混沌控制与同步的若干问题研究
|
摘要
自从20世纪60年代E. N. Lorenz发现第一个混沌吸引子以来,混沌在电子装置、激光系统、化学反应、生化系统、生命系统、力学系统、神经网络等众多领域被相继观察到,混沌的发现被称为继相对论与量子力学问世以来物理学的第三次大革命,在许多邻域获得了巨大而深远的发展,是当今举世瞩目的前沿课题及学术热点。混沌控制与混沌同步目前已经成为有着巨大应用前景的实用技术被广泛关注,因此分析自然系统和人工系统中的混沌控制与混沌同步问题,最终力求对自然系统和人工系统中的混沌及系统间的同步加以控制和利用使之为人类服务就具有重大的应用价值。
本文主要在混沌控制、混沌同步、基于完全同步的参数估计等方面进行了有益探讨,取得了如下创新结果:
1、指出了自同步方法自其提出后就存在的理论分析错误,必须将混沌动力学本身的特点融入到现有的李雅普诺夫直接法中才能在理论上确保参数估计。此外,还在如下四个方面对该方法进行了有益的拓展:1)矩阵M为半正定的情况;2)如何利用输出微分信息以减小输出维数的问题;3)噪声干扰情况下的参数估计问题;4)该方法的适用条件和限制条件是什么。
2、为解决驱动系统标量输出情况下响应系统的设计问题,原创性地提出了矩阵匹配法,该方法首先通过微分嵌入维理论获得静态重构模型,然后通过一些规则构建响应系统使得其与驱动系统完全同步,该方法不仅可以消除静态重构模型中可能存在的奇异问题,而且还可以降低微分嵌入的维数(即降低静态重构模型中微分估计器的阶次)、甚至完全不需要输出的微分。
3、为解决标量输出情况下的系统参数估计问题,原创性地提出一种参数估计律的设计准则——参数估计律设计使得同步流形附近的局部线性化系统的特征多项式的最小阶系数几乎处处为正,Lorenz系统和统一混沌系统等作为实例来证明其有效性,同时也说明全部系统参数未知、且标量输出的情况下仍可能实现全部参数估计。
4、为解决变结构混沌控制问题中的抖振问题,针对一类不确定时变混沌系统,首先构造该系统的增广系统,接下来对该增广系统设计常规的变结构控制律,最后再经过一些简单的数学变换处理就能获得一种自适应无抖振变结构控制方法。该方法不仅能减小滑模面附近的抖振现象并实现渐近跟踪,而且不需要“不确定项的上界已知”的先验知识。但该方法在实际工程应用中存在一些不足,如参数估计律在噪声和外部干扰存在时的病态问题,高频抖振不能完美去除等。为解决这些不足,进一步提出了改进的自适应无抖振变结构控制方法,该方法引入带死区和非线性学习律的参数估计器,理论分析与仿真结果都表明:只要选择合适的控制器参数,改进的方法不仅彻底消除抖振,并且能保证在有限时间内达到任意的跟踪精度。
5、研究了一种在滑模控制中引入积分的新方法,该方法仍然采用在常规滑模控制设计中采用的滑动变量,但在控制律设计中引入滑动变量的非线性比例积分作用,由于非线性积分作用的存在使得控制系统具有良好的动静态性能。
6、研究了一种简单的全状态渐近轨道控制方法实现统一混沌系统的全状态渐近跟踪控制,该方法只需要系统单一的状态信息,理论分析和仿真结果都证实所提的方法能实现渐近跟踪控制。
7、提出了一种带有限时间不确定估计的降阶同步方法,该方法能在有限时间内准确估计系统不确定项;同时对降阶同步的同步准则进行了适当探讨,研究了完全降阶同步和一般降阶同步问题的设计,理论分析和数值计算表明该方法的正确性。
Since E. N. Lorenz found the first chaotic attractor in 1960’s, chaos phenomenon was observed one after the other in many systems such as electrical devices, chemical reactions, biological systems, mechanical systems and neural networks, among others. The discovery of chaos was honored as the third revolution in physics following relative theory and quantum mechanics. Chaotic control and synchronization has now attracted much attention due to its dramatic potential applications. It is of great benefit for human beings to analyze and control chaos and coupling synchronization in natural and man-made systems.
This Dissertation focuses on the research on chaotic control, chaotic synchronization and complete synchronization based parameter estimation. Its main contributions include following seven points.
1. This dissertation points out the drawbacks of the autosynchronization approach since it was established. A new method is suggested to ensure parameter estimation by the properties of chaotic dynamics, merged into the conventional Lyapunov’s direct method. Then, the new approach is further extended to several useful cases: 1) when matrix M is semi-positive definite, 2) when output derivative is used for reducing the dimension of output, 3) in the present of noise. When a general system is considered, the scope applicable and some limitations of the new approach are also discussed.
2. To design a response system from a scalar output of the driving system, a matrix match method is proposed, which firstly uses the differential embedding theory for achieving the static reconstruction model and then constructs a response model synchronized with the driving system by some rules. The method presented cannot only remove the potential singular problem of the static reconstruction model but also reduce the dimension of differential embedding (i.e. the order of derivative estimator in the static reconstruction model) and even remove completely the output differential.
3. To estimate parameters from a scalar output, a guidance is presented for the design of parameter estimation law, namely parameter estimation is designed such that the coefficient of the lowest order of the local linearization around the synchronization manifold is positive almost everywhere. The Lorenz model and a unified chaotic system are illustrated to validate this method and to demonstrate also that it is possible to estimate all parameters from a scalar output time-series.
4. Trying to solve the high-frequency chattering of conventional variable structure control, an adaptive chattering-free variable structure control method is proposed for controlling a class of uncertain time-variant chaotic systems by three steps: 1) constructing an augmented model of the selected system, 2) designing a conventional variable structure control law for this augmented model and 3) using some mathematical operation. The method not only eliminates the chattering phenomenon and tracks arbitrarily desired trajectory asymptotically, but also removes the prior knowledge about the upper bound of the system uncertainty. However this approach exhibits some drawbacks in practice such as the ill-pose problem in parameter estimation law happening in the present of noise and external disturbances, as well as imperfect avoidance of high-frequency chattering. An improved method is suggested to solve the drawbacks, which introduces a parameter adaptive estimator with dead-zone and nonlinearly learning rate, and in addition replaces the signum function by the saturation one as well. Theoretical analysis and numerical simulation validate that the improved method not only avoids the high-frequency chattering completely but also obtains high-accuracy tracking as desired in a finite time.
5. A new approach is suggested to introduce an integral action in the sliding mode control, which uses the same sliding variable in the conventional sliding mode but adds a nonlinearly integral action of the sliding variable in the controller. Due to the nonlinear integral action applied in the new sliding mode controller, the system controlled can achieve good dynamical and static performances.
6. A simple full-state asymptotic trajectory control method is suggested to asymptotically drive full states of a unified chaotic system to arbitrarily desired trajectories from only a scalar state. Theoretic analysis and numerical simulation validate that the method proposed can ensure the asymptotic trajectory control.
7. An approach to reduced-order synchronization is suggested with a finite-time uncertainty estimation which evaluates correctly the system uncertainty in a finite time. In addition, the reduced-order synchronization criterions are discussed, and the design of complete and general reduced-order synchronizations is then investigated. Theoretical analysis and numerical simulation validate the effectiveness of the method proposed.
本文主要在混沌控制、混沌同步、基于完全同步的参数估计等方面进行了有益探讨,取得了如下创新结果:
1、指出了自同步方法自其提出后就存在的理论分析错误,必须将混沌动力学本身的特点融入到现有的李雅普诺夫直接法中才能在理论上确保参数估计。此外,还在如下四个方面对该方法进行了有益的拓展:1)矩阵M为半正定的情况;2)如何利用输出微分信息以减小输出维数的问题;3)噪声干扰情况下的参数估计问题;4)该方法的适用条件和限制条件是什么。
2、为解决驱动系统标量输出情况下响应系统的设计问题,原创性地提出了矩阵匹配法,该方法首先通过微分嵌入维理论获得静态重构模型,然后通过一些规则构建响应系统使得其与驱动系统完全同步,该方法不仅可以消除静态重构模型中可能存在的奇异问题,而且还可以降低微分嵌入的维数(即降低静态重构模型中微分估计器的阶次)、甚至完全不需要输出的微分。
3、为解决标量输出情况下的系统参数估计问题,原创性地提出一种参数估计律的设计准则——参数估计律设计使得同步流形附近的局部线性化系统的特征多项式的最小阶系数几乎处处为正,Lorenz系统和统一混沌系统等作为实例来证明其有效性,同时也说明全部系统参数未知、且标量输出的情况下仍可能实现全部参数估计。
4、为解决变结构混沌控制问题中的抖振问题,针对一类不确定时变混沌系统,首先构造该系统的增广系统,接下来对该增广系统设计常规的变结构控制律,最后再经过一些简单的数学变换处理就能获得一种自适应无抖振变结构控制方法。该方法不仅能减小滑模面附近的抖振现象并实现渐近跟踪,而且不需要“不确定项的上界已知”的先验知识。但该方法在实际工程应用中存在一些不足,如参数估计律在噪声和外部干扰存在时的病态问题,高频抖振不能完美去除等。为解决这些不足,进一步提出了改进的自适应无抖振变结构控制方法,该方法引入带死区和非线性学习律的参数估计器,理论分析与仿真结果都表明:只要选择合适的控制器参数,改进的方法不仅彻底消除抖振,并且能保证在有限时间内达到任意的跟踪精度。
5、研究了一种在滑模控制中引入积分的新方法,该方法仍然采用在常规滑模控制设计中采用的滑动变量,但在控制律设计中引入滑动变量的非线性比例积分作用,由于非线性积分作用的存在使得控制系统具有良好的动静态性能。
6、研究了一种简单的全状态渐近轨道控制方法实现统一混沌系统的全状态渐近跟踪控制,该方法只需要系统单一的状态信息,理论分析和仿真结果都证实所提的方法能实现渐近跟踪控制。
7、提出了一种带有限时间不确定估计的降阶同步方法,该方法能在有限时间内准确估计系统不确定项;同时对降阶同步的同步准则进行了适当探讨,研究了完全降阶同步和一般降阶同步问题的设计,理论分析和数值计算表明该方法的正确性。
Since E. N. Lorenz found the first chaotic attractor in 1960’s, chaos phenomenon was observed one after the other in many systems such as electrical devices, chemical reactions, biological systems, mechanical systems and neural networks, among others. The discovery of chaos was honored as the third revolution in physics following relative theory and quantum mechanics. Chaotic control and synchronization has now attracted much attention due to its dramatic potential applications. It is of great benefit for human beings to analyze and control chaos and coupling synchronization in natural and man-made systems.
