文档介绍：华中科技大学硕士学位论文
摘要
最近几十年来,混沌控制的研究受到了人们越来越多的关注。目前,混沌作为
一门新兴科学,已经被广泛应用于保密通信、信号处理等领域。混沌系统的分析与
控制也因此成为非线性科学领域一个富有挑战性的课题,具有巨大的应用前景。
混沌学的控制方法有很多种。本文选取的是当前极具吸引力的脉冲控制方法对
受扰动的统一混沌系统进行分析和研究。脉冲控制方法具有控制所需能量少、控制
响应速度快的特点。
论文首先对国内外关于混沌控制的研究和发展的现状进行了综述,然后在介绍
了几种典型的混沌系统后简述了有关混沌系统的脉冲控制的研究现状,接着系统的
展示了作者在混沌系统的脉冲控制方面的研究成果。
在混沌系统的脉冲镇定方面首先介绍了受脉冲控制的混沌系统鲁棒镇定的基本
知识,然后运用 Lyapunov 函数给出受不确定扰动的统一混沌系统达到脉冲鲁棒镇定
的充分条件,并且运用数值仿真说明了给出的条件的有效性。
在混沌系统的脉冲鲁棒同步方面首先介绍了混沌系统同步的基本知识后,运用
脉冲系统的比较定理和 Lyapunov 函数给出受不确定扰动的两个统一混沌系统达到脉
冲鲁棒同步的充分条件,最后也运用数值仿真说明了给出的条件的有效性。
关键词:混沌; 脉冲控制; 鲁棒稳定性; 混沌同步; Lyapunov 函数
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华中科技大学硕士学位论文
Abstract
These years, more and more experts are interested in chaos. Recently, chaos has
extensive and essful applications as a burgeoning technology in many fields such as
munication and signal processing et al. So chaos has been a challenging subject
in the area of nonlinear control.
Nowadays there are many methods to research on choas. This thesis introduces the
impulsive approach to control the unified chaos system with uncertain disturbance. This
approach is easier to control and faster to response.
Firstly we introduce the background of the thesis and the development of chaos. After
we summarize the typical chaotic systems and the impulsive control of the chaotic systems,
the research on the unified chaos system is discussed.
We introduce the basic theory of impulsive control and then put forward a impulsive
control method to obtain the robust stability of a disturbed unified chaotic system by
employing Lyapunov function, and finally we have a simulation to show the effectivity of
the proposed approach.
The robust synchronization of two disturbed unified chaotic systems is discussed also.
We get the condition to make them robust asymptotic synchronization based on the theory
pare principle of the impulsive system and Lyapunov function. And numerical
simulation is given.
Key words: Chaos; Impulsive control; Ro