基于非线性控制的超混沌Chen系统混沌同步

研究了基于非线性控制的超混沌Chen系统的混沌同步问题.基于Lyapunov稳定性理论，设计了非线性控制器，改进了Jiang和Huang等设计的同步误差系统的Lyapunov函数形式，理论证明了超混沌Chen系统的自同步和超混沌Chen系统与超混沌R?ssler系统的异结构同步.数值模拟进一步验证了所提出方案的有效性. 关键词： 超混沌Chen系统 自同步 异结构同步 非线性控制器     

Circuitry implementation of a novel four-dimensional nonautonomous hyperchaotic Liu system and its experimental studies on synchronization control

Based on the three-dimensional Liu chaotic system, this paper appends a feedback variable to construct a novel hyperchaotic Liu system. Then, a control signal is further added to construct a novel nonautonomous hyperchaotic Liu system. Through adjusting the frequency of the control signal, the chaotic property of the system can be controlled to show some different dynamic behaviors such as periodic, quasi-periodic, chaotic and hyperchaotic dynamic behaviours. By numerical simulations, the Lyapunov exponent spectrums, bifurcation diagrams and phase diagrams of the two new systems are studied, respectively. Furthermore, the synchronizing circuits of the nonautonomous hyperchaotic Liu system are designed via the synchronization control method of single variable coupling feedback. Finally, the hardware circuits are implemented, and the corresponding waves of chaos are observed by an oscillograph.     

Synchronization between two different noise-perturbed chaotic systems with unknown parameters

In this paper, a general method of synchronizing noise-perturbed chaotic systems with unknown parameters is proposed. Based on the LaSalle-type invariance principle for stochastic differential equations and by employing a combination of feedback control and adaptive control, some sufficient conditions of chaos synchronization between these noise-perturbed systems with unknown parameters are established. The model used in the research is the chaotic system, but the method is also applicable to the hyperchaotic systems. Unified system and noise-perturbed RSssler system, hyperchaotic Chen system and nolse-perturbed hyperchaotic RSssler system are taken for illustrative examples to demonstrate this technique.[第一段]     

Control of fractional chaotic and hyperchaotic systems based on a fractional order controller

We present a new fractional-order controller based on the Lyapunov stability theory and propose a control method which can control fractional chaotic and hyperchaotic systems whether systems are commensurate or incommensurate.The proposed control method is universal, simple, and theoretically rigorous. Numerical simulations are given for several fractional chaotic and hyperchaotic systems to verify the effectiveness and the universality of the proposed control method.     

一类受扰混沌系统的自适应滑模控制

针对受扰混沌系统,在参数未知的情形下利用自适应滑模控制法实现了驱动系统和响应系统的鲁棒同步. 该方法几乎适用于所有的混沌系统,且无需知道系统外部干扰的上界,它由自适应控制律实现. 以双涡卷系统、Lorenz系统、Rssler超混沌系统为例,说明该方法的有效性和正确性. 关键词： 混沌同步 滑模面 到达条件 自适应滑模控制     

A novel methodology for constructing a multi-wing chaotic and hyperchaotic system with a unified step function switching control

This paper aims at developing a novel method of constructing a class of multi-wing chaotic and hyperchaotic system by introducing a unified step function. In order to overcome the essential difficulties in iteratively adjusting multiple parameters of conventional multi-parameter control, this paper introduces a unified step function controlled by a single parameter for constructing various multi-wing chaotic and hyperchaotic systems. In particular, to the best of the authors' knowledge, this is also the first time to find a non-equilibrium multi-wing hyperchaotic system by means of the unified step function control. According to the heteroclinic loop Shilnikov theorem, some properties for multi-wing attractors and its chaos mechanism are further discussed and analyzed. A circuit for multi-wing systems is designed and implemented for demonstration, which verifies the effectiveness of the proposed approach.     

分数阶混沌系统的异结构同步

基于分数阶线性系统稳定性理论,结合反馈控制和主动控制方法,提出了一种分数阶混沌系统异结构同步方法,给出了同步控制器解析式. 以分数阶Chen混沌系统和分数阶Liu混沌系统、分数阶新超混沌系统和分数阶超混沌Rssler系统的异结构同步为例, 进行了数值模拟,证实了该方法的有效性和可行性. 关键词： 分数阶混沌 异结构混沌同步 新超混沌系统 超混沌Rssler系统     

A new criterion for chaos and hyperchaos synchronization using linear feedback control

Based on the characteristic of the chaotic or hyperchaotic system and linear feedback control method, synchronization of the two identical chaotic or hyperchaotic systems with different initial conditions is studied. The range of the control parameter for synchronization is derived. Simulation results are provided to show the effectiveness of the proposed synchronization method.     