This Dissertation focuses on the research on chaotic control, chaotic synchronization and complete synchronization based parameter estimation. Its main contributions include following seven points.
1. This dissertation points out the drawbacks of the autosynchronization approach since it was established. A new method is suggested to ensure parameter estimation by the properties of chaotic dynamics, merged into the conventional Lyapunov’s direct method. Then, the new approach is further extended to several useful cases: 1) when matrix M is semi-positive definite, 2) when output derivative is used for reducing the dimension of output, 3) in the present of noise. When a general system is considered, the scope applicable and some limitations of the new approach are also discussed.
2. To design a response system from a scalar output of the driving system, a matrix match method is proposed, which firstly uses the differential embedding theory for achieving the static reconstruction model and then constructs a response model synchronized with the driving system by some rules. The method presented cannot only remove the potential singular problem of the static reconstruction model but also reduce the dimension of differential embedding (i.e. the order of derivative estimator in the static reconstruction model) and even remove completely the output differential.
3. To estimate parameters from a scalar output, a guidance is presented for the design of parameter estimation law, namely parameter estimation is designed such that the coefficient of the lowest order of the local linearization around the synchronization manifold is positive almost everywhere. The Lorenz model and a unified chaotic system are illustrated to validate this method and to demonstrate also that it is possible to estimate all parameters from a scalar output time-series.
4. Trying to solve the high-frequency chattering of conventional variable structure control, an adaptive chattering-free variable structure control method is proposed for controlling a class of uncertain time-variant chaotic systems by three steps: 1) constructing an augmented model of the selected system, 2) designing a conventional variable structure control law for this augmented model and 3) using some mathematical operation. The method not only eliminates the chattering phenomenon and tracks arbitrarily desired trajectory asymptotically, but also removes the prior knowledge about the upper bound of the system uncertainty. However this approach exhibits some drawbacks in practice such as the ill-pose problem in parameter estimation law happening in the present of noise and external disturbances, as well as imperfect avoidance of high-frequency chattering. An improved method is suggested to solve the drawbacks, which introduces a parameter adaptive estimator with dead-zone and nonlinearly learning rate, and in addition replaces the signum function by the saturation one as well. Theoretical analysis and numerical simulation validate that the improved method not only avoids the high-frequency chattering completely but also obtains high-accuracy tracking as desired in a finite time.
5. A new approach is suggested to introduce an integral action in the sliding mode control, which uses the same sliding variable in the conventional sliding mode but adds a nonlinearly integral action of the sliding variable in the controller. Due to the nonlinear integral action applied in the new sliding mode controller, the system controlled can achieve good dynamical and static performances.
6. A simple full-state asymptotic trajectory control method is suggested to asymptotically drive full states of a unified chaotic system to arbitrarily desired trajectories from only a scalar state. Theoretic analysis and numerical simulation validate that the method proposed can ensure the asymptotic trajectory control.
7. An approach to reduced-order synchronization is suggested with a finite-time uncertainty estimation which evaluates correctly the system uncertainty in a finite time. In addition, the reduced-order synchronization criterions are discussed, and the design of complete and general reduced-order synchronizations is then investigated. Theoretical analysis and numerical simulation validate the effectiveness of the method proposed.
引文
[1] Lorenz E N.Deterministic nonperiodic flow. J. Atmos. Sci., 1963, 20(20): 130-141.
[2] Li T and Yorke J. Period three implles chaos. Amer Math Monthly, 1975, 82(1): 985-992.
[3] Devancy R L. An Introduction to Chaotic Dynamical Systems. Addison- Wesley, 1982.
[4] Smale S. Differentiable Dynamical Systems. Bull. Amer. Math. Soc., 1967, 73:747-817.
[5] 程极泰, 混沌的理论与应用, 上海: 上海科学技术文献出版社,1992.
[6] 郑伟谋, 郝柏林, 实用符号动力学, 物理学进展,1990,10(3):316-373.
[7] Wolf A, Swift J B, Swinney H L, and Vastano J A Determining Lyapunov’s exponents from a time series. Physica 1985,16 D: 285-317.
[8] 吕金虎,陆君安,陈士化,混沌时间序列分析及其应用,武汉大学出版社,武汉,2002
[9] 张建树,管忠,于学文,混沌生物学(第二版),北京:科学出版社,2006年
[10] Ott E, Grebogi C, and Yorke J A. Controlling chaos. Phys. Rev. Lett., 1990, 64: 1196-1199.
[11] Ditto W L, Rauseo S N, and Spano M L. Experimental control of chaos.Phys. Rev. Lett., 1990, 65: 3211-3214.
[12] Boccaletti S, Grebogi C, Lai Y C, Mancini H, and Maza D. The control of chaos: theory and applications, Physics Reports, 2000, 329(3): 103-197.
[13] Shinbrot T, Ott E, Grebogi C, and Yorke J A. Using chaos to direct trajectories to targets. Phys. Rev. Lett., 1990, 65: 3215-3218.
[14] Shinbrot T, Ott E, Grebogi C, and Yorke J A. Using chaos to direct orbits to targets in systems describable by a one-dimensional map. Phys. Rev. A, 1992, 45: 4165-4168.
[15] Epureanu B I and Dowell E H. System identification for the Ott-Grebogi- Yorke controller design. Phys. Rev. E, 1997, 56: 5327-5331.
[16] Romeiras F J, Grebogi C, Ott E, Dayawansa W P. Controlling chaotic dynamical systems. Physica D, 1992, 58: 165-192.
[17] In V, Ditto W L, and Spano M L. Adaptive control and tracking of chaos in a magnetoelastic ribbon. Phys. Rev. E, 1995, 51: R2689-R2692.
[18] Pyragas K. Continuous control of chaos by self-controlling feedback. Phys. Lett. A, 1992, 170: 421-428.
[19] Pyragas K. Control of chaos via extended delay feedback. Physics Letters A, 1995, 206: 323-330.
[20] Pyragas K and Tamasevicius A. Experimental control of chaos by delayed self-controlling feedback. Physics Letters A, 1993, 180(1,2): 99 -102.
[21] Chen G and Dong X. On feedback control of chaotic continuous-time systems. IEEE Trans. Circuits Syst. I. 1993, 40(9): 591 - 601.
[22] Chen G and Dong X. From chaos to order: methodologies, perspectives and applications. Singapore: World Scientific, 1998.
[23] Isidori A. Nonlinear control system. Springer-Verlag, Berlin,Germany, 1995.
[24] Fuh C C and Tsai H H. Control of discrete-time chaotic systems via feedback linearization. Chaos, Solitons & Fractals, 2002, 13(2): 285-294.
[25] Tsai H H and Fuh C C. Combining dither smoothing technique and state feedback linearization to control undifferentiable chaotic systems. Chaos, Solitons & Fractals, In Press, Corrected Proof, Available online 14 June 2006.
[26] Lu Z, Shieh L S, Chen G and Coleman N P. Adaptive feedback linearization control of chaotic systems via recurrent high-order neural networks. Information Sciences, 2006, 176(16): 2337-2354.
[27] Wang C and Ge S S. Adaptive synchronization of uncertain chaotic systems via backstepping design. Chaos, Solitons & Fractals, 2001, 12(7): 1199-1206.
[28] Li G H, Zhou S P, and Yang K. Generalized projective synchronization between two different chaotic systems using active backstepping control. Physics Letters A, 2006, 355(4-5): 326-330.
[29] Deng B, Wang J, and Fei X. Synchronizing two coupled chaotic neurons in external electrical stimulation using backstepping control. Chaos, Solitons & Fractals, 2006, 29(1): 182-189.
[30] Li G H. Projective synchronization of chaotic system using backstepping control. Chaos, Solitons & Fractals, 2006, 29(2): 490-494.
[31] Harb A M, Zaher A A, Al-Qaisia A A and Zohdy M A. Recursive backstepping control of chaotic Duffing oscillators. Chaos, Solitons & Fractals, In Press, Corrected Proof, Available online 14 June 2006.
[32] Park J H. Synchronization of Genesio chaotic system via backstepping approach. Chaos, Solitons & Fractals, 2006, 27(5): 1369-1375.
[33] Yassen M T. Chaos control of chaotic dynamical systems using backstepping design. Chaos, Solitons & Fractals, 2006, 27(2): 537-548.
[34] Huang L, Wang M, and Feng R. Synchronization of generalized Henon map via backstepping design. Chaos, Solitons & Fractals, 2005, 23(2): 617-620.
[35] Zhang J, Li C, Zhang H and Yu J. Chaos synchronization using single variable feedback based on backstepping method. Chaos, Solitons & Fractals, 2004, 21(5): 1183-1193.
[36] Bowong S and Kakmeni F M M. Synchronization of uncertain chaotic systems via backstepping approach. Chaos, Solitons & Fractals, 2004, 21(4): 999-1011.
[37] Yu Y and Zhang S. Adaptive backstepping synchronization of uncertain chaotic system. Chaos, Solitons & Fractals, 2004, 21(3): 643-649.
[38] Yassen M T. Controlling, synchronization and tracking chaotic Liu system using active backstepping design. Physics Letters A, In Press, Corrected Proof, Available online 5 September 2006.
[39] Lü J H and Zhang S. Controlling Chen's chaotic attractor using backstepping design based on parameters identification. Physics Letters A, 2001, 286(2-3): 148-152.
[40] Tan X, Zhang J, and Yang Y. Synchronizing chaotic systems using backstepping design. Chaos, Solitons & Fractals, 2003, 16(1): 37-45.
