基于状态观测器的分数阶时滞混沌系统同步研究

研究分数阶时滞混沌系统同步问题,基于状态观测器方法和分数阶系统稳定性理论,设计分数阶时滞混沌系统同步控制器,使得分数阶时滞混沌系统达到同步,同时给出了数学证明过程.该同步控制器采用驱动系统和响应系统的输出变量进行设计,无需驱动系统和响应系统的状态变量,简化了控制器的设计,提高了控制器的实用性.利用Lyapunov稳定性理论和分数阶线性矩阵不等式,研究并给出了同步控制器参数的选择条件.以分数阶时滞Chen混沌系统为例,设计基于状态观测器的同步控制器,实现了分数阶时滞Chen混沌系统同步,并将其应用于保密通信系统中.仿真结果证明了该同步方法的有效性.     

Complete switched modified function projective synchronization of a five-term chaotic system with uncertain parameters and disturbances

A five-term three-dimensional (3D) autonomous chaotic system with an exponential nonlinear term is reported in this paper. Basic dynamical behaviours of the chaotic system are further investigated. Then a new synchronization phenomenon, complete switched modified function projective synchronization (CSMFPS), for this novel five-term chaotic system with uncertain parameters and disturbances is investigated. This paper extends previous work, where CSMFPS of chaotic systems means that all the state variables of the drive system synchronize with different state variables of the response system. As the synchronization scheme has many combined forms, it is a promising type of synchronization and can provide greater security in secure communication. Based on Lyapunov stability theory, a robust adaptive controller is contrived to acquire CSMFPS, parameter identification and suppress disturbances simultaneously. Finally, the Lorenz system and the new five-term chaotic system are taken as examples and the corresponding numerical simulations are presented to verify the effectiveness and feasibility of the proposed control scheme.     

一类参数不确定统一混沌系统的脉冲滞后同步

针对一类具有传输信道时间延迟且参数不确定的统一混沌系统，提出了一种脉冲控制同步方法.该方法将两个非自治混沌系统之间脉冲同步的实用稳定性问题转化为同步误差系统在原点的实用稳定性问题，基于脉冲微分方程的相关理论，给出了同步误差系统在原点的实用稳定判据，仿真结果验证了方法的有效性. 关键词： 统一混沌系统 混沌同步 脉冲控制 实用稳定性     

Global exponential synchronization between Lü system and Chen system with unknown parameters and channel time-delay

This paper proposes a nonlinear feedback control method to realize global exponential synchronization with channel time-delay between the Lü system and Chen system,which are regarded as the drive system and the response system respectively.Some effective observers are produced to identify the unknown parameters of the Lü system.Based on the Lyapunov stability theory and linear matrix inequality technique,some sufficient conditions of global exponential synchronization of the two chaotic systems are derived.Simulation results show the effectiveness and feasibility of the proposed controller.     

Exponential networked synchronization of master-slave chaotic systems with time-varying communication topologies

The networked synchronization problem of a class of master-slave chaotic systems with time-varying communication topologies is investigated in this paper. Based on algebraic graph theory and matrix theory, a simple linear state feedback controller is designed to synchronize the master chaotic system and the slave chaotic systems with a time- varying communication topology connection. The exponential stability of the closed-loop networked synchronization error system is guaranteed by applying Lyapunov stability theory. The derived novel criteria are in the form of linear matrix inequalities (LMIs), which are easy to examine and tremendously reduce the computation burden from the feedback matrices. This paper provides an alternative networked secure communication scheme which can be extended conveniently. An illustrative example is given to demonstrate the effectiveness of the proposed networked synchronization method.     

参数不确定时延超混沌系统的脉冲同步方法研究

针对一类参数不确定的异构时延超混沌系统,采用响应系统与驱动系统状态变量误差的线性反馈作为脉冲控制信号,基于Lyapunov稳定性理论实现了超混沌系统的脉冲同步,给出了渐近稳定条件,并构造了一个具有时延的数字保密通信系统.该方案保密性高,鲁棒性强.数值仿真表明系统能快速达到同步,应用混沌密码序列对数字信号进行加密后,信息信号可以在接收端有效地恢复出来. 关键词： 时延 脉冲同步 数字保密通信     

一类混沌系统同步时间可控的自适应投影同步

基于自适应的方法, 提出了一种同步时间可控的混沌投影同步方法. 该方法针对一类不同的混沌系统设计了通用的同步控制器和参数自适应律, 使驱动系统的状态变量和响应系统的状态变量按照给定比例矩阵达到同步, 同步误差按预设的指数速率收敛. 由于比例矩阵和指数速率不为第三方所知, 可提高信息的抗破译能力. 同时, 通过调节相关控制器参数, 可在有限时间内达到投影同步, 并实现对同步时间的有效控制. 数值模拟结果的对比和分析验证了所提方法是有效的和鲁棒的. 关键词： 混沌 自适应控制 投影同步 时间可控     

