﻿ 一类不确定分数阶混沌系统的滑模自适应同步
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Sliding mode adaptive synchronization for a class of fractional-order chaotic systems with uncertainties
Yu Mingzhe,Zhang Youan
Department of Control Engineering, Naval Aeronautical and Astronautical University, Yantai 264001, China
Abstract:A fractional-order sliding mode adaptive control approach was introduced to synchronize chaos of a class of fractional-order chaotic systems with uncertainties. The effects of model uncertainties and external disturbances were fully taken into account. An appropriate robust fractional sliding mode adaptive controller was designed by adopting a fractional sliding surface with strong robustness, and using sliding mode adaptive control theory, Lyapunov stability theory and fractional-order linear systems stability theory. The control law can ensure the occurrence of the sliding motion, and achieve synchronization between the drive system and response system. The upper bound of uncertainties was not needed in the proposed controller. The designed controller is not complicated mathematically and easy to implement. The fractional adaptive sliding mode control approach can be applied to control a broad range of nonlinear fractional-order chaotic systems with uncertainties. Numerical simulation was presented to show the efficiency and applicability of the proposed control strategy.
Key words: uncertaintiy     fractional-order chaotic system     sliding mode control     adaptive control     chaos synchronization

1 问题描述

2 控制器设计和稳定性分析

1)|argi)|>απ2时,分数阶系统是渐近稳定的;

2) |argi)|≥απ2时,分数阶系统是稳定的.

 图 1 分数阶系统状态空间稳定区域图 Fig. 1 Fractional-order system state space stability diagram

V关于时间求导

V≥0,V·≤0知V单调递减且有下界,所以V存在有限的极限

3 数值仿真

 图 2 仿真曲线 Fig. 2 Simulation curves

4 结 论

1) 系统存在的不确定性对分数阶混沌系统的同步存在较大影响；

2) 选取合适的滑模曲面，可将滑模控制方法引入分数阶混沌系统的同步控制中，进而可以直接采用Lyapunov稳定性理论对系统的稳定性进行分析；

3) 采用自适应技术估计集总干扰上界，相较其他分别处理系统不确定性的方法，可减小计算量，简化控制器结构；

4) 利用滑模控制及自适应控制的特性，能提高控制系统的鲁棒性能.

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#### 文章信息

Yu Mingzhe, Zhang Youan

Sliding mode adaptive synchronization for a class of fractional-order chaotic systems with uncertainties

Journal of Beijing University of Aeronautics and Astronsutics, 2014, 40(9): 1276-1280.
http://dx.doi.org/10.13700/j.bh.1001-5965.2013.0614