[41] Iplikci S and Denizhan Y. An improved neural network based targeting method for chaotic dynamics. Chaos, Solitons & Fractals, 2003, 17(2-3): 523-529.
[42] Akritas P, Antoniou I and Ivanov V V. Identification and prediction of discrete chaotic maps applying a Chebyshev neural network. Chaos, Solitons & Fractals, 2000, 11(1-3): 337-344.
[43] Ramesh M and Narayanan S. Chaos control of Bonhoeffer–van der Pol oscillator using neural networks. Chaos, Solitons & Fractals, 2001, 12(13): 2395-2405.
[44] Cannas B, Cincotti S, Marchesi M, and Pilo F. Learning of Chua's circuit attractors by locally recurrent neural networks. Chaos, Solitons & Fractals, 2001, 12(11): 2109-2115.
[45] Hirasawa K, Wang X, Murata J, Hu J and Jin C. Universal learning network and its application to chaos control. Neural Networks, 2000, 13(2): 239-253.
[46] Sanchez E N and Ricalde L J. Chaos control and synchronization, with input saturation, via recurrent neural networks. Neural Networks, 2003, 16(5-6): 711-717.
[47] Alsing P M, Gavrielides A, and Kovanis V. Using neural networks for controlling chaos,Phys. Rev. E, 1994, 49: 1225-1231.
[48] Louvier-Hernández J F, Rico-Martínez R, and Parmananda P. Maintenance of transient chaos using a neural-network-assisted feedback control. Phys. Rev. E, 2002, 65: 016203.
[49] Bakker R, Schouten J C, Takens F, and van den Bleek C M. Neural network model to control an experimental chaotic pendulum. Phys. Rev. E, 1996, 54: 3545-3552.
[50] Yau H T and Chen C L. Chattering-free fuzzy sliding-mode control strategy for uncertain chaotic systems. Chaos, Solitons & Fractals, 2006, 30(3): 709-718.
[51] Li D. TS fuzzy realization of chaotic Lü system. Physics Letters A, 2006, 356(1): 51-58.
[52] Alasty A and Salarieh H. Controlling the chaos using fuzzy estimation of OGY and Pyragas controllers. Chaos, Solitons & Fractals, 2005, 26(2): 379-392.
[53] Kim J H, Park C W, Kim E and Park M. Fuzzy adaptive synchronization of uncertain chaotic systems. Physics Letters A, 2005, 334(4): 295-305
[54] Xue Y and Yang S. Synchronization of discrete-time spatiotemporal chaos via adaptive fuzzy control. Chaos, Solitons & Fractals, 2003, 17(5): 967-973.
[55] Park C W, Lee C H and Park M. Design of an adaptive fuzzy model based controller for chaotic dynamics in Lorenz systems with uncertainty. Information Sciences, 2002, 147(1-4): 245-266.
[56] Chen L, Chen G and Lee Y W. Fuzzy modeling and adaptive control of uncertain chaotic systems. Information Sciences, 1999, 121(1-2): 27-37.
[57] Kim J H, Park C W, Kim E and Park M. Fuzzy adaptive synchronization of uncertain chaotic systems. Physics Letters A, 2005, 334(4): 295-305
[58] Bonakdar M, Samadi M, Salarieh H and Alasty A. Stabilizing periodic orbits of chaotic systems using fuzzy control of Poincaré map. Chaos, Solitons & Fractals, In Press, Corrected Proof, Available online 1 September 2006.
[59] Chen B, Liu X P and Tong S C. Adaptive fuzzy approach to control unified chaotic systems. Chaos, Solitons & Fractals, In Press, Corrected Proof, Available online 27 June 2006.
[60] Lee W K, Hyun C H, Lee H, Kim E and Park M. Model reference adaptive synchronization of T–S fuzzy discrete chaotic systems using output tracking control. Chaos, Solitons & Fractals, In Press, Corrected Proof, Available online 21 June 2006.
[61] Vasegh N and Majd V J. Adaptive fuzzy synchronization of discrete-time chaotic systems. Chaos, Solitons & Fractals, 2006, 28(4): 1029-1036.
[62] Hyun C H, Kim J H, Kim E and Park M. Adaptive fuzzy observer based synchronization design and secure communications of chaotic systems. Chaos, Solitons & Fractals, 2006, 27(4): 930-940.
[63] Guan X P and Chen C L. Adaptive fuzzy control for chaotic systems with H∞ tracking performance. Fuzzy Sets and Systems, 2003, 139(1): 81-93.
[64] Hu S S and Liu Y. Robust H∞ control of multiple time-delay uncertain nonlinear system using fuzzy model and adaptive neural network. Fuzzy Sets and Systems, 2004, 146(3): 403-420.
[65] Yeh I C. Modeling chaotic two-dimensional mapping with fuzzy-neuron networks. Fuzzy Sets and Systems, 1999, 105(3): 421-427.
[66] Utkin V I. Sliding modes in control and optimization. New York: Springer-Verlag, CCES, 1992.
[67] Huang J Y, Gao W, Huang J C. Variable structure control: A survey. IEEE Trans. Ind. Elect., 1993, 40: 2-22.
[68] Slotine J J, Sastry S. Tracking control of nonlinear systems using sliding surfaces, with application to a robot manipulator. Int. J. Control, 1993, 38: 465-492.
[69] Esfandri F, Khalil H K. Design of a continuous implementation of variable structure control. IEEE Trans. Autom. Cont., 1991, 36: 645-649.
[70] Konishi K, Hirai M and Kokame H. Sliding mode control for a class of chaotic systems. Physics Letters A, 1998, 245(6): 511-517.
[71] Yau H T and Yan J J. Design of sliding mode controller for Lorenz chaotic system with nonlinear input. Chaos, Solitons & Fractals, 2004, 19(4): 891-898.
[72] Lin J S, Yan J J and Liao T L. Chaotic synchronization via adaptive sliding mode observers subject to input nonlinearity. Chaos, Solitons & Fractals, 2005, 24(1): 371-381.
[73] Chang W D and Yan J J. Adaptive robust PID controller design based on a sliding mode for uncertain chaotic systems. Chaos, Solitons & Fractals, 2005, 26(1): 167-175.
[74] Cannas B, Cincotti S and Usai E. A chaotic modulation scheme based on algebraic observability and sliding mode differentiators. Chaos, Solitons & Fractals, 2005, 26(2): 363-377.
[75] Chiang T Y, Hung M L, Yan J J, Yang Y S and Chang J F. Sliding mode control for uncertain unified chaotic systems with input nonlinearity. Chaos, Solitons & Fractals, In Press, Corrected Proof, Available online 5 May 2006.
[76] Yan J J, Hung M L, Chiang T Y and Yang Y S. Robust synchronization of chaotic systems via adaptive sliding mode control. Physics Letters A, 2006, 356(3): 220-225.
[77] Zhang Q, Chen S H, Hu Y, Wang C. Synchronizing the noise-perturbed unified chaotic system by sliding mode control. Physica A, 2006, 371(2): 317-324.
[78] Yan J J, Hung M L and Liao T L. Adaptive sliding mode control for synchronization of chaotic gyros with fully unknown parameters. Journal of Sound and Vibration, 2006, 298(1-2): 298-306.
[79] Haeri M and Emadzadeh A A. Synchronizing different chaotic systems using active sliding mode control. Chaos, Solitons & Fractals, 2007, 31(1): 119-129.
[80] Lima R, Pettini M. Suppression of chaos by resonant parametric perturbations. Phys. Rev. A, 1990,41: 726-733.
[81] Braiman Y, Goldhirsch I. Taming chaotic dynamics with weak periodic perturbation. Phys. Rev. Lett., 1991, 66: 2545-2548.
[82] Pikovsky A, Rosemblum M, and Kurths J. Synchronization, a universal concept in nonlinear sciences. Cambridge University Press: Cambridge. 2001.
[83] Ditto W L and Showalter K (ed). Focus issue on control and synchronization of chaos. Chaos, 1997, 7(4).
[84] Kennedy M P and M. J. Ogorzalek M J. Special issue on chaos synchronization, control and applications. IEEE Trans. Circuits Syst. I: Fundam. Theory Appl. 1997, 44(10).
[85] Strogatz S. Sync: The Emerging Science of Spontaneous Order,Theia, New York, 2003.
[86] Boccaletti S, Kurths J, Osipov G, Valladares D L, and Zhou C S. The synchronization of chaotic systems. Phys. Reports, 2002, 366: 1-101.
[87] Mosekilde E, Maistrenko Y, and Postnov D. Chaotic Synchronization: Applications to Living Systems. World Scientific Nonlinear Science Series A. 2002.
[88] Wu C W. Synchronization in Coupled Chaotic Circuits and Systems, World Scientific, Singapore, 2002.
[89] Pecora L M and Carroll T L. Synchronization in chaotic systems. Phys. Rev. Lett. 1990, 64: 821-824.
[90] Kocarev L, Tasev Z, and Parlitz U. Synchronizing Spatiotemporal Chaos of Partial Differential Equations. Phys. Rev. Lett., 1997, 79: 51-54.
[91] Kocarev L, Halle K S, Eckert K, Chua L O and Parlitz U. Experimental demonstration of secure communications via chaos synchronization. Int. J. Bifurcation Chaos Appl. Sci. Eng., 1992, 2(3): 709-713.
[92] Wu C W and Chua L O. A simple way to synchronize chaotic systems with applications to secure communication systems. Int. J. Bifurcation Chaos Appl. Sci. Eng., 1993, 3(6): 1619-1627.
[93] Wu L. and Zhu S Q. Communications using multi-mode laser system based on chaotic synchronization. Chinese Phys. 2003, 12: 300-304.
[94] Murali K and Lakshmanan M. Transmission of signals by synchronization in a chaotic Van der Pol–Duffing oscillator. Phys. Rev. E, 1993, 48: R1624-R1626.
[95] Cuomo K M and Oppenheim A V. Circuit implementation of synchronized chaos with applications to communications. Phys. Rev. Lett., 1993, 71: 65-68.
