利用标量控制器实现一类混沌系统同步

研究了一类混沌系统的混沌同步，对此类混沌系统，通过设计一个合适标量控制器，可以实现系统的混沌同步.给出了该标量控制器设计的一般方法，并从理论上得到了混沌同步的充分和必要条件，且此充分和必要条件与混沌系统的性质无关. 关键词： 混沌系统 标量控制器 混沌同步     

Generalized Synchronization Between Different Fractional-Order Chaotic Systems

In this paper, using scalar feedback controller and stability theory of fractional-order systems, a generalized synchronization method for different fractional-order chaotic systems is established. Simulation results show the effectiveness of the theoretical results.     

Generalized projective synchronization of a class of chaotic (hyperchaotic) systems with uncertain parameters

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.     

Generalized projective synchronization of chaotic systems with unknown dead-zone input: observer-based approach

In this paper we investigate the synchronization problem of drive-response chaotic systems with a scalar coupling signal. By using the scalar transmitted signal from the drive chaotic system, an observer-based response chaotic system with dead-zone nonlinear input is designed. An output feedback control technique is derived to achieve generalized projective synchronization between the drive system and the response system. Furthermore, an adaptive control law is established that guarantees generalized projective synchronization without the knowledge of system nonlinearity, and/or system parameters as well as that of parameters in dead-zone input nonlinearity. Two illustrative examples are given to demonstrate the effectiveness of the proposed synchronization scheme.     

一种参数摄动的混沌异结构同步方法

研究了参数摄动情形下的混沌异结构同步问题,基于Lyapunov稳定性定理并结合范数理论给出了系统参数摄动下实现混沌异结构同步的一个充分条件,为同步控制器的设计提供了一般方法.只要两混沌系统维数相等,状态变量可测,就可利用所提方法实现系统参数摄动下的异结构同步,并能够保证在同步实现后同步控制量伴随误差变量一同收敛至零.该方法鲁棒性强,适用范围广,通过对混沌系统、超混沌系统的同步仿真,证实了该方法的有效性. 关键词： 混沌 超混沌 同步 Lyapunov函数     

Generalized reduced-order synchronization of chaotic system based on fast slide mode

A new kind of generalized reduced-order synchronization of different chaotic systems is proposed in this paper. It is shown that dynamical evolution of third-order oscillator can be synchronized with the canonical projection of a fourth-order chaotic system generated through nonsingular states transformation from a cell neural net chaotic system. In this sense, it is said that generalized synchronization is achieved in reduced-order. The synchronization discussed here expands the scope of reduced-order synchronization studied in relevant literatures. In this way, we can achieve generalized reduced-order synchronization between many famous chaotic systems such as the second-order D\"{u}ffing system and the third-order Lorenz system by designing a fast slide mode controller. Simulation results are provided to verify the operation of the designed synchronization.     

参数不确定的分数阶混沌系统广义错位延时投影同步

为进一步增强通信系统中保密通信的安全性,结合广义错位投影同步和延时投影同步,提出了广义错位延时投影同步.以分数阶Chen系统和Lü系统为例,针对两系统参数都不确定,基于分数阶稳定性理论与自适应控制方法,设计了非线性控制器和参数自适应律,实现了广义错位延时同步,并辨识出驱动系统和响应系统中所有不确定参数.理论分析和数值仿真验证了该方法的可行性与有效性.     

多涡卷混沌系统的广义同步控制

基于反步自适应方法,提出了一种在初值不同以及驱动系统参数未知的情况下,保持驱动和响应两多涡卷混沌系统同步的控制律设计方法.该方法所设计的控制律能够同时适用于两混沌系统的完全同步、反同步和一类非线性广义同步,具有较高的实用价值.仿真结果表明了所设计控制律的有效性. 关键词： 多涡卷混沌 广义同步 反步 自适应     

统一混沌系统的耦合同步

对线性耦合的两个统一混沌系统同步进行研究.基于线性时变连续系统的稳定性理论，得到初始值不同的两个统一混沌系统全局渐进同步的一种新的充分条件.另外，与已经提出的判定统一混沌系统同步的方法进行比较，发现这里得到的充分条件的约束关系少、缺少保守性，而且满足的耦合系数范围更广.将该方法应用于统一混沌系统，数值仿真表明了该法的有效性与可行性. 关键词： 统一混沌系统 耦合同步 线性时变连续系统     

