【作者】 孙克辉；

【导师】 张泰山；

【作者基本信息】 中南大学 ， 控制理论与控制工程， 2005， 博士

【摘要】 为了驾驭混沌,本文融合混沌动力学、先进控制理论、现代密码学和现代通信技术的新成果,采用理论分析、数值仿真和实验研究相结合的研究方法,对混沌同步控制方法、同步性能及其在信息加密中的应用进行了广泛和深入的研究。 首先回顾了混沌理论与应用研究的发展历程,特别是混沌保密通信的研究现状;对混沌同步方法的研究进行了全面综述,总结了混沌同步研究中的热点问题;对基于混沌同步原理的混沌保密通信技术和混沌加密技术的研究现状和特点进行了归纳,明确了论文的主攻方向。 论文研究了基于Jacobi矩阵QR分解的Lyapunov指数计算算法原理;采用Matlab6.5软件平台,设计了基于该算法的Lyapunov指数计算程序,该方法不仅能够精确求解非线性动力学系统的Lyapunov指数谱和分数维,而且能计算同步系统的条件Lyapunov指数;分析了迭代次数、计算步长、解法器和初值等因素对计算精度的影响。为混沌同步控制研究奠定了理论和技术基础。 为了指导混沌同步的深入研究和提高系统的同步性能,系统地提出了混沌同步系统的七大性能指标,讨论了控制器参数与同步性能之间的关系;设计了一种能实现一般连续混沌系统和超混沌系统同步的多变量驱动误差反馈控制器;研究了离散混沌系统的线性和非线性同步控制问题,导出了离散混沌系统的同步条件。基于Matlab/Simulink的数值仿真证明了误差反馈控制同步方法的有效性和对同步性能讨论的正确性。 基于Lyapunov稳定性理论和Pecora-Carroll渐近同步原理,采用自适应同步控制策略,分别在确定参数和不确定参数情况下,研究了统一混沌系统的同步控制问题;提出了基于统一混沌系统的混沌键控(CSK)数字保密通信方案,接收端采用相干解调方式恢复信息。理论分析和数值仿真表明系统具有很好保密性能和抗干扰性能。 在比较了混沌系统与传统密码算法之间的对应关系的基础上;提出了安全混沌概念和混沌的安全性充分条件;分析了混沌序列加密的基本原理。讨论了Logistic混沌映射的统计特性,设计了基于Logistic更多还原

【Abstract】 In order to control chaos, chaotic synchronization control methods and its application in the field of information encryption are studied by merging the latest achievements from chaotic dynamics, advanced control theory, modern cryptology and modern communication technologies. Some methods, such as theory analysis, numerical simulation and experiment research, are employed in this research.The developing history of chaos theory and its application, especially the present researches on chaotic security communication, are reviewed. The researches on chaotic synchronization and present popular topics are discussed widely. The features of chaotic security communication and chaotic encryption based on synchronization are concluded. Finally, a clear study direction is given out in chapter 1.Based on the QR decompose of Jacobi matrix, the principle of computing Lyapunov Exponents (LE) algorithm is studied, and a new calculate program is designed using Matlab 6.5, which can compute the LE and fraction dimension of nonlinear dynamics systems, and the Condition Lyapunov Exponents (CLE) of chaotic synchronization system. Some affect indexes to computing results, such as iteration times, step length, solvers and initial value, are analyzed. How to calculate LE is the theoretical and technical base to study chaotic synchronization control in following chapters.In order to promote the study of chaotic synchronization and modify the performance of synchronization chaotic system, seven performance indexes of synchronization system is proposed, and the relations between control parameters and synchronization performance are discussed. A new multi variable driving error feedback controller is designed, which can realize the synchronization of continuous chaotic systems and hyper-chaotic systems. A new method called linear and nonlinear feedback is put forward to implement synchronization of two discrete systems, andthe synchronization conditions are induced. The simulation verified the correct of this control method.Using adaptive synchronization control approach, based on Lyapunov stability theory and Pecora-Carroll synchronization principle, the synchronization method for a unified chaotic system with certain parameters or uncertain parameters is studied. A scheme of CSK digital security communication based on unified chaotic system is put forward, and the coherent demodulation method is used to recover the bits in the receiver. The theory analysis and value simulation proves that it has good security performances and strong capability against interfere.After the relations between chaotic system and tradition encryption algorithm are compared, we gives out the conception of Safe Chaos and the safety conditions for Safe Chaos. The principle of chaotic sequence encryption is analyzed. After discussing the statistics performances of Logistic chaos map, a data encryption module and an encryption algorithm are designed based on Logistic chaotic map. By using modularization method and multi-threading technology, the encryption software is exploited on the platform VS.Net. It can be used for encrypt static files, such as text, data, and picture.A new network synchronization method called equal interval diving is advanced, and a new data stream encryption scheme is designed through combining 3DES with chaotic algorithm. The real-time transfer protocol library based on adaptive communication environment is realized. Speech encryption transfer over network is implemented. It has many characteristics such as fast encryption velocity, small transmission delay, strong anti-attack capability and high secure performance, and it can be applied to some high safe situations, such as military communication.更多还原