【作者】 王勇；

【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同步控制中的相关问题，取得了如下成果： 首先分析了三维自治混沌系统之间的异结构反同步问题，并采用主动控制方法实现了一类三维自治混沌系统的反同步。该控制器形式简单，易于实现，且收敛速度快，控制范围宽，可以进一步推广到含更多个状态变量的系统之间的反同步问题。通过对Lorenz系统，Chen系统和Lü系统相互之间的两两异结构反同步的仿真实验，验证了该控制器的有效性。 其次研究了新型混沌系统——类Lorenz系统的同步控制问题。基于Lyapunov稳定性理论，设计了自适应控制器和参数更新规则，理论证明了该控制器可实现类Lorenz系统的自同步和类Lorenz系统与R(o|¨)ssler系统的异结构同步，并且可以辨识出系统中的未知参数。数值模拟进一步验证了所提出方案的有效性。 随后分析了自治混沌系统的投影同步问题。基于线性系统的稳定判定准则，提出一种新的线性分离的同步方法，并采用该方法实现了Lorenz系统，R(o|¨)ssler系统和超混沌Chen系统的投影同步。该方法简单，鲁棒性强，而且不需要设计Lyapunov函数；能实现一类非线性系统的投影同步，且不要求系统必须是部分线性的。 最后研究了自治混沌系统的延迟同步问题，基于非线性观测器方法和极点配置技术，设计了一类混沌系统的延迟同步策略，使得一类混沌系统快速达到了延迟同步。并用该方法实现了Newton-Leipnik混沌系统和超混沌Chen系统的延迟同步。数值模拟进一步验证了所提出方案的有效性。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 subdisciplines of nonlinear science. The relative problems of chaos synchronization control are studied in this thesis using the methods of theoretical derivation and numerical simulation. The main achievements contained in the research are as follows:Firstly, anti-synchronizations of three-dimensional autonomous chaotic systems are analyzed. The anti-synchronizations of a class of three-dimensional autonomous chaotic systems i.e. Lorenz system, Chen system and Lu system with one another are achieved via active control. The form of the controller is simple and implemented easily. The convergence rate of the controller is very fast and the control range is very broad.Secondly, the synchronization control of a new chaotic system called Lorenz-like system is investigated. Based on the Lyapunov stability theory, an adaptive controller and the parameters update rule are designed. It is proved that the controller and update rule not only can achieve self-synchronization of Lorenz-like system but also can make the Lorenz-like system asymptotically synchronize with the Rossler system, and further identify the uncertain system parameters.Thirdly, projective synchronizations in autonomous chaotic systems are presented. Based on the stability criterion of linear systems, a new approach for constructing chaotically projective synchronization is proposed. The projective synchronizations of Lorenz system, Rossler system and hyperchaotic Chen system are achieved using the linear separation method. The proposed method is not only simple and implemented easily, but also need not design Lyapunov function and enables to realize projective synchronization in a general class of nonlinear systems without the limitation of partial-linearity.Lastly, a systematic design procedure to lag-synchronize a class of chaotic systems based on techniques from the state observer design and the pole placement technique is presented. The lag synchronizations of Newton-Leipnik system and hyperchaotic Chen system are achieved by using nonlinear observer control. Numerical simulations are provided for illustration and verification of the proposed method.更多还原