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.     

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.     

Secure Communication via Synchronization of Lur’e Systems Using Sampled-Data Controller

In this paper, synchronization of chaotic Lur’e systems using sampled-data control is applied to the secure communication problem. The message is transmitted and masked by the techniques of n-cipher and a public key obtained by the chaotic Lur’e system. The decryption of the transmitted encrypted message to recover the original message at the receiver can be achieved by synchronizing the transmitter and receiver chaotic systems. Sampled-data feedback control is used for synchronization, and a sufficient condition for obtaining feedback gain is derived in terms of linear matrix inequalities using a discontinuous Lyapunov functional. The secure communication system is simulated via Matlab along with the Chua system to show the effectiveness of the proposed result.     

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.      

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.     

Synchronization for Time-Delay Lur’e Systems with Sector and Slope Restricted Nonlinearities Under Communication Constraints

This paper presents a new approach to the output feedback control problem of master-slave synchronization of time-delay chaotic Lur’e systems with sector and slope restricted nonlinearities under communication constraints. The communication constraints involve measurement quantization and signal transmission delay. By constructing an appropriate Lyapunov functional with the idea of a discretized Lyapunov–Krasovskii functional method and utilizing the sector bound of the logarithmic quantizer, a delay-dependent synchronization criterion is derived. The desired synchronization controller can be obtained by solving a set of linear matrix inequalities. Finally, numerical simulations for Chua’s circuit are proposed to show the effectiveness 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.     

基于线性状态反馈方法的Nadolschi混沌系统同步

研究了一类新型混沌系统——Nadolschi系统的同步控制问题。首先为响应系统设计一个多变量线性状态反馈控制器,进而将Nadolschi系统的同步控制问题转化为误差系统零平衡点的镇定问题。然后,根据Lyapunov稳定性理论,得出使Nadolschi混沌系统达到渐近同步的充分条件。仿真结果验证了所提方法的有效性,所设计的控制器具用结构简单,易于实现等优点。     

连续时间混沌系统的参数自适应同步

针对参数不一致系统以及同步无法实现的系统，基于误差渐进稳定收敛到零的原理，提出参数自适应加反馈同步法。数值模拟表明，通过选择合适的反馈系数，能够成功地实现混沌同步，并进一步将结果推广到超混沌系统。     

统一混沌系统与其变形系统间的间歇反馈同步控制

采用间歇反馈控制方法,研究了统一混沌系统与其变形系统间的同步控制问题。通过合理设计间歇反馈控制器,将同步问题转化为误差动力学系统方程在原点处的收敛问题。根据连续系统的稳定性准则及相关实验,推导出了满足同步条件的同步定理。分析了初始值X(0)和Y(0)、反馈系数k、比例因子D、步长h以及统一系统参数对同步系统的同步性能的影响。最后,采用间隙反馈同步方案,设计了一个混沌掩盖保密通信系统,并进行了仿真研究。仿真实验研究证明了该同步方法的有效性。     

基于Lorenz系统切换混沌同步的保密通讯

该文提出利用Lorenz系统切换混沌同步实施保密通讯的方法。构建了有一定关联的两个Lorenz混沌系统,并通过选择器在系统间随机切换;用同一种控制方法既能实现不同Lorenz系统的混沌同步,又能实现相同Lorenz系统的混沌同步;发送系统可以在Lorenz混沌系统间随机转换,传输信道中混沌调制信号也随之不断变化;接收系统将混沌调制信号解调后,即可获取有用信号。由于发送系统的可选择性,导致保密信号的多样性和随机性,因此该保密通讯方法具有更好的保密性能。     

异结构时滞不确定混沌系统的同步/反同步控制及其应用

为了研究具有不同参数的两个不确定时滞混沌系统的同步与反同步控制及在保密通信中的应用,首先对反馈时滞Lorenz混沌系统的系统参数进行重新设计,并引入正弦函数扰动,获得两个具有不同吸引子的时滞混沌系统.采用主动控制方法实现了具有不同参数的时滞混沌系统的同步及反同步控制.为了实现保密通信,将明文信号参与混沌运算,并结合混沌...     