[96] Kocarev L and Parlitz U. General Approach for Chaotic Synchronization with Applications to Communication. Phys. Rev. Lett., 1995, 74: 5028-5031.
[97] Sharma N and Poonacha P G. Tracking of synchronized chaotic systems with applications to communications. Phys. Rev. E, 1997, 56: 1242-1245
[98] Zhou C S, Chen T L. Digital communication robust to transmission error via chaotic synchronization based on contraction maps. Phys. Rev. E, 1997, 56: 1599-1604.
[99] Minai A Aand Anand T. Synchronization of chaotic maps through a noisy coupling channel with application to digital communication. Phys. Rev. E, 1999, 59: 312-320.
[100] White J K and Moloney J V. Multichannel communication using an infinite dimensional spatiotemporal chaotic system. Phys. Rev. A, 1999, 59: 2422-2426.
[101] Yoshimura K. Multichannel digital communications by the synchronization of globally coupled chaotic systems. Phys. Rev. E, 1999, 60: 1648-1657.
[102] Sivaprakasam S and Shore K A. Critical signal strength for effective decoding in diode laser chaotic optical communications. Phys. Rev. E, 2000, 61: 5997-5999.
[103] Fischer I, Liu Y, and Davis P. Synchronization of chaotic semiconductor laser dynamics on subnanosecond time scales and its potential for chaos communication. Phys. Rev. A, 2000, 62: 011801.
[104] Sundar S and Minai A A. Synchronization of Randomly Multiplexed Chaotic Systems with Application to Communication. Phys. Rev. Lett., 2000, 85: 5456-5459.
[105] Udaltsov V S, Goedgebuer J P, Larger L, and Rhodes W T. Communicating with Optical Hyperchaos: Information Encryption and Decryption in Delayed Nonlinear Feedback Systems. Phys. Rev. Lett., 2001, 86: 1892-1895.
[106] García-Ojalvo J and Roy R. Spatiotemporal Communication with Synchronized Optical Chaos. Phys. Rev. Lett., 2001, 86: 5204-5207.
[107] Kim C M, Rim S and Kye W H. Sequential Synchronization of Chaotic Systems with an Application to Communication. Phys. Rev. Lett., 2002, 88: 014103.
[108] Leung H, Yu H and Murali K. Ergodic chaos-based communication schemes. Phys. Rev. E, 2002, 66: 036203.
[109] Tang S and Liu J M. Message encoding--decoding at 2.5 Gbits/s through synchronization of chaotic pulsing semiconductor lasers. Optics Lett., 2001, 26(23): 1843-1845.
[110] Roy R, Murphy T W, Maier J T D, Gills Z and Hunt E R. Dynamical control of a chaotic laser: Experimental stabilization of a globally coupled system. Phys. Rev. Lett., 1992, 68: 1259-1262.
[111] Lewis C T, Abarbanel H D I, Kennel M B, Buhl M, and Illing L. Synchronization of chaotic oscillations in doped fiber ring lasers. Phys. Rev. E, 2001, 63: 016215.
[112] Fischer I et al. Zero-Lag Long-Range Synchronization via Dynamical Relaying. Phys. Rev. Lett., 2006, 97: 123902.
[113] Byrd J M, Hao Z, Martin M C, Robin D S, Sannibale F, Schoenlein R W, Zholents A A, and Zolotorev M S. Laser Seeding of the Storage-Ring Microbunching Instability for High-Power Coherent Terahertz Radiation. Phys. Rev. Lett., 2006, 97: 074802.
[114] Tanguy Y, Houlihan J, Huyet G, Viktorov E A, and Mandel P. Synchronization and Clustering in a Multimode Quantum Dot Laser. Phys. Rev. Lett., 2006, 96: 024102.
[115] Soto-Crespo J M and Akhmediev N. Soliton as Strange Attractor: Nonlinear Synchronization and Chaos. Phys. Rev. Lett., 2005, 95: 024101.
[116] Wünsche H J, Bauer S, Kreissl J, Ushakov O, Korneyev N, Henneberger F, Wille E, Erzgr?ber H, Peil M, Els??er W, and Fischer I. Synchronization of Delay-Coupled Oscillators: A Study of Semiconductor Lasers. Phys. Rev. Lett., 2005, 94: 163901.
[117] Tang S and Liu J M. Experimental Verification of Anticipated and Retarded Synchronization in Chaotic Semiconductor Lasers. Phys. Rev. Lett., 2003, 90: 194101.
[118] Scirè A, Mulet J, Mirasso C R, Danckaert J, and San Miguel M. Polarization Message Encoding through Vectorial Chaos Synchronization in Vertical-Cavity Surface-Emitting Lasers. Phys. Rev. Lett., 2003, 90: 113901.
[119] Yang S C et al. Data Assimilation as Synchronization of Truth and Model: Experiments with the Three-Variable Lorenz System. Journal of the Atmospheric Sciences, in press.
[120] Belykh I, de Lange E, and Hasler M. Synchronization of Bursting Neurons: What Matters in the Network Topology. Phys. Rev. Lett., 2005, 94: 188101.
[121] Jia L C, Sano M, Lai P Y, and Chan C K. Connectivities and Synchronous Firing in Cortical Neuronal Networks. Phys. Rev. Lett., 2004, 93: 088101.
[122] Neiman A B and Russell D F. Synchronization of Noise-Induced Bursts in Noncoupled Sensory Neurons. Phys. Rev. Lett., 2002, 88: 138103.
[123] Elson R C, Selverston A I, Huerta R, Rulkov N F, Rabinovich M I, and Abarbanel H D I. Synchronous Behavior of Two Coupled Biological Neurons. Phys. Rev. Lett., 1998, 81: 5692-5695.
[124] Hansel D and Sompolinsky H. Synchronization and computation in a chaotic neural network. Phys. Rev. Lett., 1992, 68: 718-721.
[125] Lehnertz K and Elger C E. Can Epileptic Seizures be Predicted? Evidence from Nonlinear Time Series Analysis of Brain Electrical Activity. Phys. Rev. Lett., 1998, 80: 5019-5022.
[126] Masuda N and Aihara K. Bridging Rate Coding and Temporal Spike Coding by Effect of Noise. Phys. Rev. Lett., 2002, 88: 248101.
[127] Tass P A, Fieseler T, Dammers J, Dolan K, Morosan P, Majtanik M, Boers F, Muren A, Zilles K, and Fink G R. Synchronization Tomography: A Method for Three-Dimensional Localization of Phase Synchronized Neuronal Populations in the Human Brain using Magnetoencephalography. Phys. Rev. Lett., 2003, 90: 088101.
[128] Rabinovich M I, Huerta R, and Varona P. Heteroclinic Synchronization: Ultrasubharmonic Locking. Phys. Rev. Lett., 2006, 96: 014101.
[129] Neiman A, Pei X, Russell D, Wojtenek W, Wilkens L, Moss F, Braun H A, Huber M T, and Voigt K. Synchronization of the Noisy Electrosensitive Cells in the Paddlefish. Phys. Rev. Lett., 1999, 82: 660-663.
[130] Zhou T, Chen L, and Aihara K. Molecular Communication through Stochastic Synchronization Induced by Extracellular Fluctuations. Phys. Rev. Lett., 2005, 95: 178103.
[131] Battogtokh D, Aihara K, and Tyson J J. Synchronization of Eukaryotic Cells by Periodic Forcing. Phys. Rev. Lett., 2006, 96: 148102.
[132] Duane G S and Tribbia J J. Synchronized Chaos in Geophysical Fluid Dynamics. Phys. Rev. Lett., 2001, 86: 4298-4301.
[133] Paoletti M S, Nugent C R, and Solomon T H. Synchronization of Oscillating Reactions in an Extended Fluid System. Phys. Rev. Lett., 2006, 96: 124101.
[134] Veser G, Mertens F, Mikhailov A S, and Imbihl R. Global coupling in the presence of defects: Synchronization in an oscillatory surface reaction. Phys. Rev. Lett., 1993, 71: 935-938.
[135] Kortlüke O, Kuzovkov V N, and von Niessen W. Global Synchronization via Homogeneous Nucleation in Oscillating Surface Reactions. Phys. Rev. Lett., 1999, 83: 3089-3092.
[136] 方锦清,非线性系统中的混沌控制方法、同步原理及其应用前景(二),物理学进展,1996, 16, 190-195
[137] Wu C W and Chua L O. A unified framework for synchronization and control of dynamical systems. Int. J. Bifurcation Chaos, 1994, 4(4): 979-998.
[138] Fujisaka H and Yamada T. Stability theory of synchronized motion in coupled oscillator systems. Prog. Theor. Phys., 1983, 69: 32-47.
[139] Nijmeijer H and Mareels I M Y. An observer looks at synchronization. IEEE Trans. Circuits Syst. I,1997, 44(10): 882-890.
[140] Kocarev L and Parlitz U. Generalized Synchronization, Predictability, and Equivalence of Unidirectionally Coupled Dynamical Systems. Phys. Rev. Lett., 1996, 76: 1816-1819.
[141] Rosenblum M G, Pikovsky A S and Kurths J. Phase Synchronization of Chaotic Oscillators. Phys. Rev. Lett., 1996, 76: 1804-1807.
[142] Kocarev L and Parlitz U. General Approach for Chaotic Synchronization with Applications to Communication. Phys. Rev. Lett., 1995, 74: 5028-5031.
[143] Mritan A and Banavar J R. Chaos, noise, and synchronization. Phys. Rev. Lett., 1994, 72: 1451-1454.
[144] Mritan A, Banavar J R. Maritan and Banavar Reply. Phys. Rev. Lett., 1994, 73: 2932.
[145] Zhou C S, Kurths J. Noise-induced phase synchronization and synchronization transitions in chaotic oscillators. Phys. Rev. Lett., 2002, 88: 230602.
[146] Zhou C S, Kurths J, Kiss I Z, Hudson J L. Noise enhanced phase synchronization of chaotic oscillators. Phys. Rev. Lett., 2002, 89: 014101.
[147] Parlitz U. Estimating model parameters from time series by autosynchronization. Phys. Rev. Lett., 1996, 76: 1232-1235.
