分数阶Arneodo混沌系统的自适应同步研究
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摘要
选取了三维分数阶Arneodo混沌系统作为研究对象,基于分数阶系统的稳定性定理,对该系统的动力学性质进行分析,发现该系统存在周期态、稳态、混沌态等多种运动状态。通过理论推导和数值计算,得出了分数阶Arneodo系统处于混沌状态时的阶数范围。基于李亚普诺夫稳定性定理和自适应控制理论,通过设计合理的控制器,实现了分数阶Arneodo系统在阶数相同和阶数不同情况下的同步。该结果为混沌系统的同步控制问题及相关研究提供参考。
This paper studied the Arneodo Chaotic System of the three-dimensional fractional order. The dynamic characteristics of the system are made detailed in here through theoretic deduction and numerical simulation and the stability theory of fractional-order system is cited in here.As a result,the range of order is figured out when the system in a chaotic state. It was found that the system has periodic states,steady state,chaotic states. An appropriate control unit is designed based on the adaptive control theory and the stability theory of Lyapunov Function by applying the adaptive technique in the Synchronous Control of the Chaotic System. The complete synchronization is produced when the orders of the system are in the same or different state by applying the adaptive synchronization method. The above result represents important significance to the study on synchronization of chaotic system.
This paper studied the Arneodo Chaotic System of the three-dimensional fractional order. The dynamic characteristics of the system are made detailed in here through theoretic deduction and numerical simulation and the stability theory of fractional-order system is cited in here.As a result,the range of order is figured out when the system in a chaotic state. It was found that the system has periodic states,steady state,chaotic states. An appropriate control unit is designed based on the adaptive control theory and the stability theory of Lyapunov Function by applying the adaptive technique in the Synchronous Control of the Chaotic System. The complete synchronization is produced when the orders of the system are in the same or different state by applying the adaptive synchronization method. The above result represents important significance to the study on synchronization of chaotic system.
引文
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[16]李宁,李亚光,王宏兴,等.分数阶永磁同步电机混沌系统模糊跟踪控制[J].信息与控制,2016,45(1):8-13.
[2]薛怀庆,彭建奎,安新磊,等.分数阶混沌系统全状态混合投影同步及在保密通信中的应用[J].信息与控制,2013,42(2):229-235.
[3]薛薇,徐进康,贾红艳.一个分数阶超混沌系统同步及其保密通信研究[J].系统仿真学报,2016,28(8):1915-1921,1928.
[4]郝建红,熊雪艳,米昕禾.不确定分数阶同步发电机混沌系统的滑模自适应控制及参数辨识[J].河北师范大学学报:自然科学版,2016,40(2):116-123.
[5]李雄,李生刚,刘恒,等.带未知参数的分数阶超混沌系统自适应同步控制[J].陕西师范大学学报:自然科学版,2016(1):19-23.
[6]杨叶红,肖剑,马珍珍.一个新分数阶混沌系统的同步和控制[J].山东大学学报(理学版),2014,49(2):76-83,88.
[7]李东,张兴鹏,胡玉婷,等.参数不确定的不同分数阶的混沌系统的自适应同步[J].西南大学学报:自然科学版,2015,37(11):69-76.
[8]马铁东,江伟波,浮洁,薛方正.基于改进脉冲控制方法的超混沌系统同步[J].物理学报,2012,61(10):69-75.
[9]马铁东,江伟波,浮洁,等.基于比较系统方法的分数阶混沌系统脉冲同步控制[J].物理学报,2012,61(9):39-44.
[10]毛北行,王东晓.分数阶多涡卷系统滑模控制混沌同步[J].山东大学学报(工学版),2017,47(3):79-83.
[11]潘光,魏静.一种分数阶混沌系统同步的自适应滑模控制器设计[J].物理学报,2015,64(4):45-51.
[12]Chen,D Y,Liu. Control of a class of fractional-or-der chaotic systems via sliding mode[J]. NonlinearDynamics,2012,67(1):893-901.
[13]黄雯迪,闵富红.单一驱动多响应分数阶混沌系统的完全同步[J].南京师范大学学报(工程技术版),2015,15(2):1-8.
[14]张友安,余名哲,吴华丽.不确定分数阶多驱动一响应混沌系统同步[J].电子学报,2016,44(3):607-612.
[15]陈晔,李生刚,刘恒.基于自适应模糊控制的分数阶混沌系统同步[J].物理学报,2016,65(17):258-268.
[16]李宁,李亚光,王宏兴,等.分数阶永磁同步电机混沌系统模糊跟踪控制[J].信息与控制,2016,45(1):8-13.