Improved Global Asymptotical Synchronization of Chaotic Lur'e Systems With Sampled-Data Control

This brief investigates the global asymptotical synchronization problem of chaotic Lur'e systems with sampled-data control. Based on a time-varying delay system transformed from the sampled-data error system, an augmented Lyapunov functional containing some useful system information is constructed, no useful terms in the derivative of the Lyapunov functional are ignored, and the relationship among the time-varying delay, its upper bound, and their difference is taken into account. A less conservative delay-dependent synchronization criterion expressed in terms of linear matrix inequalities is obtained. The effectiveness and merits of the proposed method are finally illustrated via numerical simulations for Chua's circuits.     

Impulsive Synchronization of Chaotic Lur'e Systems by Linear Static Measurement Feedback: An LMI Approach

In this brief, we consider impulsive control for master-slave synchronization schemes that consist of identical chaotic Lur'e systems. Impulsive control laws are investigated which make use of linear static measurement feedback, instead of full state feedback. A less conservative sufficient condition than existing results for global asymptotic impulsive synchronization is presented, in which synchronization is proven for the error between the full state vectors. And then an linear matrix inequality (LMI)-based approach for designing linear static output feedback impulsive control laws to globally asymptotically synchronize Lur'e chaotic systems is derived. With the help of the LMI solvers, we can easily obtain the linear output feedback impulsive controller and the bound of the impulsive interval for global asymptotic synchronization. The method is illustrated on Chua's circuit.     

Adaptive Stabilization and Synchronization for Chaotic Lur'e Systems With Time-Varying Delay

In this paper, we propose an adaptive scheme for the stabilization and synchronization of chaotic Lur'e systems with time-varying delay. Based on the invariant principle of functional differential equations, the strength of the feedback controller is enhanced adaptively to stabilize and synchronize chaotic Lur'e systems. The derivative-constraint that the time-varying delay is required to be differentiable and its derivation is less than one can be removed by using LaSalle-Razumikhin-type theorems. The time-varying delay is allowed to be bounded without any additional constraint or unbounded with derivative-constraint. This method is analytical, rigorous and simple to implement in practice. In addition, it is quite robust against the effect of parameters uncertainty and noise. Two examples are provided to show the effectiveness of the proposed scheme. The results of the paper demonstrate the fruitfulness of the modern feedback and adaptive control theory application to the stabilization and synchronization problems for delayed chaotic systems.     

Fault-Tolerant Master–Slave Synchronization for Lur'e Systems Using Time-Delay Feedback Control

This paper deals with fault-tolerant master–slave synchronization for Lur'e systems using time-delay feedback control. Taking a general nature of fault in the master system into account, a new synchronization scheme, namely, fault-tolerant master–slave synchronization, is proposed, by which the master–slave synchronization can be achieved no matter if the fault occurs or not. By making use of an observer-based fault estimator and a modified time-delay feedback controller, the fault-tolerant master–slave synchronization is formulated so as to discuss the global asymptotic stability of the error system and the bound of energy gain from fault to state and fault estimation error vectors. Some new delay-dependent criteria are derived to analyze the synchronization error system, and based on the analysis results, a sufficient condition on the existence of such a master–slave synchronization scheme and a solution to the controller and fault-estimator gain matrices are obtained in terms of linear matrix inequalities. Finally, a Chua's circuit is used to illustrate the effectiveness of the proposed method.      

Synchronization of Chaotic Systems Using Time-Delayed Fuzzy State-Feedback Controller

This paper presents the fuzzy-model-based control approach to synchronize two chaotic systems subject to parameter uncertainties. A fuzzy state-feedback controller using the system state of response chaotic system and the time-delayed system state of drive chaotic system is employed to realize the synchronization. The time delay which complicates the system dynamics makes the analysis difficult. To investigate the system stability and facilitate the design of fuzzy controller, Takagi-Sugeno (T-S) fuzzy models are employed to represent the system dynamics of the chaotic systems. Furthermore, the membership grades of the T-S fuzzy models become uncertain due to the existence of parameter uncertainties which further complicates the system analysis. To ease the stability analysis and produce less conservative analysis result, the membership functions of both T-S fuzzy models and fuzzy controller are considered. Stability conditions are derived using Lyapunov-based approach to aid the design of fuzzy state-feedback controller to synchronize the chaotic systems. Simulation examples are presented to illustrate the merits of the proposed approach.     