[148] Parlitz U, Junge L and L. Kocarev. Synchronization-based parameter estimation from time series. Phys. Rev. E, 1996, 54: 6253-6259.
[149] Sakaguchi H. Parameter evaluation from time sequences using chaos synchronization. Phys. Rev. E, 2002, 65: 027201.
[150] Maybhate A and Amritkar R E. Use of synchronization and adaptive control in parameter estimation from a time series. Phys. Rev. E, 1999, 59: 284-293.
[151] Maybhate A and Amritkar R E. Dynamic algorithm for parameter estimation and its applications. Phys. Rev. E, 2000, 61: 6461.
[152] Konnur R. Synchronization-based approach for estimating all model parameters of chaotic systems. Phys. Rev. E, 2003, 67: 027204.
[153] Tao C, Zhang Y, Du G and Jiang J J. Estimating model parameters by chaos synchronization. Phys. Rev. E, 2004, 69: 036204.
[154] Marino I P and Miguez J. Adaptive approximation method for joint parameter estimation and identical synchronization of chaotic systems. Phys. Rev. E, 2005, 72: 057202.
[155] Huang D B. Synchronization-based estimation of all parameters of chaotic systems from time series. Phys. Rev. E, 2004, 69: 067201.
[156] Huang D B and Guo R. Identifying parameter by identical synchronization between different systems. Chaos, 2004, 14: 152-159.
[157] Lu J and Cao J. Adaptive complete synchronization of two identical or different chaotic (hyperchaotic) systems with fully unknown parameters. Chaos 2005, 15: 043901.
[158] Yu W and Cao J. Adaptive Q-S (lag, anticipated, and complete) time-varying synchronization and parameters identification of uncertain delayed neural networks. Chaos, 2006, 16: 023119.
[159] Yu D C and Wu A G. Comment on Estimating Model Parameters from Time Series by Autosynchronization. Phys. Rev. Lett., 2005, 94: 219401.
[160] Li L, Peng H, Wang X, and Yang Y. Comment on two papers of chaotic synchronization. Phys. Lett. A, 2004, 333: 269-270.
[161] 高铁杠,混沌系统同步及其在信息安全中的应用:[博士学位论文],天津:南开大学,2005
[162] 禹东川,孟庆浩,不确定时变混沌系统的一种自适应无抖振变结构控制,” 物理学报, 2005, 54: 1092-1097.
[163] 高为炳,变结构控制的理论及设计方法, 北京:科学出版社,1996.
[164] Huang J and Rugh W. On a nonlinear multivariable servomechanism problem. Automatica, 1990, 26: 963-972.
[165] Huang J and Rugh W. Stabilization on zero-error manifolds and the nonlinear servomechanism problem. IEEE Tran.saitions on Automatic Control, 1992, 37: 1009-1013.
[166] Isidori A and Byrnks C. Output regulation of nonlinear systems. IEEE Transactions on Automatic Control, 1990, 35: 131-140.
[167] Khalil H. Universal integral controller for minimumphase nonlinear systems. IEEE Transactions on Automatic Controt. 2000, 45: 490-494.
[168] Ho E and Sen P. Control dynamics of speed drive systems using sliding mode controllers with integral compensation. IEEE Trans. Industrial Application, 1991, 27(5): 883-892.
[169] Chern T L and Wu Y C. Design of integral variable structure controller and application to electrohydraulic velocity. IEE Proceedings-D, 1991, 138(5): 439-444.
[170] Chern T L and Wu Y C.Integral variable structure control approach for robot manipulators,” IEE Proceedings-D, 1992, 139(2): 161-166.
[171] Sira-Ramirez H. On the generalized PI sliding mode control of DC-to-DC power converters: A tutorial. International Journal of Control, 2003, 76(9):1018-1033.
[172] Bhat S P and Bernstein D S. Continuous, Finite-Time Stabilization of the Translational and Rotational Double Integrators. IEEE Transactions on Automatic Control, 1998, 43: 678-682.
[173] Chen G and Ueta T. Yet another chaotic attractor. Int. J. Bifurcation Chaos. 1999, 9: 1465-1466.
[174] Ueta T and Chen G. Bifurcation analysis of Chen's attractor. Int. J. Bifurcation Chaos, 2000, 10: 1917-1931.
[175] Lu J H and Chen G. A new chaotic attractor coined. Int. J. Bifurcation Chaos, 2002, 12: 659-661.
[176] Lu J H, Chen G and Zhang S. Dynamical analysis of a new chaotic attractor. Int. J. Bifurcation Chaos. 2002, 12: 1001-1015.
[177] Lu J H, Chen G, Cheng D Z and Celikovsky S. Bridge the gap between Loren system and the Chen system. Int. J. Bifurcation Chaos, 2002, 12 (12): 2917-1926.
[178] Lu J, Wu X and Lu J H. Synchronization of a unifed chaotic system and the application in secure communication. Phys. Lett. A, 2002, 305: 365-370.
[179] Lu J, Wu X, Han X and Lu J H. Adaptive feedback synchronization of a unifed chaotic system. Phys. Lett. A, 2004, 329: 327-333.
[180] Liu J, Chen S and Xie J. Parameter identifcation and control of uncertain unifed chaotic system via adaptive extending equilibrium manifold approach. Chaos, Solitons and Fractals, 2004, 19: 533-540.
[181] Ucr A, Lonngren K E and Bai E W. Synchronization of the unifed chaotic systems via active control. Chaos, Solitons and Fractals, 2006, 27: 1292-1297.
[182] Tao C H, Xiong H X and Hu F. Two novel synchronization criterions for a unifed chaotic system. Chaos, Solitons and Fractals. 2006, 27: 115-120.
[183] Rossler O E. An equation for continuous chaos. Phys Lett A , 1976, 57(5): 397 -398.
[184] Rossler, O. E. An equation for hyperchaos. Phys. Lett. A, 1979, 71(2-3): 155-157.
[185] http://www.dddas.org
[186] Sastry S. Nonlinear Systems: Analysis, Stability, and Control. Springer Verlag, 1999.
[187] Slotine J J and Li W. Applied nonlinear control. Prentice-Hall, Englewood Cliffs, 1991.
[188] Peixoto M. Structural stability on two dimensional manifolds. Topology, 1962, 1: 101-120.
[189] Levant A. Robust exact differentiation via sliding mode technique. Automatica, 1998, 34(3): 379-384.
[190] Levant A. Higher-order sliding modes, differentiation and output-feedback control. Int. J. Control, 2003, 76(9/10): 924-941.
[191] Bowong S. Stability analysis for the synchronization of chaotic systems with different order: application to secure communications. Physics Letters A, 2004, 326(1-2): 102-113.
[192] Bowong S and McClintock P V E. Adaptive synchronization between chaotic dynamical systems of different order. Physics Letters A, 2006, 358(2): 134-141.
[193] Ho M C, Hung Y C, Liu Z Y and Jiang I M. Reduced-order synchronization of chaotic systems with parameters unknown. Physics Letters A, 2006, 348(3-6): 251-259.
[2] Li T and Yorke J. Period three implles chaos. Amer Math Monthly, 1975, 82(1): 985-992.
[3] Devancy R L. An Introduction to Chaotic Dynamical Systems. Addison- Wesley, 1982.
[4] Smale S. Differentiable Dynamical Systems. Bull. Amer. Math. Soc., 1967, 73:747-817.
[5] 程极泰, 混沌的理论与应用, 上海: 上海科学技术文献出版社,1992.
[6] 郑伟谋, 郝柏林, 实用符号动力学, 物理学进展,1990,10(3):316-373.
[7] Wolf A, Swift J B, Swinney H L, and Vastano J A Determining Lyapunov’s exponents from a time series. Physica 1985,16 D: 285-317.
[8] 吕金虎,陆君安,陈士化,混沌时间序列分析及其应用,武汉大学出版社,武汉,2002
[9] 张建树,管忠,于学文,混沌生物学(第二版),北京:科学出版社,2006年
[10] Ott E, Grebogi C, and Yorke J A. Controlling chaos. Phys. Rev. Lett., 1990, 64: 1196-1199.
[11] Ditto W L, Rauseo S N, and Spano M L. Experimental control of chaos.Phys. Rev. Lett., 1990, 65: 3211-3214.
[12] Boccaletti S, Grebogi C, Lai Y C, Mancini H, and Maza D. The control of chaos: theory and applications, Physics Reports, 2000, 329(3): 103-197.
[13] Shinbrot T, Ott E, Grebogi C, and Yorke J A. Using chaos to direct trajectories to targets. Phys. Rev. Lett., 1990, 65: 3215-3218.
[14] Shinbrot T, Ott E, Grebogi C, and Yorke J A. Using chaos to direct orbits to targets in systems describable by a one-dimensional map. Phys. Rev. A, 1992, 45: 4165-4168.
[15] Epureanu B I and Dowell E H. System identification for the Ott-Grebogi- Yorke controller design. Phys. Rev. E, 1997, 56: 5327-5331.
[16] Romeiras F J, Grebogi C, Ott E, Dayawansa W P. Controlling chaotic dynamical systems. Physica D, 1992, 58: 165-192.
[17] In V, Ditto W L, and Spano M L. Adaptive control and tracking of chaos in a magnetoelastic ribbon. Phys. Rev. E, 1995, 51: R2689-R2692.
[18] Pyragas K. Continuous control of chaos by self-controlling feedback. Phys. Lett. A, 1992, 170: 421-428.
[19] Pyragas K. Control of chaos via extended delay feedback. Physics Letters A, 1995, 206: 323-330.
[20] Pyragas K and Tamasevicius A. Experimental control of chaos by delayed self-controlling feedback. Physics Letters A, 1993, 180(1,2): 99 -102.
[21] Chen G and Dong X. On feedback control of chaotic continuous-time systems. IEEE Trans. Circuits Syst. I. 1993, 40(9): 591 - 601.
[22] Chen G and Dong X. From chaos to order: methodologies, perspectives and applications. Singapore: World Scientific, 1998.
[23] Isidori A. Nonlinear control system. Springer-Verlag, Berlin,Germany, 1995.
