混沌系统的同步控制研究

【作者】 徐勇；

【导师】 李军；

【作者基本信息】 南京理工大学 ， 控制理论与控制工程， 2007， 硕士

【摘要】 混沌是一种不规则的复杂运动形式，广泛地存在于各个领域。由于混沌运动表现出的对初值的极端敏感性、高度随机性以及非线性方程的确定性，使得它一直受到人们的广泛关注。混沌同步作为混沌研究的重要方向，在保密通讯、图像处理等应用方面取得了可喜的进展。本文的主要研究内容如下：(1)对Liu混沌系统的同步方法进行了研究，分别构造了Liu系统在无干扰和有干扰下的同步观测器。首先采用简单的线性反馈实现了Liu系统的同步；接着针对无扰动和有扰动的情况，分别提出了一种Liu系统的同步观测器；然后实现了含有未知参数的Liu系统自适应同步；最后提出了Liu系统的一种变结构Backstepping同步方法。(2)分析了一个新的Qi系统的结构特性，提出了Qi系统的两种线性反馈同步方法和参数未知时的自适应同步方法。在分析了Qi系统的结构特点的基础上，提出了Qi系统的单变量驱动同步方法；提出了Qi系统的两种线性反馈方法，并进行了对比分析；最后提出了Qi系统参数不确定的自适应同步方法。(3)异结构混沌系统的同步研究。基于追踪控制理论，实现了Liu系统与统一混沌系统的追踪同步；采用改进的自适应同步方法实现了Qi系统和统一系统的同步；最后将上述两种方法拓展到超混沌系统。更多还原

【Abstract】 Chaos is an irregular complicated dynamical behavior, which is ubiquitous in everyfield. In virtue of its characteristics such as sensitivity to initial values, high randomicityand certainty to nonlinear equations, chaos attracts great attention of people. Chaoticsynchronization is an important research aspect in chaotic science, which has receivedrapidly development in the application of secure communications and image processing.The main contributions of this paper are list as follows:(1) Synchronization study of Liu chaotic system. For the Liu systems withdisturbance or non-disturbance, two state observers are constructed respectively. Firstly,carries out synchronization of Liu System successfully with simple linear feedback. Thentwo kinds of state observer synchronization approaches are proposed to the Liu systemswith disturbance or non-disturbance. And then an adaptive synchronization approache isproposed to the Liu systems with unknown parameters. Finally backsteppingsynchronization method is put forward to Liu system with uncertain parameters.(2) The structure Characteristics of the new-proposed Qi chaotic system are analyzed,and two kinds of linear feedback synchronization are presented. After analyzing thestructure characteristics of the new Qi chaotic system, synchronization methods of Qisystem such as the single variable drive synchronization method and two kinds of linearfeedback synchronization methods are presented. Then an adaptive synchronizationapproache is proposed to the Qi systems with unknown parameters.(3) Study for chaotic synchronization with diverse structures. Based on the theory oftracking control, a tracking synchronization approache is put forward to synchrize Liusystem and unified chaotic system. Then a modified adaptive synchronization method ofQi system and unified chaotic system is presented. Then the two differentsynchronization approaches are extended to hyperchaotic systems.更多还原