【作者】 赵国辉；

【导师】 舒永录； 朱长荣；

【作者基本信息】 重庆大学 ， 应用数学， 2011， 硕士

【摘要】 混沌动力学是一门新兴的学科,混沌本身是不稳定的,对初值非常敏感。混沌吸引子的存在性由两个条件确定:一是有吸引域,保证吸引子的存在,二是在吸引子上存在混沌行为。本文围绕非线性动力系统的混沌系统的控制与同步问题进行了深入的研究与探讨。主要包括以下几个方面的内容:第一章,介绍了混沌系统的背景和现状。第二章,阐述了混沌的定义,以及混沌动力学反馈控制与同步的基本概念和基本理论。第三章,本章讨论最近提出的一个新混沌系统的控制与同步问题。在系统的控制中,设计了在参数已知时的两个线性反馈控制器,得到了将系统控制到任意不稳定平衡点的充分条件,并且对控制前后的情况用图像作了比较,形象地说明了控制的有效性和科学性;在系统的同步中,设计了两个同步问题:1.在参数已知时,设计了两个非线性控制器,得到了实现全局完全同步的充分条件;2.在参数未知时,设计了三个非线性控制器和参数估计的自适应律,得到了实现全局完全同步的充分条件。理论与仿真结果都验证了本章结论的有效性。第四章,本章讨论最近提出的一个新超混沌系统的控制及同步问题。在参数已知时,设计了一个线性反馈控制器和一个速度反馈控制器,得到将系统控制到不稳定平衡点的充分条件,并且对控制前后的情况用图像作了比较,形象地说明了控制的有效性和科学性;在参数未知的时候,科学地设计了四个非线性控制器和参数估计的自适应律,得到了实现全局完全同步的充分条件。理论与仿真结果都验证了本章结论的有效性和科学性。第五章,给出了的工作总结和混沌研究及应用的展望。更多还原

【Abstract】 Chaotic dynamics is a new subject, chaotic is unstable itself, it is sensitive to the initial value. A chaotic attractor is ensured by two things, one is that the system has a trapping region which guarantees the existence of an attractor, the other is that the system displays chaotic behavior on the attractor. The thesis mainly focuses on the control and synchronization of chaos of nonlinear system. The main content is depicted as follows:In chapter 1, background and study conditions of chaos are introduced.In chapter 2, the basic theory and the definition of the control and synchronization for chaos dynamics are presented.In chapter 3, we consider the issues of chaotic control and chaotic synchronization for a new presented chaotic system. In the chaotic control, when the parameter is known, two linear controllers are designed and a sufficient condition is presented to stabilize the chaotic system to any unstable equilibrium points, control the pre-image and control over their images are compared to more graphically illustrate the control of an effective and scientific. Meanwhile, In the chaotic synchronization, two different issues of chaotic synchronization are designed: 1. when the parameter is known, two nonlinear controllers are designed and a sufficient condition is presented to assure globally complete synchronization; 2. when the parameter is unknown, three nonlinear controllers are designed, an adaptive role for estimating the unknown parameter is found and a sufficient condition is presented to assure globally complete synchronization. Theoretical analysis and numerical simulation show that the design is feasible.In chapter 4, we consider the issues of hyper-chaotic control and hyper-chaotic synchronization for a new presented hyper-chaotic system: In the hyper-chaotic control , when the parameter is known, two controls are designed scientifically, One is linear controller, the other is velocity feedback controller, and sufficient conditions are presented to stabilize the chaotic system to any appointed unstable equilibrium points, control the pre-image and control over their images are compared to more graphically illustrate the control of an effective and scientific. In the hyper-chaotic synchronization, when the parameter is unknown, four nonlinear controllers and an adaptive role for estimating the unknown parameter are designed scientifically, and a sufficient condition is presented to assure globally complete synchronization. Theoretical analysis and numerical simulation show that the design is feasible.In chapter 5, we give the summary of the work and the prospect of research and application of chaos.更多还原