[24] Fuh C C and Tsai H H. Control of discrete-time chaotic systems via feedback linearization. Chaos, Solitons & Fractals, 2002, 13(2): 285-294.
[25] Tsai H H and Fuh C C. Combining dither smoothing technique and state feedback linearization to control undifferentiable chaotic systems. Chaos, Solitons & Fractals, In Press, Corrected Proof, Available online 14 June 2006.
[26] Lu Z, Shieh L S, Chen G and Coleman N P. Adaptive feedback linearization control of chaotic systems via recurrent high-order neural networks. Information Sciences, 2006, 176(16): 2337-2354.
[27] Wang C and Ge S S. Adaptive synchronization of uncertain chaotic systems via backstepping design. Chaos, Solitons & Fractals, 2001, 12(7): 1199-1206.
[28] Li G H, Zhou S P, and Yang K. Generalized projective synchronization between two different chaotic systems using active backstepping control. Physics Letters A, 2006, 355(4-5): 326-330.
[29] Deng B, Wang J, and Fei X. Synchronizing two coupled chaotic neurons in external electrical stimulation using backstepping control. Chaos, Solitons & Fractals, 2006, 29(1): 182-189.
[30] Li G H. Projective synchronization of chaotic system using backstepping control. Chaos, Solitons & Fractals, 2006, 29(2): 490-494.
[31] Harb A M, Zaher A A, Al-Qaisia A A and Zohdy M A. Recursive backstepping control of chaotic Duffing oscillators. Chaos, Solitons & Fractals, In Press, Corrected Proof, Available online 14 June 2006.
[32] Park J H. Synchronization of Genesio chaotic system via backstepping approach. Chaos, Solitons & Fractals, 2006, 27(5): 1369-1375.
[33] Yassen M T. Chaos control of chaotic dynamical systems using backstepping design. Chaos, Solitons & Fractals, 2006, 27(2): 537-548.
[34] Huang L, Wang M, and Feng R. Synchronization of generalized Henon map via backstepping design. Chaos, Solitons & Fractals, 2005, 23(2): 617-620.
[35] Zhang J, Li C, Zhang H and Yu J. Chaos synchronization using single variable feedback based on backstepping method. Chaos, Solitons & Fractals, 2004, 21(5): 1183-1193.
[36] Bowong S and Kakmeni F M M. Synchronization of uncertain chaotic systems via backstepping approach. Chaos, Solitons & Fractals, 2004, 21(4): 999-1011.
[37] Yu Y and Zhang S. Adaptive backstepping synchronization of uncertain chaotic system. Chaos, Solitons & Fractals, 2004, 21(3): 643-649.
[38] Yassen M T. Controlling, synchronization and tracking chaotic Liu system using active backstepping design. Physics Letters A, In Press, Corrected Proof, Available online 5 September 2006.
[39] Lü J H and Zhang S. Controlling Chen's chaotic attractor using backstepping design based on parameters identification. Physics Letters A, 2001, 286(2-3): 148-152.
[40] Tan X, Zhang J, and Yang Y. Synchronizing chaotic systems using backstepping design. Chaos, Solitons & Fractals, 2003, 16(1): 37-45.
[41] Iplikci S and Denizhan Y. An improved neural network based targeting method for chaotic dynamics. Chaos, Solitons & Fractals, 2003, 17(2-3): 523-529.
[42] Akritas P, Antoniou I and Ivanov V V. Identification and prediction of discrete chaotic maps applying a Chebyshev neural network. Chaos, Solitons & Fractals, 2000, 11(1-3): 337-344.
[43] Ramesh M and Narayanan S. Chaos control of Bonhoeffer–van der Pol oscillator using neural networks. Chaos, Solitons & Fractals, 2001, 12(13): 2395-2405.
[44] Cannas B, Cincotti S, Marchesi M, and Pilo F. Learning of Chua's circuit attractors by locally recurrent neural networks. Chaos, Solitons & Fractals, 2001, 12(11): 2109-2115.
[45] Hirasawa K, Wang X, Murata J, Hu J and Jin C. Universal learning network and its application to chaos control. Neural Networks, 2000, 13(2): 239-253.
[46] Sanchez E N and Ricalde L J. Chaos control and synchronization, with input saturation, via recurrent neural networks. Neural Networks, 2003, 16(5-6): 711-717.
[47] Alsing P M, Gavrielides A, and Kovanis V. Using neural networks for controlling chaos,Phys. Rev. E, 1994, 49: 1225-1231.
[48] Louvier-Hernández J F, Rico-Martínez R, and Parmananda P. Maintenance of transient chaos using a neural-network-assisted feedback control. Phys. Rev. E, 2002, 65: 016203.
[49] Bakker R, Schouten J C, Takens F, and van den Bleek C M. Neural network model to control an experimental chaotic pendulum. Phys. Rev. E, 1996, 54: 3545-3552.
[50] Yau H T and Chen C L. Chattering-free fuzzy sliding-mode control strategy for uncertain chaotic systems. Chaos, Solitons & Fractals, 2006, 30(3): 709-718.
[51] Li D. TS fuzzy realization of chaotic Lü system. Physics Letters A, 2006, 356(1): 51-58.
[52] Alasty A and Salarieh H. Controlling the chaos using fuzzy estimation of OGY and Pyragas controllers. Chaos, Solitons & Fractals, 2005, 26(2): 379-392.
[53] Kim J H, Park C W, Kim E and Park M. Fuzzy adaptive synchronization of uncertain chaotic systems. Physics Letters A, 2005, 334(4): 295-305
[54] Xue Y and Yang S. Synchronization of discrete-time spatiotemporal chaos via adaptive fuzzy control. Chaos, Solitons & Fractals, 2003, 17(5): 967-973.
[55] Park C W, Lee C H and Park M. Design of an adaptive fuzzy model based controller for chaotic dynamics in Lorenz systems with uncertainty. Information Sciences, 2002, 147(1-4): 245-266.
[56] Chen L, Chen G and Lee Y W. Fuzzy modeling and adaptive control of uncertain chaotic systems. Information Sciences, 1999, 121(1-2): 27-37.
[57] Kim J H, Park C W, Kim E and Park M. Fuzzy adaptive synchronization of uncertain chaotic systems. Physics Letters A, 2005, 334(4): 295-305
[58] Bonakdar M, Samadi M, Salarieh H and Alasty A. Stabilizing periodic orbits of chaotic systems using fuzzy control of Poincaré map. Chaos, Solitons & Fractals, In Press, Corrected Proof, Available online 1 September 2006.
[59] Chen B, Liu X P and Tong S C. Adaptive fuzzy approach to control unified chaotic systems. Chaos, Solitons & Fractals, In Press, Corrected Proof, Available online 27 June 2006.
[60] Lee W K, Hyun C H, Lee H, Kim E and Park M. Model reference adaptive synchronization of T–S fuzzy discrete chaotic systems using output tracking control. Chaos, Solitons & Fractals, In Press, Corrected Proof, Available online 21 June 2006.
[61] Vasegh N and Majd V J. Adaptive fuzzy synchronization of discrete-time chaotic systems. Chaos, Solitons & Fractals, 2006, 28(4): 1029-1036.
[62] Hyun C H, Kim J H, Kim E and Park M. Adaptive fuzzy observer based synchronization design and secure communications of chaotic systems. Chaos, Solitons & Fractals, 2006, 27(4): 930-940.
[63] Guan X P and Chen C L. Adaptive fuzzy control for chaotic systems with H∞ tracking performance. Fuzzy Sets and Systems, 2003, 139(1): 81-93.
[64] Hu S S and Liu Y. Robust H∞ control of multiple time-delay uncertain nonlinear system using fuzzy model and adaptive neural network. Fuzzy Sets and Systems, 2004, 146(3): 403-420.
[65] Yeh I C. Modeling chaotic two-dimensional mapping with fuzzy-neuron networks. Fuzzy Sets and Systems, 1999, 105(3): 421-427.
[66] Utkin V I. Sliding modes in control and optimization. New York: Springer-Verlag, CCES, 1992.
[67] Huang J Y, Gao W, Huang J C. Variable structure control: A survey. IEEE Trans. Ind. Elect., 1993, 40: 2-22.
[68] Slotine J J, Sastry S. Tracking control of nonlinear systems using sliding surfaces, with application to a robot manipulator. Int. J. Control, 1993, 38: 465-492.
[69] Esfandri F, Khalil H K. Design of a continuous implementation of variable structure control. IEEE Trans. Autom. Cont., 1991, 36: 645-649.
[70] Konishi K, Hirai M and Kokame H. Sliding mode control for a class of chaotic systems. Physics Letters A, 1998, 245(6): 511-517.
[71] Yau H T and Yan J J. Design of sliding mode controller for Lorenz chaotic system with nonlinear input. Chaos, Solitons & Fractals, 2004, 19(4): 891-898.
[72] Lin J S, Yan J J and Liao T L. Chaotic synchronization via adaptive sliding mode observers subject to input nonlinearity. Chaos, Solitons & Fractals, 2005, 24(1): 371-381.
[73] Chang W D and Yan J J. Adaptive robust PID controller design based on a sliding mode for uncertain chaotic systems. Chaos, Solitons & Fractals, 2005, 26(1): 167-175.
[74] Cannas B, Cincotti S and Usai E. A chaotic modulation scheme based on algebraic observability and sliding mode differentiators. Chaos, Solitons & Fractals, 2005, 26(2): 363-377.
[75] Chiang T Y, Hung M L, Yan J J, Yang Y S and Chang J F. Sliding mode control for uncertain unified chaotic systems with input nonlinearity. Chaos, Solitons & Fractals, In Press, Corrected Proof, Available online 5 May 2006.
[76] Yan J J, Hung M L, Chiang T Y and Yang Y S. Robust synchronization of chaotic systems via adaptive sliding mode control. Physics Letters A, 2006, 356(3): 220-225.
[77] Zhang Q, Chen S H, Hu Y, Wang C. Synchronizing the noise-perturbed unified chaotic system by sliding mode control. Physica A, 2006, 371(2): 317-324.
