【作者】 武相军；

【导师】 王兴元；

【作者基本信息】 大连理工大学 ， 计算机应用技术， 2006， 硕士

【摘要】 非线性科学是一门研究非线性现象共性的基础科学,其中混沌理论是非线性科学的一个重要分支。本文利用理论推导和数值模拟相结合的方法研究了混沌的控制、同步以及混沌在密码学中的应用,作者取得的主要创新工作如下: 研究了Chen系统的混沌同步和参数辨识问题。基于Lyapunov稳定性理论,设计了控制器,使得驱动系统和具有未知参数的响应系统渐近地达到同步,并且可以辨识出响应系统的未知参数。改进了Jiang和Huang等设计的同步误差系统的Lyapunov函数的形式,实现了超混沌Chen系统的自同步和异结构同步。 提出了一个新的变形耦合发电机系统,研究了该系统的混沌特性。分别利用反馈(单反馈、双反馈)和非反馈方法实现了变形耦合发电机系统的混沌控制。利用反馈法、激活控制法、全局同步法研究了变形耦合发电机系统的自同步问题。基于Lyapunov稳定性理论、激活控制技术和Gerschgorin定理,解析出系统达到自同步的充分条件。 研究了超混沌R(?)ssler系统的追踪控制问题。基于参考信号设计了控制器,使得超混沌R(?)ssler系统不仅能快速追踪任意给定信号,还可以实现自同步以及异结构同步。 基于状态观测器方法和极点配置技术,设计出一种反同步方法,使得一类混沌系统快速达到了反同步。与其他反同步方法相比,本文的方法简便,易于实现,并且达到反同步时间短。 提出了利用多个一维混沌映射和多个动态S-box的块加密算法。从理论和实践两个层面分析了本文密码系统的安全性。并与Kocarev算法进行了对比,对于选择多少个S-box进行明文加密能获得最佳效果,给出了初步实验结果。 以上研究成果已在《Chaos》上录用1篇,在《物理学报》上发表1篇、录用4篇,在《控制理论与应用》上录用1篇。更多还原

【Abstract】 Nonlinear science is a foundational discipline which concerns the common properties of nonlinear phenomena. Particularly, Chaos theory is one of important subdiscipline of nonlinear science. The research has studied the relative problems of chaos control, chaos synchronization and its application in cryptography using the methods of theoretical derivation and numerical simulation. The main originality in this paper can be summarized as follows:Chaos synchronization and parameters identification problem of two Chen systems is studied. Based on the Lyapunov stability theory, we design the controller which can make the states of the drive system and the response system with unknown system parameters asymptotically synchronized, and identify the system parameters. A new method improving the Lyapunov function of error dynamic of synchronization designed by Jiang and Huang et al. overcomes the limitation of the Lyapunov function having only one form. And the synchronization of two identical systems (two identical hyperchaotic Chen systems) and two different chaotic systems (the hyperchaotic Chen system and the hyperchaotic RQssler system) is achieved.A new modified coupled dynamos system is proposed firstly. The chaotic features of the modified coupled dynamos system are analyzed. The problem of control chaotic behavior of the modified coupled dynamos system is studied. Two different methods, i.e. feedback (one feedback and two feedbacks) and non-feedback methods are used to control chaos in the modified coupled dynamos system. Chaos synchronization of the modified coupled dynamos system is investigated. Three different methods, i.e. feedback, activate control and global synchronization methods are applied in this study. Based on the Lyapunov stability theory, active control technique and Gerschgorin theorem, the sufficient conditions for achieving synchronization of two identical modified coupled dynamos systems are derived.The problem of hyperchaotic Rossler system tracking control is discussed. A controller based on the reference signal is designed. The controller can not only make the Rossler system track any reference signal fast, but can make the hyperchaotic Rossler system synchronize with identical or different chaotic systems.A systematic design procedure to anti-synchronize a class of chaotic systems based on techniques from the state observer design and the pole placement technique is presented. In contrast to the conventional anti-synchronization approaches, the proposed method is rathersimple and convenient to realize anti-synchronization. Furthermore, the rate of achieving anti-synchronization is very fast.A new block encryption algorithm using multiple one-dimension chaotic maps and active S-boxes is proposed. The crypto-analysis of this algorithm has also been given in this paper. We contrast the proposed cryptosystem with Kocarev’s algorithm. The preliminary experimental result about the number of S-box encrypting the plaintext for optimum effect is presented.In the studies above, one paper has been accepted by Chaos, one published and four accepted by Acta Physica Sinica, and one accepted by Chinese Journal of Control Theory and Application.更多还原