Reduced-order anti-synchronization of the projections of the fractional order hyperchaotic and chaotic systems

The article aims to study the reduced-order anti-synchronization between projections of fractional order hyperchaotic and chaotic systems using active control method. The technique is successfully applied for the pair of systems viz., fractional order hyperchaotic Lorenz system and fractional order chaotic Genesio-Tesi system. The sufficient conditions for achieving anti-synchronization between these two systems are derived via the Laplace transformation theory. The fractional derivative is described in Caputo sense. Applying the fractional calculus theory and computer simulation technique, it is found that hyperchaos and chaos exists in the fractional order Lorenz system and fractional order Genesio-Tesi system with order less than 4 and 3 respectively. The lowest fractional orders of hyperchaotic Lorenz system and chaotic Genesio-Tesi system are 3.92 and 2.79 respectively. Numerical simulation results which are carried out using Adams-Bashforth-Moulton method, shows that the method is reliable and effective for reduced order anti-synchronization.     

一类五阶超混沌电路系统的加速追踪控制与投影同步

设计了一种统一形式的非线性状态反馈控制器,实现了一类五阶超混沌电路系统的状态变量与任意给定参考信号的追踪广义投影同步.通过取不同的比例因子和加速因子,可以快速获得与超混沌系统和多个不同维混沌系统之间的异结构广义投影同步、周期信号的广义投影同步,以及将五阶超混沌系统快速控制到周期态和期望的平衡点.数值仿真进一步表明了该方法的有效性. 关键词： 超混沌电路 追踪控制 广义投影同步 加速因子     

Adaptive synchronisation of fractional-order chaotic systems

A new stability theory of nonlinear dynamic systems is proposed, and a novel adaptive synchronisation method is presented for fractional-order chaotic and hyperchaotic systems based on the theory described in this paper. In comparison with previous methods, not only is the present control scheme simple but also it employs only one control strength, converges very fast, and it is also suitable for a large class of fractional-order chaotic and hyperchaotic systems. Moreover, this scheme is analytical and simple to implement in practice. Numerical and circuit simulations are used to validate and demonstrate the effectiveness of the method.     

Comparison of feedback control methods for a hyperchaotic Lorenz system

More and more attention has been payed to the hyperchaotic system for the huge potential applications of hyperchaotic system such as secure communication and more complex structure than chaotic system. So at present the controlling of the hyperchaotic system simply and effectively is a frontier topic of nonlinear science. In this Letter, for the latest hyperchaotic Lorenz system, four feedback control methods were studied with analytic solution and necessary numerical simulations. It is found that the enhancing feedback control approach is the best choice of the given four feedback control methods for its relatively simple external inputs and relatively small necessary feedback coefficient after comparison. The conclusion is a helpful for the choice of control methods of any other chaotic and hyperchaotic systems.     

基于快速全线性预测控制的混沌系统控制与同步

针对连续时间混沌(超混沌)系统的控制问题, 提出了一种基于扩张状态观测器的快速全线性广义预测控制算法. 利用线性扩张状态观测器估计和补偿混沌(超混沌)系统的非线性动力学和存在的不确定性, 将原始对象近似转化为积分器形式, 随后针对单积分器设计广义预测控制, 解决了预测控制计算量大的问题. 阶跃系数矩阵可以直接得到解析解, 而对于未来输出的预测则可以根据最近两个时刻的输出采样值直接计算得到, 避免了使用自校正算法和在线求解丢番图方程. 该线性算法可以直接应用于非线性对象的控制系统设计. 将该算法应用于典型Lorenz混沌系统的控制中, 数学仿真结果验证了有效性.     

