混沌反同步研究及其在保密通信中的应用

【作者】 谢雪平；

【导师】 秦宣云；

【作者基本信息】 中南大学 ， 应用数学， 2011， 硕士

【摘要】 混沌系统的混沌同步与反同步是近年来非线性科学领域研究的热点问题,也是混沌保密通信的关键。本文用理论推导和数值模拟相结合的方法研究了混沌系统的反同步以及混沌在保密通信中的应用。对于阶数相同的混沌系统,先设计了一类主动控制器,把误差系统的项全部抵消,实现了参数已知的Lorenz系统和Chen系统的反同步；然后采用参数自适应辨识与反馈控制的方法,设计出一种自适应控制器,实现了参数未知的Lorenz混沌系统和Lu系统的反同步。对不同阶数的两个混沌系统,先采用降阶的思想,把多余的阶数当成干扰项看待,从而把不同阶数混沌系统的反同步问题转化为相同阶数混沌系统的反同步,结合自适应控制方法,实现了参数未知的超混沌Lorenz系统与新系统的完全反同步,并估计出系统的部分未知参数；然后在不改变系统混沌特性的基础上,用升阶的方法把系统变为相同的阶数,也实现了超混沌Lorenz系统与新系统的完全反同步,并使系统所有的“未知参数”都得到估计。每种方法都用Matlab软件进行数值模拟,并画出反同步的误差图。最后,基于混沌掩盖和混沌参数调制技术,构造了混沌保密通信系统,数值仿真表明,在接收端,有用信号能被有效地恢复出来。更多还原

【Abstract】 The synchronization and anti-synchronization of chaotic systems are hotspots in nonlinear science fields in recent years and also be the key point in secure communication. Using the methods of theoretical derivation and numerical simulation, this dissertation studies the anti-synchronization of chaotic systems as well as the application of chaos in secure communication.For two chaotic systems with the same order, firstly, an active controller is designed to realize the anti-synchronization of Lorenze chaotic system and Chen chaotic system with the known parameter by eliminating the items of erroneous system. Then, using the strategies of adaptive control for parameters and feedback control method, an adaptive controller is designed, which realizes the anti-synchronization of Lorenze chaotic system and Lu chaotic system with the unknown parameters.For two chaotic systems with different order, firstly, using the depressed-order method, we view the redundant order as distractors to translate the problem of anti-synchronization with different orders into the same order. At the same time, combining adaptive control method, the anti-synchronization of hyper-chaotic Lorenze system and the New chaotic system is realized and parts of parameters are estimated. Then, without changing the chaos characteristics of the system, using add-order method, the anti-synchronization of hyper-chaotic Lorenze system and the New chaotic system is also realized, and all of the unknown parameters are estimated. Numerical simulations with Matlab software is carried out for each method and the anti-synchronized charts of the erroneous system are drawn. Finally, the secure communication systems are set up by chaotic masking and chaotic parameter modulation, and the simulation results show that, useful signals can be recovered from the receiver system effectively.更多还原