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Global adaptive synchronization of chaotic systems with uncertain parameters
Li Zhi,Han Chong-Zhao,
李智
,韩崇昭

中国物理 B , 2002,
Abstract: We propose a novel adaptive synchronization method for a class of nonlinear chaotic systems with uncertain parameters. Using the chaos control method, we derive a synchronizer, which can make the states of the driven system globally track the states of the drive system asymptotically. The advantage of our method is that our problem setting is more general than those that already exist, and the synchronizer is simply constructed by an analytic formula, without knowledge in advance of the unknown bounds of the uncertain parameters. A computer simulation example is given to validate the proposed approach.
Function Projective Synchronization of a Class of Chaotic Systems with Uncertain Parameters
Junbiao Guan
Mathematical Problems in Engineering , 2012, DOI: 10.1155/2012/431752
Abstract: This paper investigates the function projective synchronization of a class of chaotic systems with uncertain parameters. Based on Lyapunov stability theory, the nonlinear adaptive control law and the parameter update law are derived to make the state of two chaotic systems function projective synchronized. Numerical simulations are presented to demonstrate the effectiveness of the proposed adaptive scheme.
Adaptive Lag Synchronization of Lorenz Chaotic System with Uncertain Parameters  [PDF]
Yanfei Chen, Zhen Jia, Guangming Deng
Applied Mathematics (AM) , 2012, DOI: 10.4236/am.2012.36083
Abstract: The paper discusses lag synchronization of Lorenz chaotic system with three uncertain parameters. Based on adaptive technique, the lag synchronization of Lorenz chaotic system is achieved by designing a novel nonlinear controller. Furthermore, the parameters identification is realized simultaneously. A sufficient condition is given and proved theoreticcally by Lyapunov stability theory and LaSalle’s invariance principle. Finally, the numerical simulations are provided to show the effectiveness and feasibility of the proposed method.
Generalized projective synchronization of a class of chaotic (hyperchaotic) systems with uncertain parameters
Generalized projective synchronization of a class of chaotic (hyperchaotic) systems with uncertain parameters

Jia Zhen,Lu Jun-An,Deng Guang-Ming,Zhang Qun-Jiao,
贾 贞
,陆君安,邓光明,张群娇

中国物理 B , 2007,
Abstract: In this paper is investigated the generalized projective synchronization of a class of chaotic (or hyperchaotic) systems, in which certain parameters can be separated from uncertain parameters. Based on the adaptive technique, the globally generalized projective synchronization of two identical chaotic (hyperchaotic) systems is achieved by designing a novel nonlinear controller. Furthermore, the parameter identification is realized simultaneously. A sufficient condition for the globally projective synchronization is obtained. Finally, by taking the hyperchaotic Lü system as example, some numerical simulations are provided to demonstrate the effectiveness and feasibility of the proposed technique.
Anti-synchronization of uncertain chaotic system and parameters identification
不确定混沌系统的反同步与参数辨识

Li Nong,Li Jian-Fen,Liu Yu-Ping,
李农
,李建芬,刘宇平

物理学报 , 2010,
Abstract: We present a systematic design procedure to anti-synchronize a class of chaotic systems. An adaptive control method for anti-synchronization of uncertain chaotic system is proposed based on the scheme,by which the uncertain parameters of response system are identified. Numerical simulations show the effectiveness of the developed approache.
Function Vector Synchronization of Uncertain Chaotic Systems with Parameters Variable  [PDF]
Ning Li,Heng Liu,Wei Xiang,Hui Lv
Information Technology Journal , 2012,
Abstract: In this study, a state variable Function Vector Synchronization (FVS) of two non-identical chaotic systems with both varying parameters and delay is investigated. Based on feedback principle and Lyapunov stability theory, the adaptive fuzzy controller is constructed. The synchronization for the state variable function vector of systems can be reached by using the proposed controller. The control is robust for varying parameters and disturbance of systems. Compared with the traditional synchronization, aided by appropriate state variable function vectors of master and slave systems instead of state variables, signal transmission security can be improved. The simulation results shows the effectiveness of the method.
ADAPTIVE SYNCHRONIZATION OF UNCERTAIN LI AND T CHAOTIC SYSTEMS
Dr. V. SUNDARAPANDIAN,,R. KARTHIKEYAN
International Journal of Engineering Science and Technology , 2011,
Abstract: In this paper, we use adaptive control method to derive new results for the global chaos synchronization of identical uncertain Li systems (2009), identical uncertain T systems (2008) and non-identical Li and uncertain T systems. In adaptive synchronization of identical chaotic systems, the parameters of the master and slave systems are unknown and we devise feedback control laws using estimates of the system parameters. In adaptive synchronization of non-identical chaotic systems, the parameters of the master system are known, but the parameters of the slave systems are unknown and we devise feedback control laws using the estimates of the parameters of the slave system. Our adaptive synchronization results derived in this paper for uncertain Li and T systems are established using Lyapunov stability theory. Since the Lyapunov exponents are not required for these calculations, the adaptive control method is very effective and convenient to synchronize identical and non-identical Li and T chaotic systems. Numerical simulations are given to demonstrate the effectiveness of the proposed adaptive synchronization schemes for the global chaos synchronization of the uncertain chaotic systems addressed in this paper.
Synchronization of chaotic Liu system with uncertain parameters
具有不确定参数的Liu混沌系统的同步

Wang Hua,Han Zheng-Zhi,Zhang Wei,Xie Qi-Yue,
王划
,韩正之,章伟,谢七月

物理学报 , 2008,
Abstract: Based on the control Lyapunov function (CLF), a method of synchronizing chaotic Liu system with uncertain parameters is proposed. The feedback control law presented does not depend on the parameters but on the boundary of the parameters. It shows that the feedback is simple and robust. Simulation studies on Liu chaotic system also verify the effectiveness of the proposed scheme when the parameters vary largely.
Parameter identification and synchronization of an uncertain Chen chaotic system via adaptive control
Chen Shi-Hu,Zhao Li-Min,Liu Jie,
陈士华
,赵立民,刘杰

中国物理 B , 2002,
Abstract: A systematic design process of adaptive synchronization and parameter identification of an uncertain Chen chaotic system is provided. With this new and effective method, parameter identification and synchronization of the Chen system, with all the system parameters unknown, can be achieved simultaneously. Theoretical proof and numerical simulation demonstrate the effectiveness and feasibility of the proposed method.
Projective synchronization of a five-term hyperbolic-type chaotic system with fully uncertain parameters
具有完全不确定参数的五项双曲型混沌系统的投影同步

Yu Fei,Wang Chun-Hu,Hu Yan,Yin Jin-Wen,
余飞
,王春华,胡燕,尹晋文

物理学报 , 2012,
Abstract: A new simple hyperbolic-type three-dimensional autonomous chaotic system is proposed. It is of interest that the chaotic system has only five terms which mainly rely on a nonlinear quadratic hyperbolic sine term and a quadratic cross-product term. Compared with other three-dimensional chaotic systems, the new system has not only less terms, but also a wider range of chaos when the parameter varies. Basic dynamical properties of the system are studied by numerical and theoretical analysis. Moreover the projective synchronization of the five-term hyperbolic-type chaotic system with fully uncertain parameters is also investigated in this paper. Based on Lyapunov stability theory and Barbalat's lemma, a new adaptive controller with parameter update law is designed to projectivly synchronize two chaotic systems asymptotically and globally, including two identical exponential-type chaotic systems and two non-identical chaotic systems. Numerical simulations show the effectiveness and the feasibility of the developed methods.
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