Bidirectional Partial Generalized Synchronization in Chaotic and Hyperchaotic Systems via a New Scheme

In this paper, a bidirectional partial generalized (lag, complete, and anticipated) synchronization of a class of continuous-time systems is defined. Then based on the active control idea, a new systematic and concrete scheme is developed to achieve bidirectional partial generalized (lag, complete, and anticipated) synchronization between two chaotic systems or between chaotic and hyperchaotic systems. With the help of symbolic-numerical computation, we choose the modified Chua system, Lorenz system, and the hyperchaotic Tamasevicius-Namajunas-Cenys system to illustrate the proposed scheme. Numerical simulations are used to verify the effectiveness of the proposed scheme. It is interesting that partial chaos synchronization not only can take place between two chaotic systems, but also can take place between chaotic and hyperchaotic systems. The proposed scheme can also be extended to research bidirectional partial generalized (lag, complete, and anticipated) synchronization between other dynamical systems.     

一个新的超混沌系统及其自适应追踪控制

通过在一个三维混沌系统中加入状态反馈控制器, 构造出一个新的四维超混沌系统. 分析表明, 随着不同参数变化该系统呈现周期、复杂周期、准周期、混沌及超混沌运动. 同时设计出模拟电子电路对该超混沌系统进行了实验验证. 最后, 设计了一个自适应追踪控制器,实现了其对各种不同参考信号的单变量追踪控制.     

超混沌R?ssler系统构成的星形网络的混沌同步

通过对超混沌系统线性项与非线性项的适当分离配置，构造一个特殊的非线性耦合函数作为单元之间的耦合函数，提出非线性非对称耦合混沌同步方法，研究超混沌Rssler系统单元按照星形连接形式组成网络的同步问题.发现耦合强度在某一区域里存在着稳定的混沌同步现象.分析并讨论了不同参数在耦合过程中对混沌同步过程及其稳定性的影响.数值模拟结果证实该方法的有效性. 关键词： 超混沌同步 非线性耦合 R ssler系统 星形网络     

Complete synchronization between two bi-directionally coupled chaotic systems via an adaptive feedback controller

In this paper, we apply a simple adaptive feedback control scheme to synchronize two bi-directionally coupled chaotic systems. Based on the invariance principle of differential equations, sufficient conditions for the global asymptotic synchronization between two bi-directionally coupled chaotic systems via an adaptive feedback controller are given. Unlike other control schemes for bi-directionally coupled systems, this scheme is very simple to implement in practice and need not consider coupling terms. As examples, the autonomous hyperchaotic Chen systems and the new non-autonomous 4D systems are illustrated. Numerical simulations show that the proposed method is effective and robust against the effect of weak noise.     

Synchronization between integer-order chaotic systems and a class of fractional-order chaotic systems via sliding mode control

In this paper, we focus on the synchronization between integer-order chaotic systems and a class of fractional-order chaotic system using the stability theory of fractional-order systems. A new sliding mode method is proposed to accomplish this end for different initial conditions and number of dimensions. More importantly, the vector controller is one-dimensional less than the system. Furthermore, three examples are presented to illustrate the effectiveness of the proposed scheme, which are the synchronization between a fractional-order Chen chaotic system and an integer-order T chaotic system, the synchronization between a fractional-order hyperchaotic system based on Chen's system and an integer-order hyperchaotic system, and the synchronization between a fractional-order hyperchaotic system based on Chen's system and an integer-order Lorenz chaotic system. Finally, numerical results are presented and are in agreement with theoretical analysis.     

Nonlinear feedback control of a novel hyperchaotic system and its circuit implementation

This paper reports a new hyperchaotic system by adding an additional state variable into a three-dimensional chaotic dynamical system. Some of its basic dynamical properties, such as the hyperchaotic attractor, Lyapunov exponents, bifurcation diagram and the hyperchaotic attractor evolving into periodic, quasi-periodic dynamical behaviours by varying parameter k are studied. An effective nonlinear feedback control method is used to suppress hyperchaos to unstable equilibrium. Furthermore, a circuit is designed to realize this new hyperchaotic system by electronic workbench (EWB). Numerical simulations are presented to show these results.     

A new hyperchaotic system and its linear feedback control

This paper reports a new hyperchaotic system by adding an additional state variable into a three-dimensional chaotic dynamical system, studies some of its basic dynamical properties, such as the hyperchaotic attractor, Lyapunov exponents, bifurcation diagram and the hyperchaotic attractor evolving into periodic, quasi-periodic dynamical behaviours by varying parameter k. Furthermore, effective linear feedback control method is used to suppress hyperchaos to unstable equilibrium, periodic orbits and quasi-periodic orbits. Numerical simulations are presented to show these results.