chaos synchronization for fractional-order Brussel system

CHENG Chunrui

1. College of Mathematics, Zhengzhou University of Aeronautics, Zhengzhou 450015, Henan, China
• Published:2020-08-13

Abstract: Based on the fractional calculus theory, three synchronous control schemes were proposed to make the error system of the fractional Brussel system converge the error system states to the equilibrium point. An appropriate controller was designed in the first control scheme and the convergence of the error system was obtained by using Mittag-Leffler function. In the second control scheme, the fractional sliding mode surface was introduced, and the chaos synchronization of the fractional order Brussel master-slave systems was achieved based on the fractional version of the Lyapunov stability and the sliding mode control method. The effects of model uncertainties and external disturbances were fully taken into account in the third control scheme. A new sliding mode reaching law was designed and the fast convergence of the error system to the equilibrium point was obtained based on fractional order terminal sliding mode control. It was proved that master-slave systems were chaos synchronization under proper controllers. Numerical simulations were presented to illustrate the effectiveness and applicability of the proposed schemes and to validate the theoretical results of the paper.

• O482.4
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