Chaotic Synchronization Using Sampled-Data Fuzzy Controller Based on Fuzzy-Model-Based Approach

This paper presents the synchronization of chaotic system using a sampled-data fuzzy controller. To carry out the system analysis, a fuzzy model is employed to represent the chaotic systems. Linear-matrix-inequality (LMI)-based system stability and performance conditions are derived using a Lyapunov-based approach. The derived LMI-based stability and performance conditions are employed to aid the design of a stable and well-performing sampled-data fuzzy controller to achieve the synchronization of chaotic systems. An application example is given to illustrate the merits of the proposed approach.     

利用非线性函数控制的混沌异结构同步

研究了利用非线性函数控制的混沌异结构同步问题.基于Lyapunov稳定性理论,设计了非线性控制函数,使得同步误差系统的Lyapunov函数的形式为V(e)=eTPe(P为正定矩阵),根据数学公式推导,理论证明了该方法可以实现不同混沌系统之间的异结构同步.数值模拟进一步验证了所提出方案的有效性.     

研究混沌系统同步问题的一种解析方法

本文利用解析方法研究Ｌｏｒｅｎｚ和Ｒｏｓｓｌｅｒ两种混沌系统中的一驱动二响应和二驱动一响应过程。得到了在各种中实现同步的条件。其结论与以前文献中的结论一致,但更加普适。     

A Linear Time-Varying Controller for Synchronization of LÜ Chaotic Systems With One Input

This brief addresses the problem of synchronization of two LÜ chaotic systems. As opposed to nonlinear Lyapunov-based controllers, which are designed with the aim of rendering the derivative of a Lyapunov function negative along trajectories of the closed-loop system, control design exploits the natural stability properties of the system. The proof relies not only on basic Lyapunov stability theory but also on other concepts, such as persistency of excitation. The contribution with respect to other works is to show that one control input is enough to force synchronization; moreover, the controllers are linear time varying.      

一类不确定混沌系统的自适应同步控制

研究了一类不确定混沌系统的自适应同步控制问题。基于Lyapunov稳定性理论和微分不等式技巧,提出了一种新的自适应控制器的设计方法。该控制器仅用到了不确定性的导数信息。即使不确定性是时变的或无界的,只要其导数有界,自适应控制器就能保证误差系统的状态收敛到平衡点附近很小的邻域内。特别地,当不确定性是慢变时,该控制器就能保证误差状态渐近稳定。最后,以Lorenz系统为例进行数值仿真,结果证明了该方法的有效性。     

一种可完全线性化的不同类型混沌系统同步方法

讨论可完全线性化的不同类型混沌系统之间的同步问题.根据滑模控制原理求取混沌同步控制形式,利用扩张状态观测器对系统信息进行渐进估计,把复杂的滑模控制策略变为可实现的控制方式,以此实现具有不确定性混沌系统的同步.以Duffing和Vander Pol系统为例进行仿真,效果良好.     

混沌同步的方法及其若干问题

本文首先详细了讨论了现有的几种主要混沌同步的方法，原理及其特点，并作了简要的评述。然后，针对现有的一些方法的不足，指出了需要进一步研究和解决的若干问题。     

一种新的混沌调制和线性解调方法

提出一种新的用于保密通信的混沌调制和线性解调方法.发送端和接收端各有一个相同的混沌电路,将有用信号接入发送端混沌电路的线性子电路,使其对该混沌电路进行调制.调制后的混沌信号传送到接收端的混沌电路,检测该电路中某一电流或电压变量,经线性滤波器解调可恢复原始有用信号.基于这一调制、解调方法的混沌通信系统保密性强且电路简单.对两个混沌保密通信系统的仿真实验取得了满意的结果.     

