连续混沌系统的混沌同步控制

给出了一种实现混沌系统混沌同步的控制方法．通过引入一待定的控制项,将两系统的混沌同步问题转化为讨论与其对应的线性系统的0解渐近稳定性问题,然后根据线性系统控制理论确定此控制项,以实现两混沌系统的同步目的．该方法简单易行,可有效的实现两个混沌系统的混沌同步,且其同步是全局渐近稳定的．     

基于直接构造法的不同参数统一混沌系统的同步

研究不同参数统一混沌系统的同步问题.首先采用直接构造法为响应系统设计适当的控制器,将误差系统 化成三对角结构;然后根据具有三对角结构的非线性系统状态全局渐近稳定的性质,得到误差系统状态在原点渐近稳定,进而实现驱动系统与响应系统的同步;最后在参数相同和参数不同两种情况下.分别对统一混沌系统的同步进行数值仿真,仿真结果表明所提出的设计方法是有效的.     

基于直接构造法的不同参数统一混沌系统的同步

研究了统一混沌系统的同步问题,所讨论的驱动系统和响应系统是两个参数不同的统一混沌系统。采用直接构造的方法,为响应系统设计适当的控制器,在该控制器的作用下,误差系统能够化成三对角结构的形式,再根据具有三对角结构的非线性系统状态变量全局渐近稳定的性质,使得误差系统状态在原点渐近稳定,最终实现驱动系统与响应系统的同步。并对相同参数和不同参数的统一混沌系统的同步进行仿真,数值仿真的结果说明了所给设计方法的有效性。     

基于自适应无源化的蔡氏电路混沌同步

根据蔡氏电路混沌系统的特点,得出了蔡氏电路混沌驱动系统与响应系统的误差系统.根据混沌系统的同步条件,可将混沌的同步问题转化成为误差系统的稳定性问题,即使混沌同步误差系统渐近稳定以实现混沌同步控制.针对蔡氏电路混沌系统的误差系统,采用自适应无源化方法,设计了使同步误差系统渐近稳定的具有自适应功能的反馈镇定器.该控制方法实现了2个蔡氏电路混沌系统同步,仿真研究验证了该方法的有效性.     

广义Lorenz系统的模糊建模和同步

广义Lorenz系统包括经典Lorenz系统和无穷多个结构相似但不拓扑等价的混沌系统.针对广义Lorenz规范式(GLCF)结构,基于T-S模型进行了系统的模糊重构;利用Lyapunov稳定性理论和反馈同步的思想实现了重构系统的同步,并推导了误差系统以衰减率α实现全局渐近稳定的充分条件.统一混沌系统和扩展Liu系统均属于典型的广义Lorenz系统.利用LMI方法对这两个混沌系统所进行的仿真实验结果表明,该模糊同步方法对于满足GLCF的所有混沌系统均适用.     

基于参数自适应方法的统一混沌系统的同步控制

采用参数自适应控制方法，根据Lyapunov稳定性原理，通过构造适当的控制函数和设计参数的自适应控制律，分别实现了系统在不同确定参数和相同不确定参数两种情况下的统一混沌系统的同步导出在这两种情况下的统一混沌系统能实现同步的充分条件.相同不确定参数情况下的同步系统控制器结构更简单、同步性能更优．数值仿真证明了该方法的有效性．     

超混沌Lu系统的线性与非线性耦合同步

针对由Aimin chen等人最近提出来的一个新的超混沌系统一超混沌Lu系统的同步问题展开研究．对两个恒同的超混沌Lu系统，分别给出了它们在线性耦合和非线性耦合情形下在全局范围内实现同步的充分条件，用Lyapunov方法从理论上证明了结论，并用数值仿真验证了理论结果．     

基于线性控制的一类金融系统的混沌同步

研究了一类金融混沌系统的同步问题,给出了同步金融混沌系统的三种线性控制方案。仅使用简单的线性控制器就实现了全局渐近同步,因此可看作是已有结果的改进。在第一种方案中,利用李雅普诺夫稳定性理论,使用线性反馈控制得到了同步两个金融混沌系统的充分条件,后两种方案通过数值方法得到了同步条件。数值仿真结果说明了文中所给方法的有效性。     

统一混沌系统的自适应控制同步

基于Pecora-Carroll混沌同步原理和参数自适应控制策略,提出一种单参数统一混沌系统的自适应同步控制方法;推导出实现不同参数、不同初值的两统一混沌系统同步的参数自适应控制律和同步条件;研究了确定控制常数边界和范围的方法,并讨论了控制常数对同步性能的影响.理论分析和数值仿真表明,选择合适的控制常数,可实现两统一混沌系统的大范围渐近稳定同步.     

基于直接构造法的不同参数统一混沌系统的同步

研究不同参数统一混沌系统的同步问题.首先采用直接构造法为响应系统设计适当的控制器,将误差系统化成三对角结构;然后根据具有三对角结构的非线性系统状态全局渐近稳定的性质,得到误差系统状态在原点渐近稳定,进而实现驱动系统与响应系统的同步;最后在参数相同和参数不同两种情况下,分别对统一混沌系统的同步进行数值仿真,仿真结果表明所提出的设计方法是有效的.