A new chaotic communication scheme based on adaptive synchronization

A new chaotic communication scheme using adaptive synchronization technique of two unified chaotic systems is proposed. Different from the existing secure communication methods, the transmitted signal is modulated into the parameter of chaotic systems. The adaptive synchronization technique is used to synchronize two identical chaotic systems embedded in the transmitter and the receiver. It is assumed that the parameter of the receiver system is unknown. Based on the Lyapunov stability theory, an adaptive control law is derived to make the states of two identical unified chaotic systems with unknown system parameters asymptotically synchronized; thus the parameter of the receiver system is identified. Then the recovery of the original information signal in the receiver is successfully achieved on the basis of the estimated parameter. It is noticed that the time required for recovering the information signal and the accuracy of the recovered signal very sensitively depends on the frequency of the information signal. Numerical results have verified the effectiveness of the proposed scheme.     

适合传输快变信息信号的混沌调制保密通信

提出一种新的混沌调制通信方法.利用一个自适应控制器跟踪信息信号的误差对产生混沌载波的发射系统进行参数调制.同时，信息信号直接与混沌载波相乘作为发射信号驱动接收系统.在接收端，另一个自适应控制器维持收发系统的混沌同步并恢复出信息信号.由于同步误差与信息信号无关，从而实现了大幅度、快时变信息信号的混沌调制通信.理论分析和数值模拟的结果表明该方法增强了低维混沌系统的通信保密性. 关键词： 混沌调制 保密通信 自适应控制器 蔡氏电路     

SC混沌比例投影同步方法在保密通信中的应用

利用基于线性稳定性准则的SC混沌比例投影同步方法,提出一种应用于保密通信的混沌掩盖方案.适当分离出混沌系统的线性项与非线性项,构造一个非线性驱动向量函数,混沌状态变量包含用于投影同步的比例因子,把所需传递的有用信息掩盖入其中一个分量上,得到混沌载波信号,提高加密信息的复杂度和解码的困难度.以Lorenz吸引子和超混沌Rössler吸引子为例进行数值仿真,详细分析传输的正弦信息加密解密全过程,给出简单、最优的混沌掩盖方案,数值分析证明比例投影同步方法应用于保密通信领域的有效性.     

On multi switching compound synchronization of non identical chaotic systems

Multi switching compound synchronization (MSCOS) between four non identical chaotic systems is investigated. Chen system is considered as scaling drive system. Lorenz and Lü systems are taken as base drive systems. The compound of the multi drive system is then synchronized with Rössler response system using multi switching synchronization scheme. In MSCOS, the state variables of three drive systems synchronize with different state variables of response system, simultaneously. For suitable choice of scaling factors, switched modified function projective synchronization is obtained as a special case of MSCOS among chaotic systems. To achieve the desired synchronization among four non identical chaotic systems, sufficient condition is obtained using a nonlinear controller and Lyapunov stability theory, and corresponding theoretical proofs are given. The effectiveness of the proposed controllers is verified by numerical simulations using MATLAB.     

基于广义混沌映射切换的混沌同步保密通信

提出了一种基于广义混沌映射切换的混沌同步保密通信方式.这种通信方式首先构建产生多种混沌序列的广义混沌映射模型,然后在不同时段根据切换策略产生不同混沌序列,在发送端,将信号与混沌载波之和取模运算后再嵌入混沌映射的输入端进行迭代运算以实现调制;在接收端,根据切换协议,用同一个相应的广义混沌映射模型从接收信号中提取混沌载波并进而恢复信息信号.研究结果表明:这种基于广义混沌映射切换的混沌同步通信方式比基于单一混沌系统的保密通信方式具有更强的抗干扰能力,保密性能更好,且实现简单. 关键词： 混沌 混沌映射切换 同步 保密通信     

超混沌Qi系统的错位投影同步及其在保密通信中的应用

提出了一种新型的混沌系统同步方法,即错位投影同步,要求驱动系统和响应系统中的所有状态向量,至少有一对不是按照原有的对应关系成比例同步,而是按照向量的错位关系成比例投影同步.以新型的四维超混沌Qi系统为例,分析出23种混沌系统的同步方案.针对其中一种同步,基于Lyapunov稳定性理论,设计有效的非线性控制器,实现初始值不同的两个超混沌Qi系统错位投影同步.另外,将该方法应用于混沌保密通信中,基于改进的混沌掩盖通信原理,在发送端使用超混沌信号对信息信号进行加密并发送,最后从同步后的接收端系统不失真地恢复出有用信号.数值仿真表明,该方案有着良好的通信和保密特性.     

