分数阶统一混沌系统的修正函数投影同步
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摘要
对分数阶统一混沌系统的混沌特性进行了分析。当分数阶取某一定值时,系统表现出混沌性态。通过构造适当的响应系统,设计了一种自适应修正函数投影同步的控制方案。选取合适的控制器以及自适应控制率,利用分数阶微分系统的稳定性理论,证明了分数阶误差系统为渐近稳定,进而得出驱动系统和响应系统最终实现自适应修正函数投影同步,且可以对驱动系统的不确定参数进行估计。最后,利用Adams-Bashforth-Moultom算法,对文中的结论进行数值仿真,其结果说明了该方法的有效性和可行性。
For the fractional-order united chaotic system, the chaos behavior is displayed when the fractional-order is used as certain fixed values in this paper. A controlling scheme of adaptive modified function projective synchronization about the united chaotic system is designed by structuring a suitable response system. By means of stability theory of the fractional-order differential systems, it is proved that the zero solution of the error system is asymptotically stable by choosing appropriate controller and adaptive law. Accordingly, it is concluded that master system and response system arrive at adaptive modified function projective synchronization, and the uncertain parameters of master system could be estimated. Finally, an illustrative example with simulations via Adams-Bashforth-Moultom algorithm is used to demonstrate the validity and feasibility of the proposed results.
For the fractional-order united chaotic system, the chaos behavior is displayed when the fractional-order is used as certain fixed values in this paper. A controlling scheme of adaptive modified function projective synchronization about the united chaotic system is designed by structuring a suitable response system. By means of stability theory of the fractional-order differential systems, it is proved that the zero solution of the error system is asymptotically stable by choosing appropriate controller and adaptive law. Accordingly, it is concluded that master system and response system arrive at adaptive modified function projective synchronization, and the uncertain parameters of master system could be estimated. Finally, an illustrative example with simulations via Adams-Bashforth-Moultom algorithm is used to demonstrate the validity and feasibility of the proposed results.
引文
[1]Huang Tingwen,Li Chuangdong,Liu Xinzhi.Synchronization of chatic systems with delay using intermittent linear state feedback[J].Chaos:Interdisciplinary J Nonlinear Sci,2008,18(3):1-8.
[2]耿彦峰,蹇继贵,张炎彪.一类互联电力系统的部分联结稳定性分析[J].江西理工大学学报:自然科学版,2013,34(3):67-70.
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[4]Du H Y,Zeng Q S,Wang C H.Modified function projective synchronization of chaotic systems[J].Chaos,Solitons&Fractals,2009,42(4):2399-2404.
[5]Yu Y G,Li H X.Adaptive generalized function projective synchronization of uncertain chaotic systems[J].Nonlinear Analysis:Real World Applications,2010,11(4):2456-2464.
[6]方洁,胡智宏,江泳.耦合混沌系统自适应修正函数投影同步[J].信息与控制,2013,42(1):39-45.
[7]Sudheer K S,Sabir M.Adaptive modified function projective synchronization between hyperchaotic Lorenz system and hyperchaotic Lu system with uncertain parameters[J].Physics Letters A,2009,373(41):3743-3748.
[8]刘杰,李新杰,何小亚,等.分数阶超混沌系统的线性广义同步观测器设计[J].动力学与控制学报,2009,7(3):245-251.
[9]张广军,董俊,姚宏,等.分数阶Chen混沌系统的完全同步与反相同步[J].应用力学学报,2013,30(2):201-206.
[10]孙克辉,杨静利,丘水生.分数阶混沌系统的仿真方法研究[J].系统仿真学报,2011,23(11):2361-2370.
[11]LüJinhu,Chen Guanrong,Zhang Suochun.A unified chaotic system and it’s research[J].Journal of the Graduate School of the Chinese Academy of Sciences,2003,20(1):123-129.
[12]张若洵,杨洋,杨世平.分数阶统一混沌系统的自适应同步[J].物理学报,2009,58(9):6039-6044.
[13]Podlubny I.Fractional differential equations[M].New York:Academic Press,1999.
[2]耿彦峰,蹇继贵,张炎彪.一类互联电力系统的部分联结稳定性分析[J].江西理工大学学报:自然科学版,2013,34(3):67-70.
[3]Wu Quanjun,Zhou Jin,Xiang Lan,et al.Impulsive control and synchionization of chaotic Hindmarsh-Rose models for neuronal activity[J].Chaos,Solitons and Fractals,2009,41(5):2706-2715.
[4]Du H Y,Zeng Q S,Wang C H.Modified function projective synchronization of chaotic systems[J].Chaos,Solitons&Fractals,2009,42(4):2399-2404.
[5]Yu Y G,Li H X.Adaptive generalized function projective synchronization of uncertain chaotic systems[J].Nonlinear Analysis:Real World Applications,2010,11(4):2456-2464.
[6]方洁,胡智宏,江泳.耦合混沌系统自适应修正函数投影同步[J].信息与控制,2013,42(1):39-45.
[7]Sudheer K S,Sabir M.Adaptive modified function projective synchronization between hyperchaotic Lorenz system and hyperchaotic Lu system with uncertain parameters[J].Physics Letters A,2009,373(41):3743-3748.
[8]刘杰,李新杰,何小亚,等.分数阶超混沌系统的线性广义同步观测器设计[J].动力学与控制学报,2009,7(3):245-251.
[9]张广军,董俊,姚宏,等.分数阶Chen混沌系统的完全同步与反相同步[J].应用力学学报,2013,30(2):201-206.
[10]孙克辉,杨静利,丘水生.分数阶混沌系统的仿真方法研究[J].系统仿真学报,2011,23(11):2361-2370.
[11]LüJinhu,Chen Guanrong,Zhang Suochun.A unified chaotic system and it’s research[J].Journal of the Graduate School of the Chinese Academy of Sciences,2003,20(1):123-129.
[12]张若洵,杨洋,杨世平.分数阶统一混沌系统的自适应同步[J].物理学报,2009,58(9):6039-6044.
[13]Podlubny I.Fractional differential equations[M].New York:Academic Press,1999.