On Designing Time-Varying Delay Feedback Controllers for Master–Slave Synchronization of Lur'e Systems

This paper is concerned with the problem of designing time-varying delay feedback controllers for master-slave synchronization of Lur'e systems. Two cases of time-varying delays are fully considered; one is the time-varying delay being continuous uniformly bounded while the other is the time-varying delay being differentiable uniformly bounded with the derivative of the delay bounded by a constant. Based on Lyapunov-Krasovskii functional approach, some delay-dependent synchronization criteria are first obtained and formulated in the form of linear matrix inequalities (LMIs). The relationship between synchronization criteria for the two cases of time-varying delays is built. Then, sufficient conditions on the existence of a time-varying delay feedback controller are derived by employing these newly-obtained synchronization criteria. The controller gains can be achieved by solving a set of LMIs. Finally, Chua's circuit is used to illustrate the effectiveness of the design method.     

Observer Based Projective Synchronization Method for a Class of Chaotic System-Part I: Linear Synchronization Subsystem

In this three-part paper, an observer based projective synchronization method for a class of chaotic system is proposed. At the transmitter, a general observer is used to create the scalar signal for synchronizing. In this part, the structure of the projective synchronization method is presented. And the condition of projection synchronization is theoretically analyzed when the synchronization subsystem is linear.     

不确定分数阶多驱动一响应混沌系统同步

针对一类新的多驱动一响应混沌系统同步方式,基于分数阶系统稳定性理论和Lyapunov稳定性理论,运用追踪控制和滑模自适应控制方法设计了同步控制律和参数自适应律.对象模型考虑了不确定因素的影响,首先选取一类稳定的分数阶滑模曲面,然后提出了一种鲁棒同步方案.最后数值仿真验证了方案的正确性和有效性.     

基于自适应状态观测器的混沌同步仿真研究

针对一类特定结构的含有未知参数的混沌系统,给出了一种基于状态观测器的自适应同步控制方法。通过一个带有控制器的非线性状态观测器实现混沌系统的渐进同步并对未知参数进行估计。该控制方法简单易行,且能通过自适应律自动调整以跟随参数的变化,具有较强的鲁棒性。理论分析和仿真实验都证明了该方法的有效性。     

耦合混沌同步和多路保密通信

本文针对混沌系统在通信中具有理想的保密作用，讨论了离散多振子耦合混沌系统的特性和两个耦合混沌系统的同步行为，结果表明，两个耦全合混沌系统通过简单调制能很快同步，并且具有通信保密性和多路传输特性。     

一类非均匀采样非线性系统的无模型自适应控制

对一类未知的非均匀采样离散时间非线性非仿射系统,基于在受控系统当前工作点处的等价数据模型,利用输入输出数据对伪雅可比矩阵（PJM）的在线估计,设计出相应的无模型自适应控制器.所提出的控制方法具有如下特点：控制器的设计仅需要非均匀采样的输入输出数据,不包含系统模型的任何信息;控制算法计算量小,算法容易实现.最后,通过一个非均匀采样离散时间非线性系统仿真结果验证提出方法的有效性.     

Analysis of the Linear GSIC Multiuser Detector Using a Matrix Iterative Approach

In this work, we use a new approach that relies on the theory of matrix iterative analysis to study the convergence behavior of the linear group-wise successive interference cancellation (GSIC) detector. Particularly, we show that the linear GSIC detector is in fact a realization of a modified block successive over-relaxation (BSOR) iterative method where the relaxation factor is a matrix instead of scalar. Consequently, to study the convergence behavior of the GSIC detector, we propose two new corollaries that extend the famous work of Kahan (Varga, Matrix iterative analysis, 2000) to the case where the relaxation factor is a matrix instead of a scalar. Using the two new corollaries we develop two new conditions of convergence for the linear GSIC detector. Simulation results are in excellent agreement with theory.