Synchronization,circuit and secure communication implementation of a memristor-based hyperchaotic system using single input controller

In this paper, we investigate a circuit implementation of memristor-based chaotic synchronization with a single input controller. Firstly, based on the cubic function model of memristor, a circuit with the grounded flux-control memristor-based hyperchaotic system is designed and implemented. Secondly, a single input controller is proposed to synchronize the two memristor-based hyperchaotic systems, and a sufficient condition of the synchronized system is obtained by the Routh-Hurwitz criterion and minimum phase theory. Then, a circuit of the proposed controller for memristor-based chaotic synchronization system is designed and implemented. Finally, secure communication based on memristor-based chaotic synchronization system is given to show the feasibility of the signal encryption scheme.     

Projective Synchronization Between Two Nonidentical Variable Time Delayed Systems

In this paper,we propose a method for the projective synchronization between two different chaotic systems with variable time delays.Using active control approach,the suitable controller is constructed to make the states of two different diverse time delayed systems asymptotically synchronize up to the desired scaling factor.Based on the Lyapunov stability theory,the sufficient condition for the projective synchronization is calculated theoretically.Numerical simulations of the projective synchronization between Mackey-Glass system and Ikeda system with variable time delays are shown to validate the effectiveness of the proposed algorithm.     

Generalized projective synchronization between two chaotic gyros with nonlinear damping

In this paper, the chaotic generalized projective synchronization of a controlled, noised gyro with an expected gyro is investigated by a simple control law. Based on the theory of discontinuous dynamical systems, the necessary and sufficient conditions for such a synchronization are achieved. From such conditions, non-synchronization, partial and full synchronizations between the two coupled gyros are discussed. The switching scenarios between desynchronized and synchronized states of the two dynamical systems are shown. Numerical simulations are illustrated to verify the effectiveness of this method.     

基于状态观测器的分数阶时滞混沌系统同步研究

研究分数阶时滞混沌系统同步问题,基于状态观测器方法和分数阶系统稳定性理论,设计分数阶时滞混沌系统同步控制器,使得分数阶时滞混沌系统达到同步,同时给出了数学证明过程.该同步控制器采用驱动系统和响应系统的输出变量进行设计,无需驱动系统和响应系统的状态变量,简化了控制器的设计,提高了控制器的实用性.利用Lyapunov稳定性理论和分数阶线性矩阵不等式,研究并给出了同步控制器参数的选择条件.以分数阶时滞Chen混沌系统为例,设计基于状态观测器的同步控制器,实现了分数阶时滞Chen混沌系统同步,并将其应用于保密通信系统中.仿真结果证明了该同步方法的有效性.     

基于模糊模型的不同结构的混沌系统同步

针对不同结构的混沌系统广义同步问题，提出了基于T-S 模糊模型的H_∞控制方法，利用Lyapunov方法和线性矩阵不等式技术,给出了误差闭环系统稳定的充分条件.仿真结果表明了方法的有效性. 关键词： H_∞控制')" href="#">H_∞控制 广义同步 混沌系统 模糊控制     

Complete and generalized synchronization in a class of noise perturbed chaotic systems

In the paper, in light of the LaSalle-type invariance principle for stochastic differential equations, chaos synchronization is investigated for a class of chaotic systems dissatisfying a globally Lipschitz condition with noise perturbation. Sufficient criteria for both complete synchronization and generalized synchronization are rigorously established and thus successfully applied to realize chaos synchronization in the coupled unified chaotic systems. Furthermore, concrete examples as well as their numerical simulations are provided to illustrate the possible application of the established criteria.     

