不确定临界混沌系统的有限时间同步与参数识别
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摘要
针对不确定临界混沌系统,研究了它的有限时间同步和参数识别.基于有限时间李雅谱诺夫稳定性理论以及自适应控制技术,通过分步骤,设置合适的控制器,分别使得在参数具有扰动和参数完全未知的情况下,不确定的驱动系统和响应系统达到有限时间同步;同时,对参数未知的驱动系统,利用有限时间同步识别出未知参数.最后的数值模拟验证了所提出的方法的正确性和有效性.
In this paper, the finite-time synchronization and parameters identification of a uncertain critical chaotic system is investigated. Based on finite-time Lyapunov stability theory and adaptive method, several steps setting up three controllers in turn are established to guarantee the finite-time asymptotical synchronization of the drive system and the response system with disturbance and unknown parameters separately. At the same time, the unknown parameters of the drive system are identified with the finite-time asymptotical synchronization.Finally, numerical simulations show the correctness and effectiveness of the theoretical results.
In this paper, the finite-time synchronization and parameters identification of a uncertain critical chaotic system is investigated. Based on finite-time Lyapunov stability theory and adaptive method, several steps setting up three controllers in turn are established to guarantee the finite-time asymptotical synchronization of the drive system and the response system with disturbance and unknown parameters separately. At the same time, the unknown parameters of the drive system are identified with the finite-time asymptotical synchronization.Finally, numerical simulations show the correctness and effectiveness of the theoretical results.
引文
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[10] Cai N, Li W, Jing Y. Finite-time generalized synchronization of chaotic systems with different order[J]. Nonlinear Dynamics, 2011, 64(4):385-393.
[11] Sun Y, Li W, Zhao D. Finite-time stochastic outer synchronization between two complex dynamical networks with different topologies[J]. Chaos, 2012, 22:023152.
[12] Wang H, Han Z Z, Xie Q Y. Finite-time chaos synchronization of unified chaotic system with uncertain parameters[J]. Commun Nonlinear Sci Numer Simulat, 2009, 14:2239~2247
[13] L(u|¨)J, Chen G, A new chaotic attractor coined[J]. Int J Bifur Chaos, 2002, 12(3):659-661
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[16] Wang L, Xiao F. Finite-time consensus problems for networks of dynamic agents[J]. IEEE T Automat Contr, 2010, 55:950-955.
[2] Agiza H N, Yassen M T. Synchronization of Rossler and Chen chaotic dynamical system using active control[J]. Phys Lett A, 2000, 278:191-197
[3]吕金虎,陈关荣.Lorenz系统族的动力学分析、控制与同步[M].北京:科学出版社,2003:9
[4] Chen M Y, Han Z Z. Controlling and synchronizing chaotic Genesio system via nonlinear feedback control[J]. Chaos Solitons&Fractals, 2003, 17(7):09-16
[5] Wang Y W, Guan Z I, Xiao J W. Impulsive control for synchronization of a class of continuous systems[J]. Chaos, 2004, 14:199~203
[6] Tu L L, Lu J A. Adaptive synchronization of a critical chaotic system[J]. Chin Phys, 2005, 14(9):1755-1759
[7] Mahboobi S H, Shahrokhi M, Pishkenari H N. Observer-based control design for three well-known chaotic systems[J]. Chaos Solitons&Fractals, 2006, 29(3):81-92
[8]陈姚,吕金虎.复杂动恣网络的有限时间同步[J].系统科学与数学,2009, 29(10):1419-1430.
[9]赵灵冬,胡建兵,包志华,章国安,徐晨,张士兵.分数阶系统有限时间稳定性理论及分数阶超混沌Lorenz系统有限时间同步[J].物理学报,2011,60(10):100507
[10] Cai N, Li W, Jing Y. Finite-time generalized synchronization of chaotic systems with different order[J]. Nonlinear Dynamics, 2011, 64(4):385-393.
[11] Sun Y, Li W, Zhao D. Finite-time stochastic outer synchronization between two complex dynamical networks with different topologies[J]. Chaos, 2012, 22:023152.
[12] Wang H, Han Z Z, Xie Q Y. Finite-time chaos synchronization of unified chaotic system with uncertain parameters[J]. Commun Nonlinear Sci Numer Simulat, 2009, 14:2239~2247
[13] L(u|¨)J, Chen G, A new chaotic attractor coined[J]. Int J Bifur Chaos, 2002, 12(3):659-661
[14] Liu C X, Liu T, Liu L. A new chaotic attractor[J]. Chaos, Solutions&Fractals, 2004, 22:1031-1038
[15] Feng Y, Sun LX, Yu X H. Finite time synchronization of chaotic systems with unmatched uncertainties[J]. In:The 30th annual conference of the IEEE industrial electronics society, Busan Korea,2004.
[16] Wang L, Xiao F. Finite-time consensus problems for networks of dynamic agents[J]. IEEE T Automat Contr, 2010, 55:950-955.