Adaptive synchronization of a switching system and its applications to secure communications

This paper studies the adaptive synchronization of a switching system with unknown parameters which switches between the R?ssler system and a unified chaotic system. Using the Lyapunov stability theory and adaptive control method, the receiver system will achieve synchronization with the drive system and the unknown parameters would be estimated by the receiver. Then the proposed switching system is used for secure communications based on the communication schemes including chaotic masking, chaotic modulation, and chaotic shift key strategies. Since the system switches between two chaotic systems and the parameters are almost unknown, it is more difficult for the intruder to extract the useful message from the transmission channel. In addition, two new schemes in which the chaotic signal used to mask (or modulate) the transmitted signal switches between two components of a chaotic system are also presented. Finally, some simulation results are given to show the effectiveness of the proposed communication schemes.     

A secure communication method for a high-power information signal based on chaotic masking

In this paper,we present a secure communication method for a high-power information signal based on chaotic masking.In the transmitter,an adaptive controller is adopted to pick up the change of the information signal ,and to inject the controller‘s error into the transmitting system.At the same time,the information is directly added to the chaotic signal in transmission to drive the receiving system.In the receiver,another adaptive controller is used to maintain chaotic synchronization of the transmitting and receiving systems and to recover the information signal.Since the synchronization error is independent from the information signal,the power of the information signal can be equivalent to that of the chaotic signal,and the frequency of the information signal can be set within the range of the principal frequencies of the chaotic signal,The results of theoretical analysis and numerical simulation show that the presented method not only enhances the degree of security of low-dimensional chaotic systems but also significantly improves the signal-to-noise ratio at the receiving end.     

Pragmatical generalized synchronization of chaotic systems with uncertain parameters by adaptive control

A new kind of generalized synchronization of two chaotic systems with uncertain parameters is proposed. Based on a pragmatical asymptotical stability theorem and an assumption of equal probability for ergodic initial conditions, an adaptive control law is derived so that it can be proved strictly that the common null solution of error dynamics and of parameter dynamics is actually asymptotically stable, i.e. these two identical systems are in generalized synchronization and the estimated parameters approach the uncertain values. It is called pragmatical generalized synchronization. Finally, two numerical examples are studied for two Quantum-CNN oscillator chaotic systems to show the effectiveness of the proposed generalized synchronization strategy with a double Duffing chaotic system as a goal system.     

一类具有可变系数的混沌系统的同步

本文基于系统传递函数矩阵的严格正实性, 针对一类具有可变系数的混沌 (或超混沌) 系统的自同步与异结构同步问题提出了解决方法. 通过在响应系统中加入同步控制器, 并将待同步系统导出的误差系统中的非线性部分作为误差系统输入, 将误差状态变量作为误差系统输出, 使误差系统的传递函数矩阵成为严格正实的, 这样可使误差系统的原点是渐近稳定的, 即两系统达到稳定的混沌 (或超混沌) 同步. 所设计的同步控制器参数选取范围明确, 均为线性的, 且对于待同步系统的系数变化具有一定的鲁棒性. 文中给出了同步控制器的具体设计过程和同步结果, 并结合数值仿真验证了该方法的可行性与有效性. 关键词： 严格正实 可变系数 混沌同步     

Secure communication using a compound signal from generalized synchronizable chaotic systems

By considering generalized synchronizable chaotic systems, the drive-auxiliary system variables are combined suitably using encryption key functions to obtain a compound chaotic signal. An appropriate feedback loop is constructed in the response-auxiliary system to achieve synchronization among the variables of the drive-auxiliary and response-auxiliary systems. We apply this approach to transmit analog and digital information signals in which the quality of the recovered signal is higher and the encoding is more secure.     

混沌Lur’e系统的线性输出反馈同步

针对一类特殊的混沌Lur’e系统,以系统最后一状态变量作为驱动信号进行误差的线性输出反馈,提出一个同步的全局控制规律,并证明了同步的渐近稳定性.最后以蔡氏振子为例进行仿真,验证该同步方法的有效性. 关键词： 混沌同步 输出反馈 Lur’e系统 蔡氏振子     

不确定自催化反应扩散时空混沌系统的延时同步

设计了一种延迟同步控制器实现了时空混沌系统之间的同步控制.基于Lyapunov稳定性定理,确定了延迟同步控制器的结构以及系统状态变量之间的误差方程.以自催化反应扩散时空混沌系统为例,仿真模拟验证了该控制器的有效性.进一步设计了参量辨识器,对不确定自催化反应扩散时空混沌系统中的参量进行了有效辨识.通过研究有界噪声影响下系统的同步效果,表明该同步方法具有较好的抗干扰能力. 关键词： 时空混沌 延时同步 参量辨识 有界噪声