通用标量混沌信号同步系统及其控制器的backstepping设计

以寻求通用标量混沌信号同步系统为目标,虚拟控制项加权为变量的严格反馈形式变参数系统为对象,采用带有调谐函数的自适应backstepping设计方法,设计了反馈控制器和相应的参数自适应律.采用所给控制器和参数自适应律,可以使通用系统的输出渐近同步于任意已知结构混沌系统的输出.理论与计算机仿真结果均证实了通用标量混沌信号同步系统及其控制器的有效性. 关键词： 混沌 严格反馈 backstepping设计 自适应控制     

参数未知的不同阶数混沌系统广义同步及参数估计

采用扩阶方法(使响应系统和驱动系统的维数相同)，把不同阶数混沌系统的广义同步问题转化为相同阶数混沌系统之间的广义同步，基于Lyapunov稳定性定理和自适应控制方法(用于相同阶数混沌系统的同步)，给出了自适应控制器和参数自适应律，进而实现了不同阶数混沌系统的广义同步.将该方法应用于参数未知的超Lü，Lorenz，广义Lorenz和Liu等系统之间的广义混沌同步，理论证明了该方法可以使这些系统达到渐近广义同步，并且可以辨识驱动系统和响应系统的所有参数，数值模拟进一步证明了该方法的有效性.     

基于自适应滑模控制的不同维分数阶混沌系统的同步

针对异结构不同维分数阶混沌系统的广义同步问题进行研究, 设计了一种将滑模变结构理论和自适应控制理论相结合的方法.通过设计一种对外界干扰具有强鲁棒性的分数阶滑模面, 以及构造合适的自适应滑模控制器, 该控制器将系统的运动控制到滑模面上, 使系统轨道沿滑动模运动到所需的控制状态, 最终实现了两个不同维异结构混沌系统之间的广义同步.以四维超混沌Chen系统和三维Chen混沌系统为例, 对这两个系统分别进行升维和降维的同步仿真. 仿真模拟结果表明, 运用本文设计的控制器, 经过短暂的时间, 两系统的广义误差变量始终平稳地趋于零, 即证明了这种控制器的有效性. 关键词： 分数阶混沌系统 异结构 自适应滑模控制 混沌同步     

Adaptive impulsive synchronization for a class of fractional-order chaotic and hyperchaotic systems

In this paper, the adaptive impulsive synchronization for a class of fractional-order chaotic and hyperchaotic systems with unknown Lipschitz constant is investigated. Firstly, based on the adaptive control theory and the impulsive differential equations theory, the impulsive controller, the adaptive controller and the parametric update law are designed, respectively. Secondly, by constructing the suitable response system, the original fractional-order error system can be converted into the integral-order one. Finally, the new sufficient criterion is derived to guarantee the asymptotical stability of synchronization error system by the Lyapunov stability theory and the generalized Barbalat's lemma. In addition, numerical simulations demonstrate the effectiveness and feasibility of the proposed adaptive impulsive control method.     

Fundamentals of synchronization in chaotic systems,concepts, and applications

The field of chaotic synchronization has grown considerably since its advent in 1990. Several subdisciplines and "cottage industries" have emerged that have taken on bona fide lives of their own. Our purpose in this paper is to collect results from these various areas in a review article format with a tutorial emphasis. Fundamentals of chaotic synchronization are reviewed first with emphases on the geometry of synchronization and stability criteria. Several widely used coupling configurations are examined and, when available, experimental demonstrations of their success (generally with chaotic circuit systems) are described. Particular focus is given to the recent notion of synchronous substitution-a method to synchronize chaotic systems using a larger class of scalar chaotic coupling signals than previously thought possible. Connections between this technique and well-known control theory results are also outlined. Extensions of the technique are presented that allow so-called hyperchaotic systems (systems with more than one positive Lyapunov exponent) to be synchronized. Several proposals for "secure" communication schemes have been advanced; major ones are reviewed and their strengths and weaknesses are touched upon. Arrays of coupled chaotic systems have received a great deal of attention lately and have spawned a host of interesting and, in some cases, counterintuitive phenomena including bursting above synchronization thresholds, destabilizing transitions as coupling increases (short-wavelength bifurcations), and riddled basins. In addition, a general mathematical framework for analyzing the stability of arrays with arbitrary coupling configurations is outlined. Finally, the topic of generalized synchronization is discussed, along with data analysis techniques that can be used to decide whether two systems satisfy the mathematical requirements of generalized synchronization. (c) 1997 American Institute of Physics.