[78] Yan J J, Hung M L and Liao T L. Adaptive sliding mode control for synchronization of chaotic gyros with fully unknown parameters. Journal of Sound and Vibration, 2006, 298(1-2): 298-306.
[79] Haeri M and Emadzadeh A A. Synchronizing different chaotic systems using active sliding mode control. Chaos, Solitons & Fractals, 2007, 31(1): 119-129.
[80] Lima R, Pettini M. Suppression of chaos by resonant parametric perturbations. Phys. Rev. A, 1990,41: 726-733.
[81] Braiman Y, Goldhirsch I. Taming chaotic dynamics with weak periodic perturbation. Phys. Rev. Lett., 1991, 66: 2545-2548.
[82] Pikovsky A, Rosemblum M, and Kurths J. Synchronization, a universal concept in nonlinear sciences. Cambridge University Press: Cambridge. 2001.
[83] Ditto W L and Showalter K (ed). Focus issue on control and synchronization of chaos. Chaos, 1997, 7(4).
[84] Kennedy M P and M. J. Ogorzalek M J. Special issue on chaos synchronization, control and applications. IEEE Trans. Circuits Syst. I: Fundam. Theory Appl. 1997, 44(10).
[85] Strogatz S. Sync: The Emerging Science of Spontaneous Order,Theia, New York, 2003.
[86] Boccaletti S, Kurths J, Osipov G, Valladares D L, and Zhou C S. The synchronization of chaotic systems. Phys. Reports, 2002, 366: 1-101.
[87] Mosekilde E, Maistrenko Y, and Postnov D. Chaotic Synchronization: Applications to Living Systems. World Scientific Nonlinear Science Series A. 2002.
[88] Wu C W. Synchronization in Coupled Chaotic Circuits and Systems, World Scientific, Singapore, 2002.
[89] Pecora L M and Carroll T L. Synchronization in chaotic systems. Phys. Rev. Lett. 1990, 64: 821-824.
[90] Kocarev L, Tasev Z, and Parlitz U. Synchronizing Spatiotemporal Chaos of Partial Differential Equations. Phys. Rev. Lett., 1997, 79: 51-54.
[91] Kocarev L, Halle K S, Eckert K, Chua L O and Parlitz U. Experimental demonstration of secure communications via chaos synchronization. Int. J. Bifurcation Chaos Appl. Sci. Eng., 1992, 2(3): 709-713.
[92] Wu C W and Chua L O. A simple way to synchronize chaotic systems with applications to secure communication systems. Int. J. Bifurcation Chaos Appl. Sci. Eng., 1993, 3(6): 1619-1627.
[93] Wu L. and Zhu S Q. Communications using multi-mode laser system based on chaotic synchronization. Chinese Phys. 2003, 12: 300-304.
[94] Murali K and Lakshmanan M. Transmission of signals by synchronization in a chaotic Van der Pol–Duffing oscillator. Phys. Rev. E, 1993, 48: R1624-R1626.
[95] Cuomo K M and Oppenheim A V. Circuit implementation of synchronized chaos with applications to communications. Phys. Rev. Lett., 1993, 71: 65-68.
[96] Kocarev L and Parlitz U. General Approach for Chaotic Synchronization with Applications to Communication. Phys. Rev. Lett., 1995, 74: 5028-5031.
[97] Sharma N and Poonacha P G. Tracking of synchronized chaotic systems with applications to communications. Phys. Rev. E, 1997, 56: 1242-1245
[98] Zhou C S, Chen T L. Digital communication robust to transmission error via chaotic synchronization based on contraction maps. Phys. Rev. E, 1997, 56: 1599-1604.
[99] Minai A Aand Anand T. Synchronization of chaotic maps through a noisy coupling channel with application to digital communication. Phys. Rev. E, 1999, 59: 312-320.
[100] White J K and Moloney J V. Multichannel communication using an infinite dimensional spatiotemporal chaotic system. Phys. Rev. A, 1999, 59: 2422-2426.
[101] Yoshimura K. Multichannel digital communications by the synchronization of globally coupled chaotic systems. Phys. Rev. E, 1999, 60: 1648-1657.
[102] Sivaprakasam S and Shore K A. Critical signal strength for effective decoding in diode laser chaotic optical communications. Phys. Rev. E, 2000, 61: 5997-5999.
[103] Fischer I, Liu Y, and Davis P. Synchronization of chaotic semiconductor laser dynamics on subnanosecond time scales and its potential for chaos communication. Phys. Rev. A, 2000, 62: 011801.
[104] Sundar S and Minai A A. Synchronization of Randomly Multiplexed Chaotic Systems with Application to Communication. Phys. Rev. Lett., 2000, 85: 5456-5459.
[105] Udaltsov V S, Goedgebuer J P, Larger L, and Rhodes W T. Communicating with Optical Hyperchaos: Information Encryption and Decryption in Delayed Nonlinear Feedback Systems. Phys. Rev. Lett., 2001, 86: 1892-1895.
[106] García-Ojalvo J and Roy R. Spatiotemporal Communication with Synchronized Optical Chaos. Phys. Rev. Lett., 2001, 86: 5204-5207.
[107] Kim C M, Rim S and Kye W H. Sequential Synchronization of Chaotic Systems with an Application to Communication. Phys. Rev. Lett., 2002, 88: 014103.
[108] Leung H, Yu H and Murali K. Ergodic chaos-based communication schemes. Phys. Rev. E, 2002, 66: 036203.
[109] Tang S and Liu J M. Message encoding--decoding at 2.5 Gbits/s through synchronization of chaotic pulsing semiconductor lasers. Optics Lett., 2001, 26(23): 1843-1845.
[110] Roy R, Murphy T W, Maier J T D, Gills Z and Hunt E R. Dynamical control of a chaotic laser: Experimental stabilization of a globally coupled system. Phys. Rev. Lett., 1992, 68: 1259-1262.
[111] Lewis C T, Abarbanel H D I, Kennel M B, Buhl M, and Illing L. Synchronization of chaotic oscillations in doped fiber ring lasers. Phys. Rev. E, 2001, 63: 016215.
[112] Fischer I et al. Zero-Lag Long-Range Synchronization via Dynamical Relaying. Phys. Rev. Lett., 2006, 97: 123902.
[113] Byrd J M, Hao Z, Martin M C, Robin D S, Sannibale F, Schoenlein R W, Zholents A A, and Zolotorev M S. Laser Seeding of the Storage-Ring Microbunching Instability for High-Power Coherent Terahertz Radiation. Phys. Rev. Lett., 2006, 97: 074802.
[114] Tanguy Y, Houlihan J, Huyet G, Viktorov E A, and Mandel P. Synchronization and Clustering in a Multimode Quantum Dot Laser. Phys. Rev. Lett., 2006, 96: 024102.
[115] Soto-Crespo J M and Akhmediev N. Soliton as Strange Attractor: Nonlinear Synchronization and Chaos. Phys. Rev. Lett., 2005, 95: 024101.
[116] Wünsche H J, Bauer S, Kreissl J, Ushakov O, Korneyev N, Henneberger F, Wille E, Erzgr?ber H, Peil M, Els??er W, and Fischer I. Synchronization of Delay-Coupled Oscillators: A Study of Semiconductor Lasers. Phys. Rev. Lett., 2005, 94: 163901.
[117] Tang S and Liu J M. Experimental Verification of Anticipated and Retarded Synchronization in Chaotic Semiconductor Lasers. Phys. Rev. Lett., 2003, 90: 194101.
[118] Scirè A, Mulet J, Mirasso C R, Danckaert J, and San Miguel M. Polarization Message Encoding through Vectorial Chaos Synchronization in Vertical-Cavity Surface-Emitting Lasers. Phys. Rev. Lett., 2003, 90: 113901.
[119] Yang S C et al. Data Assimilation as Synchronization of Truth and Model: Experiments with the Three-Variable Lorenz System. Journal of the Atmospheric Sciences, in press.
[120] Belykh I, de Lange E, and Hasler M. Synchronization of Bursting Neurons: What Matters in the Network Topology. Phys. Rev. Lett., 2005, 94: 188101.
[121] Jia L C, Sano M, Lai P Y, and Chan C K. Connectivities and Synchronous Firing in Cortical Neuronal Networks. Phys. Rev. Lett., 2004, 93: 088101.
[122] Neiman A B and Russell D F. Synchronization of Noise-Induced Bursts in Noncoupled Sensory Neurons. Phys. Rev. Lett., 2002, 88: 138103.
[123] Elson R C, Selverston A I, Huerta R, Rulkov N F, Rabinovich M I, and Abarbanel H D I. Synchronous Behavior of Two Coupled Biological Neurons. Phys. Rev. Lett., 1998, 81: 5692-5695.
[124] Hansel D and Sompolinsky H. Synchronization and computation in a chaotic neural network. Phys. Rev. Lett., 1992, 68: 718-721.
[125] Lehnertz K and Elger C E. Can Epileptic Seizures be Predicted? Evidence from Nonlinear Time Series Analysis of Brain Electrical Activity. Phys. Rev. Lett., 1998, 80: 5019-5022.
[126] Masuda N and Aihara K. Bridging Rate Coding and Temporal Spike Coding by Effect of Noise. Phys. Rev. Lett., 2002, 88: 248101.
[127] Tass P A, Fieseler T, Dammers J, Dolan K, Morosan P, Majtanik M, Boers F, Muren A, Zilles K, and Fink G R. Synchronization Tomography: A Method for Three-Dimensional Localization of Phase Synchronized Neuronal Populations in the Human Brain using Magnetoencephalography. Phys. Rev. Lett., 2003, 90: 088101.
[128] Rabinovich M I, Huerta R, and Varona P. Heteroclinic Synchronization: Ultrasubharmonic Locking. Phys. Rev. Lett., 2006, 96: 014101.
[129] Neiman A, Pei X, Russell D, Wojtenek W, Wilkens L, Moss F, Braun H A, Huber M T, and Voigt K. Synchronization of the Noisy Electrosensitive Cells in the Paddlefish. Phys. Rev. Lett., 1999, 82: 660-663.