     

关于耦合混沌系统完全同步的参数选择

以系统的瞬间特征值作为高质量同步的指标 ,讨论了两个耦合的混沌系统完全同步时参数选择的问题 .当运用线性定常系统稳定性的理论判定耦合后混沌吸引子的线性化同步系统的瞬间特征值时 ,即使其处处有负实部 ,混沌完全同步也会失去 .但是 ,使用线性时变连续系统的稳定性理论分析其瞬间特征值 ,给出耦合函数参数的选择范围 ,耦合的混沌吸引子完全同步的状态就能够达到稳定 .将该分析方法分别应用于R¨ossler和Lorenz混沌系统 ,通过数值仿真 ,发现其结果与理论分析相符 ,从而表明了该分析方法的有效性     

A unified approach to output synchronization of heterogeneous multi-agent systems via L2-gain design

In this paper, a unified design procedure is given for output synchronization of heterogeneous multi-agent systems (MAS) on communication graph topologies, using relative output measurements from neighbors. Three different control protocols, namely, full-state feedback, static output-feedback, and dynamic output-feedback, are designed for output synchronization. It is seen that a unified design procedure for heterogeneous MAS can be given by formulation and solution of a suitable local $\mathcal{L}{_2}$-gain design problem. Sufficient conditions are developed in terms of stabilizing the local agents'' dynamics, satisfying a certain small-gain criterion, and solving the output regulator equations. Local design procedures are presented for each agent to guarantee that these sufficient conditions are satisfied. The proposed control protocols require only one copy of the leader''s dynamics in the compensator, regardless of the dimensions of the outputs. This results in lower-dimensional compensators for systems with high-order outputs, compared to the $p$-copy internal model approach. All three proposed control protocols are verified using numerical simulations.     

Some synchronization criteria for bidirectionally-coupled chaotic systems

1IntroductionChaos synchronization,as a very important topic in thenonlinear science ,has been developed extensivelyinthelastfew years [1,2] .A wide variety of approaches [1 ~9]have been proposed for the synchronization of chaoticsystems which include linear and nonlinear feedback,adaptive control ,etc . Most of the methods mentionedabove synchronize two coupled identical chaotic systems .Accordingto the condition of coupling signal ,they can beclassified into bidirectional [3 ~5] and unidirec…     

Some synchronization criteria for bidirectionally-coupled chaotic systems

Based on the stability theory of linear time-varying continuous system,this paper investigates the synchronization of two linear bidirectionally-coupled systems.Sufficient conditions for asymptotic synchronization are obtained for general chaotic system with bidirectional coupling via linear error feedback.Since the trajectory of chaotic system is continuous and bounded,one can choose suitable coupled parameters to satisfy the proposed criterion.The criterion can also be applied to the global synchronization for chaotic systems with linear unidirectional coupling.The chaotic Chen system and the generalized Lorenz-like system are taken as examples,the simulations verify the effectiveness of the proposed method.     

Synchronization of complex dynamical networks with switching topology: A switched system point of view

In this paper, we study the synchronization problem for complex dynamical networks with switching topology from a switched system point of view. The synchronization problem is transformed into the stability problem for time-varying switched systems. We address two basic problems: synchronization under arbitrary switching topology, and synchronization via design of switching within a pre-given collection of topologies when synchronization cannot be achieved by using any topology alone in this collection. For the both problems, we first establish synchronization criteria for general connection topology. Then, under the condition of simultaneous triangularization of the connection matrices, a common Lyapunov function (for the first problem) and a single Lyapunov and multiple Lyapunov functions (for the second problem) are systematically constructed respectively by those of several lower-dimensional dynamic systems. In order to achieve synchronization using multiple Lyapunov functions, a stability condition and switching law design method for time-varying switched systems are also presented, which avoid the usual non-increasing condition.     

Generalized chaos control and synchronization by nonlinear high-order approach

This paper investigates the generalized control and synchronization of chaotic dynamical systems. First, we show that it is possible to stabilize the unstable periodic orbits (UPOs) when we use a high-order derivation of the OGY control that is known as one of useful methods for controlling chaotic systems. Then we examine synchronization of identical chaotic systems coupled in a master/slave manner. A rigorous criterion based on the transverse stability is presented which, if satisfied, guarantees that synchronization is asymptotically stable. The Rössler attractor and Chen system are used as examples to demonstrate the effectiveness of the developed approach and the improvement over some existing results.     

Finite-time stability of linear time-varying systems with jumps

This paper deals with the finite-time stability problem for continuous-time linear time-varying systems with finite jumps. This class of systems arises in many practical applications and includes, as particular cases, impulsive systems and sampled-data control systems. The paper provides a necessary and sufficient condition for finite-time stability, requiring a test on the state transition matrix of the system under consideration, and a sufficient condition involving two coupled differential-difference linear matrix inequalities. The sufficient condition turns out to be more efficient from the computational point of view. Some examples illustrate the effectiveness of the proposed approach.     

蔡氏混沌系统网络的混沌同步及其保密通信

利用非线性函数耦合混沌同步方法,研究蔡氏混沌系统的同步问题．依据线性系统的稳定性分析准则, 证明耦合系数k = 0:5 时非线性函数耦合混沌系统的同步稳定性,并数值模拟检验其有效性．基于Routh-Hurwitz 稳 定性判据,推导出非线性耦合强度的下限,即k > 0:427．将非线性函数耦合同步方法推广到完全连接网络,证明了 网络同步的稳定性．在此基础上,利用混沌掩盖构造完全连接网络的保密通信系统,并通过数值仿真证明其可行 性．     

Exponential synchronization of chaotic systems with stochastic noise via periodically intermittent control

The problem of second‐moment exponential synchronization is discussed for chaotic systems. Different from some existing results, a unified drive‐response system is formulated, which involves stochastic noise and the time‐varying delay. Meanwhile, the feedback controller is presented by the periodically intermittent control. By exploiting the Lyapunov stability theory, the improved reciprocally convex inequality and the Itô formula, several new sufficient conditions are obtained to make two systems synchronized. In addition, the controller is determined by the control period and the control width. Finally, simulation results illustrate that the designed controller achieves the desired performance.