分数阶混沌系统有限时间稳定性分析及同步控制
Analysis of Finite-Time Stability of Fractional-Order Chaotic System and Its Synchronization Control
DOI: 10.12677/PM.2017.73022, PDF, HTML, XML, 下载: 1,325  浏览: 3,802 
作者: 刘丹丹, 高彩霞：内蒙古大学数学科学学院, 内蒙古 呼和浩特
关键词: 分数阶混沌系统；有限时间稳定；同步控制；Fractional-Order Chaotic System； Finite-Time Stability； Synchronization Control
摘要: 本文研究了分数阶混沌系统有限时间稳定性及其同步控制，并基于Lyapunov分数阶稳定性理论提出了针对一类非线性分数阶混沌系统有限时间稳定的判定方法，与现有的结果相比其更具有一般性；并应用该方法设计了同步控制器，在满足系统所有变量有界的情况下实现了驱动系统和响应系统的异结构有限时间同步。数值仿真结果进一步验证了该方法的有效性。
Abstract: In this paper, the finite time stability and synchronization control of fractional order chaotic sys-tems are studied; based on the Lyapunov fractional stability theory, the determination method of finite time stability for a class of nonlinear fractional chaotic systems is proposed, and it’s more generic than the existing results. And the synchronous controller is designed by the method; in the case of all the variables are met in the system, the different structure of the driver system and the response system are synchronized. Numerical simulation results demonstrate the effectiveness of the proposed method.
文章引用：刘丹丹, 高彩霞. 分数阶混沌系统有限时间稳定性分析及同步控制[J]. 理论数学, 2017, 7(3): 168-175. https://doi.org/10.12677/PM.2017.73022

参考文献

[1] Podlubny, I. (1999) Fractional Differential Equations. Academic Press Publishers, New York.
[2] Li, Y., Chen, Y.Q. and Podlubny, I. (2009) Mittag-Leffler Stability of Fractional Order Nonlinear Dynamic Systems. Automatica, 45, 1965-1969.
[3] Matignon, D. (1996) Stability Results for Fractional Differential Equations with Applications to Control Processing. Computational Engineering in Systems Applications, 2, 963-968.
[4] Li, C.P., Deng, W.H. and Xu, D. (2006) Chaos Synchronization of the Chua System with a Fractional Order. Physica A, 360, 171-185.
[5] Kuntanapreeda, S. (2012) Robust Synchronization of Fractional-Order Unified Chaotic Systems via Linear Control. Computers and Mathematics with Applications, 63, 183-190.
[6] Chen, L.P., Chai, Y., Wu, R.C. and Yang, J. (2012) Stability and Stabilization of a Class of Nonlinear Fractional-Order Systems with Caputo Derivative. IEEE Transactions on Circuits and Systems-II: Express Briefs, 59, 602-606.
https://doi.org/10.1109/TCSII.2012.2206936
[7] Yin, C., Zhong, S.M. and Chen, W.F. (2012) Design of Sliding Mode Controller for a Class of Fractional-Order Chaotic Systems. Communications in Nonlinear Science and Numerical Simulation, 17, 356-366.
[8] Wen, X.J., Wu, Z.M. and Lu, J.G. (2008) Stability Analysis of a Class of Nonlinear Fractional-Order Systems. IEEE Transactions on Circuits and Systems II: Express Briefs, 55, 1178-1182.
https://doi.org/10.1109/TCSII.2008.2002571
[9] Fallahi, K. and Leung, H. (2010) A Chaos Secure Communication Scheme Based on Multiplication Modulation. Communications in Nonlinear Science and Numerical Simulation, 25, 368-383.
[10] Aghababa, M.P. (2014) A Lyapunov-Based Control Scheme for Robust Stabilization of Fractional Chaotic Systems. Nonlinear Dynamics, 78, 2129-2140.
https://doi.org/10.1007/s11071-014-1594-8
[11] Du, H.B., Cheng, Y.Y., He, Y.G. and Jia, R.T. (2014) Finite-Time Output Feedback Control for a Class of Second- Order Nonlinear Systems with Application to DC-DC Buck Converters. Nonlinear Dynamics, 78, 2021-2030.
https://doi.org/10.1007/s11071-014-1593-9
[12] Huang, L.L. and Ma, N. (2012) A New Method for Projective Synchronization of Different Fractional-Order Chaotic Systems. Acta Physica Sinica, 61, 160501-160506.
[13] Rivero, M., Trujillo, J., Vazquez, L. and Velasco, M. (2011) Fractional Dynamics of Populations. Applied Mathematics and Computation, 218, 1089-1095.
[14] 谭文, 李志攀, 王耀南, 等. 一个混沌系统的同步控制研究[J]. 计算机工程与应用, 2011, 47(4): 219-222.
[15] 王兴元, 孟娟. 自治混沌系统的线性和非线性广义同步[J]. 物理学报, 2008, 57(2): 726-730.
[16] 王兴元, 王勇. 基于线性分离的自治混沌系统的投影同步[J]. 物理学报, 2007, 56(5): 2498-2503.
[17] 赵灵冬, 胡建兵, 刘旭辉. 参数未知的分数阶超混沌Lorenz系统的自适应追踪控制与同步[J]. 物理学报, 2010, 59(4): 2305-2309.
[18] 赵建利, 王京, 王慧. 洛伦兹-哈肯激光混沌系统有限时间稳定主动控制方法研究[J]. 物理学报, 2011, 61(11): 110209.
[19] Shen, J. and Lam, J. (2014) Non-Existence of Finite-Time Stable Equilibria in Fractional-Order Nonlinear Systems. Automatica, 50, 547-551.
[20] 陈国培, 杨莹, 李俊民. 非线性系统有限时间稳定的一个新的充分条件[J]. 控制与决策, 2011, 26(6): 837-840.

为你推荐