基于小波变换的超混沌系统同步

提出了一种基于反馈控制与小波变换相结合的超混沌系统同步方法。在发送端 ,将系统的部分信号进行小波变换去掉细节信息后发送 ,在接收端重构出低频信号 ,将其与接收端信号的差进行离散反馈 ,可以使两个结构相同的超混沌系统达到混沌同步。同时 ,参数失配和噪声对同步的影响被讨论。应用本同步方法可将发送信号压缩后传送 ,节约系统资源 ;滤去发送信号的高频成分 ,减小干扰对同步信号中的影响。文中给出了仿真验证结果。     

一种基于误差系统稳定性的混沌广义同步方法

该文在将混沌系统分为线性与非线性两部分的基础上,利用反馈控制及参数变换,提出了一种新的混沌广义同步方法。该方法基于线性变换,把系统广义同步问题转化为同步误差系统的稳定性问题,并给出了广义同步存在的条件。该方法可以通过配置同步速度,改善混沌广义同步的性能。且不受混沌系统线性部分稳定性的限制,扩大了混沌广义同步的通用性。通过对Lorenz系统进行仿真,结果表明该方法具有很好的适用性。     

混沌系统同步的抗干扰优化设计

本文研究混沌系统同步的抗信道噪声和参数失配干扰优化设计问题。以非线性反馈混沌同步方案为基础，推导出一种抗干扰优化设计方法。对蔡氏电路的仿真实验表明，用该方法设计的混沌同步系统具有较强的抗干扰能力。     

基于时滞不确定Lorenz混沌同步的保密通信

针对一类含保密信息的时延不确定Lorenz混沌系统,提出了基于径向基神经网络的同结构同步控制方案,在混沌系统同步的基础上,有效地恢复出隐藏的多路明文信号。利用神经网络的良好逼近能力对时延Lorenz混沌系统设计鲁棒同步控制器,实现了同步误差的收敛。当同步误差收敛时,混沌系统所传输的隐藏信号则可以正确恢复。仿真结果表明,文章所给出的同步控制器可以在5s内实现时延不确定Lorenz混沌系统同步,并能恢复出多路明文信号。     

存在参数微扰的非自治超混沌系统的同步

本文对四维非自治的超混沌光学模型的同步问题进行了讨论。结合误差反馈同步方法和参数自适应同步方法,使参数不同的两个系统达到同步,数值计算结果也表明同步效果很好。同时对控制函数的参数与同步建立的时间两者之间的关系进行了仿真,结果表明,存在最佳参数使得同步建立的时间最短。     

新型Liu混沌系统的模糊反馈同步方法

论文研究了新近提出的Liu混沌系统(2004)的模糊反馈同步方法。Liu混沌系统结构不同于以往的连续混沌系统,本文基于T-S(Takagi-Sugeno)模糊模型重构了Liu混沌系统;然后用Lyapunov理论和反馈同步的思想推导了两个重构的Liu系统同步的稳定性条件,并给出了误差系统以衰减率全局渐近稳定的充分条件;最后基于LMI方法进行了仿真实验。良好的仿真结果验证了本文算法的有效性和快速性。     

Synchronization and communication using semiconductor lasers withoptoelectronic feedback

Semiconductor lasers provide an excellent opportunity for communication using chaotic waveforms. We discuss the characteristics and the synchronization of two semiconductor lasers with optoelectronic feedback. The systems exhibit broadband chaotic intensity oscillations whose dynamical dimension generally increases with the time delay in the feedback loop. We explore the robustness of this synchronization with parameter mismatch in the lasers, with mismatch in the optoelectronic feedback delay, and with the strength of the coupling between the systems. Synchronization is robust to mismatches between the intrinsic parameters of the lasers, but it is sensitive to mismatches of the time delay in the transmitter and receiver feedback loops. An open-loop receiver configuration is suggested, eliminating feedback delay mismatch issues. Communication strategies for arbitrary amplitude of modulation onto the chaotic signals are discussed, and the bit-error rate for one such scheme is evaluated as a function of noise in the optical channel