[130] Zhou T, Chen L, and Aihara K. Molecular Communication through Stochastic Synchronization Induced by Extracellular Fluctuations. Phys. Rev. Lett., 2005, 95: 178103.
[131] Battogtokh D, Aihara K, and Tyson J J. Synchronization of Eukaryotic Cells by Periodic Forcing. Phys. Rev. Lett., 2006, 96: 148102.
[132] Duane G S and Tribbia J J. Synchronized Chaos in Geophysical Fluid Dynamics. Phys. Rev. Lett., 2001, 86: 4298-4301.
[133] Paoletti M S, Nugent C R, and Solomon T H. Synchronization of Oscillating Reactions in an Extended Fluid System. Phys. Rev. Lett., 2006, 96: 124101.
[134] Veser G, Mertens F, Mikhailov A S, and Imbihl R. Global coupling in the presence of defects: Synchronization in an oscillatory surface reaction. Phys. Rev. Lett., 1993, 71: 935-938.
[135] Kortlüke O, Kuzovkov V N, and von Niessen W. Global Synchronization via Homogeneous Nucleation in Oscillating Surface Reactions. Phys. Rev. Lett., 1999, 83: 3089-3092.
[136] 方锦清,非线性系统中的混沌控制方法、同步原理及其应用前景(二),物理学进展,1996, 16, 190-195
[137] Wu C W and Chua L O. A unified framework for synchronization and control of dynamical systems. Int. J. Bifurcation Chaos, 1994, 4(4): 979-998.
[138] Fujisaka H and Yamada T. Stability theory of synchronized motion in coupled oscillator systems. Prog. Theor. Phys., 1983, 69: 32-47.
[139] Nijmeijer H and Mareels I M Y. An observer looks at synchronization. IEEE Trans. Circuits Syst. I,1997, 44(10): 882-890.
[140] Kocarev L and Parlitz U. Generalized Synchronization, Predictability, and Equivalence of Unidirectionally Coupled Dynamical Systems. Phys. Rev. Lett., 1996, 76: 1816-1819.
[141] Rosenblum M G, Pikovsky A S and Kurths J. Phase Synchronization of Chaotic Oscillators. Phys. Rev. Lett., 1996, 76: 1804-1807.
[142] Kocarev L and Parlitz U. General Approach for Chaotic Synchronization with Applications to Communication. Phys. Rev. Lett., 1995, 74: 5028-5031.
[143] Mritan A and Banavar J R. Chaos, noise, and synchronization. Phys. Rev. Lett., 1994, 72: 1451-1454.
[144] Mritan A, Banavar J R. Maritan and Banavar Reply. Phys. Rev. Lett., 1994, 73: 2932.
[145] Zhou C S, Kurths J. Noise-induced phase synchronization and synchronization transitions in chaotic oscillators. Phys. Rev. Lett., 2002, 88: 230602.
[146] Zhou C S, Kurths J, Kiss I Z, Hudson J L. Noise enhanced phase synchronization of chaotic oscillators. Phys. Rev. Lett., 2002, 89: 014101.
[147] Parlitz U. Estimating model parameters from time series by autosynchronization. Phys. Rev. Lett., 1996, 76: 1232-1235.
[148] Parlitz U, Junge L and L. Kocarev. Synchronization-based parameter estimation from time series. Phys. Rev. E, 1996, 54: 6253-6259.
[149] Sakaguchi H. Parameter evaluation from time sequences using chaos synchronization. Phys. Rev. E, 2002, 65: 027201.
[150] Maybhate A and Amritkar R E. Use of synchronization and adaptive control in parameter estimation from a time series. Phys. Rev. E, 1999, 59: 284-293.
[151] Maybhate A and Amritkar R E. Dynamic algorithm for parameter estimation and its applications. Phys. Rev. E, 2000, 61: 6461.
[152] Konnur R. Synchronization-based approach for estimating all model parameters of chaotic systems. Phys. Rev. E, 2003, 67: 027204.
[153] Tao C, Zhang Y, Du G and Jiang J J. Estimating model parameters by chaos synchronization. Phys. Rev. E, 2004, 69: 036204.
[154] Marino I P and Miguez J. Adaptive approximation method for joint parameter estimation and identical synchronization of chaotic systems. Phys. Rev. E, 2005, 72: 057202.
[155] Huang D B. Synchronization-based estimation of all parameters of chaotic systems from time series. Phys. Rev. E, 2004, 69: 067201.
[156] Huang D B and Guo R. Identifying parameter by identical synchronization between different systems. Chaos, 2004, 14: 152-159.
[157] Lu J and Cao J. Adaptive complete synchronization of two identical or different chaotic (hyperchaotic) systems with fully unknown parameters. Chaos 2005, 15: 043901.
[158] Yu W and Cao J. Adaptive Q-S (lag, anticipated, and complete) time-varying synchronization and parameters identification of uncertain delayed neural networks. Chaos, 2006, 16: 023119.
[159] Yu D C and Wu A G. Comment on Estimating Model Parameters from Time Series by Autosynchronization. Phys. Rev. Lett., 2005, 94: 219401.
[160] Li L, Peng H, Wang X, and Yang Y. Comment on two papers of chaotic synchronization. Phys. Lett. A, 2004, 333: 269-270.
[161] 高铁杠,混沌系统同步及其在信息安全中的应用:[博士学位论文],天津:南开大学,2005
[162] 禹东川,孟庆浩,不确定时变混沌系统的一种自适应无抖振变结构控制,” 物理学报, 2005, 54: 1092-1097.
[163] 高为炳,变结构控制的理论及设计方法, 北京:科学出版社,1996.
[164] Huang J and Rugh W. On a nonlinear multivariable servomechanism problem. Automatica, 1990, 26: 963-972.
[165] Huang J and Rugh W. Stabilization on zero-error manifolds and the nonlinear servomechanism problem. IEEE Tran.saitions on Automatic Control, 1992, 37: 1009-1013.
[166] Isidori A and Byrnks C. Output regulation of nonlinear systems. IEEE Transactions on Automatic Control, 1990, 35: 131-140.
[167] Khalil H. Universal integral controller for minimumphase nonlinear systems. IEEE Transactions on Automatic Controt. 2000, 45: 490-494.
[168] Ho E and Sen P. Control dynamics of speed drive systems using sliding mode controllers with integral compensation. IEEE Trans. Industrial Application, 1991, 27(5): 883-892.
[169] Chern T L and Wu Y C. Design of integral variable structure controller and application to electrohydraulic velocity. IEE Proceedings-D, 1991, 138(5): 439-444.
[170] Chern T L and Wu Y C.Integral variable structure control approach for robot manipulators,” IEE Proceedings-D, 1992, 139(2): 161-166.
[171] Sira-Ramirez H. On the generalized PI sliding mode control of DC-to-DC power converters: A tutorial. International Journal of Control, 2003, 76(9):1018-1033.
[172] Bhat S P and Bernstein D S. Continuous, Finite-Time Stabilization of the Translational and Rotational Double Integrators. IEEE Transactions on Automatic Control, 1998, 43: 678-682.
[173] Chen G and Ueta T. Yet another chaotic attractor. Int. J. Bifurcation Chaos. 1999, 9: 1465-1466.
[174] Ueta T and Chen G. Bifurcation analysis of Chen's attractor. Int. J. Bifurcation Chaos, 2000, 10: 1917-1931.
[175] Lu J H and Chen G. A new chaotic attractor coined. Int. J. Bifurcation Chaos, 2002, 12: 659-661.
[176] Lu J H, Chen G and Zhang S. Dynamical analysis of a new chaotic attractor. Int. J. Bifurcation Chaos. 2002, 12: 1001-1015.
[177] Lu J H, Chen G, Cheng D Z and Celikovsky S. Bridge the gap between Loren system and the Chen system. Int. J. Bifurcation Chaos, 2002, 12 (12): 2917-1926.
[178] Lu J, Wu X and Lu J H. Synchronization of a unifed chaotic system and the application in secure communication. Phys. Lett. A, 2002, 305: 365-370.
[179] Lu J, Wu X, Han X and Lu J H. Adaptive feedback synchronization of a unifed chaotic system. Phys. Lett. A, 2004, 329: 327-333.
[180] Liu J, Chen S and Xie J. Parameter identifcation and control of uncertain unifed chaotic system via adaptive extending equilibrium manifold approach. Chaos, Solitons and Fractals, 2004, 19: 533-540.
[181] Ucr A, Lonngren K E and Bai E W. Synchronization of the unifed chaotic systems via active control. Chaos, Solitons and Fractals, 2006, 27: 1292-1297.
[182] Tao C H, Xiong H X and Hu F. Two novel synchronization criterions for a unifed chaotic system. Chaos, Solitons and Fractals. 2006, 27: 115-120.
[183] Rossler O E. An equation for continuous chaos. Phys Lett A , 1976, 57(5): 397 -398.
[184] Rossler, O. E. An equation for hyperchaos. Phys. Lett. A, 1979, 71(2-3): 155-157.
[185] http://www.dddas.org
[186] Sastry S. Nonlinear Systems: Analysis, Stability, and Control. Springer Verlag, 1999.
[187] Slotine J J and Li W. Applied nonlinear control. Prentice-Hall, Englewood Cliffs, 1991.
[188] Peixoto M. Structural stability on two dimensional manifolds. Topology, 1962, 1: 101-120.
[189] Levant A. Robust exact differentiation via sliding mode technique. Automatica, 1998, 34(3): 379-384.
[190] Levant A. Higher-order sliding modes, differentiation and output-feedback control. Int. J. Control, 2003, 76(9/10): 924-941.
[191] Bowong S. Stability analysis for the synchronization of chaotic systems with different order: application to secure communications. Physics Letters A, 2004, 326(1-2): 102-113.
[192] Bowong S and McClintock P V E. Adaptive synchronization between chaotic dynamical systems of different order. Physics Letters A, 2006, 358(2): 134-141.
[193] Ho M C, Hung Y C, Liu Z Y and Jiang I M. Reduced-order synchronization of chaotic systems with parameters unknown. Physics Letters A, 2006, 348(3-6): 251-259.