吉林大学学报(工学版) ›› 2017, Vol. 47 ›› Issue (4): 1225-1230.doi: 10.13229/j.cnki.jdxbgxb201704030

• 论文 • 上一篇    下一篇

无平衡点分数阶混沌系统全状态自适应控制

邵克勇, 陈丰, 王婷婷, 王季驰, 周立朋   

  1. 东北石油大学 电气信息工程学院,黑龙江 大庆 163318
  • 收稿日期:2016-05-28 出版日期:2017-07-20 发布日期:2017-07-20
  • 作者简介:邵克勇(1970-),男,教授,博士.研究方向:鲁棒控制,智能控制.E-mail:1127073951@qq.com
  • 基金资助:
    东北石油大学研究生创新科研项目(YJSCX2015-032NEPU,YTSGX2015-031NEPU).

Full state based adaptive control of fractional order chaotic system without equilibrium point

SHAO Ke-yong, CHEN Feng, WANG Ting-ting, WANG Ji-chi, ZHOU Li-peng   

  1. College of Electrical Engineering and Information, Northeast Petroleum University, Daqing 163318,China
  • Received:2016-05-28 Online:2017-07-20 Published:2017-07-20

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摘要： 针对一类无平衡点的分数阶混沌系统,首先通过分数阶微分变换方法(FDTM)得到它的解序列。然后,研究了系统的Kaplan-Yorke维数和耗散性,基于系统的离散映射通过QR分解得到最大Lyapunov特征指数,通过该特征指数可以判断系统是否保持混沌。最后,给出一种全状态自适应控制方法,使系统的状态变量追踪期望轨迹,并通过数值模拟验证了本文算法的可行性。

关键词: 自动控制技术, 人工智能, 无平衡点的混沌系统, 分数阶微分变换方法, 全状态自适应控制, Lyapunov特征指数

Abstract: For a class of chaotic system without equilibrium point, its solution series is obtained by the Fractional Differential Transformation Method (FDTM). Then, the Kaplan-Yorke dimension and the dissipativity of the system are investigated. The Lyapunov characteristic exponents are calculated based on the discrete map of the system through QR factorization algorithm, and the largest Lyapunov characteristic exponent is applied to judge whether the system keeps chaos or not. Finally, a full state based adaptive controller for the fractional order chaotic system is designed, which allows the states of the system to track the desired constant. The feasibility of the proposed algorithm is verified by numerical simulation.

Key words: automatic control technology, artificial intelligence, chaotic system without equilibrium point, fractional differential transformation method(FDTM), full state based adaptive control, Lyapunov characteristic exponent

中图分类号: 

  • TP273
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