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.     

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.     

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.      

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.     

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。     

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。     

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.     

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。     

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.

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。     

Synchronization and Parameters Identification of Chaotic Systems via Adaptive Control

Based on Lyapunov stability theory, a novel adaptive controller is designed for a class of chaotic systems. The parameters identification and synchronization of chaotic systems can be carried out simultaneously. The controller and the updating law of parameters identification are directly constructed by analytic formula. Simulation results with Chen‘s system and Roessler system show the effectiveness of the proposed controller.     

基于状态观测器的一类混沌系统的投影同步

研究了基于状态观测器的一类混沌系统的投影同步问题.基于状态观测器方法和极点配置技术,设计出一种投影同步方案,使得一类混沌系统达到了投影同步.与以往的投影同步方法相比,该方法简便,易于实现,达到投影同步的时间短,并且在同步控制过程中可任意调整缩放比例因子.最后,用Lǖ系统进行了数值仿真,仿真结果进一步证明了该方法的有效性.     

参数未知混沌动力学系统滑模变结构同步控制研究

将自适应技术、系统辨识技术应用于混沌动力学系统的同步控制，提出了一种基于参数估计的自适应混沌变结构同步控制方法。针对混沌动力学系统参数未知的情况，根据已知系统的输入输出序列，构造系统的误差方程，并利用误差方程的Jacob矩阵，求解使系统收敛的取值条件，在状态控制器的作用下，使系统中的未知参数逐步逼近精确值，实现具有不同初始点、系统参数未知的混沌动力学系统的同步控制。     

不确定分数阶高维混沌系统的自适应滑模同步

混沌及其同步已经成为研究的热点,随着分数阶混沌系统建模的需要,分数阶低阶混沌系统的同步控制已经取得了很多结果,国内外针对分数阶高维混沌系统的同步控制方面的研究还十分罕见,本文考虑了不确定因素和外部扰动的影响,利用自适应滑模方法研究高维不确定分数阶混沌系统的同步,基于同步控制理论给出了滑模函数的设计和控制器的构造,获得分...     

具有时变信道的线性逆系统混沌通讯

用线性逆系统法实现混沌信号掩盖是一种不需要同步的混沌通讯方法。本文提出当信道增益为时变函数时,利用自适应控制器来补偿信道增益的变化,以便在接收端能准确地恢复出信息信号,实例分析和计算机模拟结果表明所恢复出的信号与原信号的均方误差小于４．２８×１０＾－６。说明该方法是可行的。     

A New Data Rotation Based CP Synchronization Scheme for OFDM Systems

In this paper, a new data rotation scheme for improving the symbol timing and carrier frequency offset (CFO) estimation of orthogonal frequency-division multiplexing (OFDM) systems is proposed. The new data rotation scheme intentionally introduces a cyclic shift after the inverse fast Fourier transform (IFFT) in the transmitter so that a higher energy cyclic prefix (CP) is obtained. This cyclic shift will not impair the orthogonality among the subcarriers and will only results in phase shift in the demodulated signal at the receiver. To recover the cyclic shift and for data detection, the scheme makes use of double differential encoding and decoding at the transmitter and the receiver. We analyze the performance of the new data rotation scheme by using order statistics theory. Our results show that the new scheme can provide a 1.6 dB gain in the performance of the CFO estimator and a 6 dB gain for the timing estimator at 15 dB SNR over AWGN channel, as well as a 6 dB gain in lock-in probability and a 4 dB gain in CFO performance at 5 dB SNR over frequency selective fading channel.