节点文献
混沌系统的若干同步方法研究
Study on Some Synchronization Methods of Chaotic Systems
【作者】 单梁；
【导师】 王执铨；
【作者基本信息】 南京理工大学 ， 控制科学与工程， 2006， 博士
【摘要】 混沌是一种特殊复杂的非线性系统，普遍存在于自然界中。由于它的初值极端敏感性、高度随机性以及非线性方程的确定性，一直受到研究者的极大关注。混沌同步作为混沌科学的一个重要研究方向，自九十年代以来发展迅速，并在保密通信、图像处理等应用方面取得了可喜的进展。本文基于非线性系统控制理论，研究了连续时间混沌系统、分段线性混沌系统的若干同步控制方法。论文的主要研究成果如下：(1)提出了统一混沌系统的广义同步、脉冲时滞同步和SDRE同步三种方法首先，提出了统一系统的广义同步方法。通过控制参数的不同选择，实现了状态完全同步和广义同步两种形式，该方法在保密通信中具有更高的安全性。然后，提出了统一系统的脉冲时滞反馈同步方法，同等脉冲信号强度下该方法加快了同步速度。最后，提出了统一系统的SDRE同步方法，具有给定稳定度的状态调节器改善了同步的动态性能。(2)提出了含不确定参数的Liu混沌系统的自适应同步和变结构Backstepping同步两种方法通过研究Liu混沌系统的单变量驱动和状态观测器两种同步方法，深入分析了Liu系统的结构特点。在此基础上，提出了自适应同步方法，设计了两种控制器，分别实现了线性项和非线性项不确定参数的辨识。然后，提出了变结构Backstepping同步方法，该方法系统性强，构造全局Lyapunov函数方便，成功实现了未知参数辨识和系统快速同步。(3)为增强同步控制方法的通用性，提出了广义Lorenz系统的鲁棒H_∞模糊同步方法广义Lorenz系统的鲁棒H_∞模糊同步方法在噪声干扰和系统参数不确定的情况下，仍具有较好的同步性能。该同步策略和控制模型适用于满足GLCF形式的一系列连续混沌系统。(4)提出了异结构Liu-Genesio系统的Backstepping同步和超混沌Liu-R(?)ssler系统的Active同步方法首先，提出了Liu混沌系统和Genesio混沌系统的Backstepping同步方法，设计了单一驱动和多驱动两种同步控制器，实现了Q-S同步形式，简化了控制器的结构。然后，提出了超混沌Liu系统和超混沌R(?)ssler系统的Active同步方法，并建立了状态完全同步、广义同步和滞后同步的统一控制模型。(5)提出了一个新的分段线性混沌系统的基于LMI的反馈同步方法在分析了新的分段线性混沌系统结构特点，研究了线性反馈和状态观测器两种同步方法的基础上，提出了一种基于LMI的反馈同步方法。转换后的分段混沌系统具有整体形式，只需利用LMI求取控制参量的可行解，避免了按分段函数讨论同步条件的麻烦，为一类分段混沌系统的同步控制研究提供了新思路。最后总结分析了论文在混沌同步研究中的成果和不足，并指出了进一步的研究方向。
【Abstract】 Chaos is a kind of special complicated nonlinear system, which is ubiquitous innature. Since it has the characteristics of sensitivity to initial values, high randomicityand certainty to nonlinear equations, chaos attracts great attentions from investigators.Chaotic synchronization is an important research aspect in chaotic science. Since1990, chaotic synchronization has achieved rapid development, its application insecure communications and image processing progress remarkably as well.Based on control theories of nonlinear systems, this dissertation studies thesynchronization control methods of continuous-time and piecewise linear chaoticsystems. The main contributions are listed as follows:(1) Three synchronization methods, including generalized synchronization,impulsive delay feedback synchronization and SDRE synchronization, are proposedfor unified chaotic system.Firstly, the generalized synchronization method of unified system is proposed. Bychoosing different control parameters, the state completed synchronization (CS) andgeneralized synchronization (GS) of unified system are achieved. This method hashigher security in secure communications. Secondly, the impulsive delay feedbacksynchronization method is presented. It makes the synchronization speed quicker atthe same intensity of impulsive signals. Finally, the SDRE synchronization method ofunified system is brought forward. The state adjustors with given stability improve thesynchronization dynamic performance.(2) Adaptive synchronization and variable structure Backstepping synchronizationmethods are proposed for Liu chaotic system with uncertain parameters.After investigating the single variable driving synchronization and state observersynchronization methods, the structure characteristics of Liu chaotic system aredeeply analyzed. Based on it, the adaptive synchronization approach is presented.Two kinds of controllers are designed for identifying unknown linear or nonlinearparameters. Then the variable structure Backstepping synchronization method is putforward, which has strong systematization, easily constructs global Lyapunovfunctions and quickly realizes unknown parameters identification andsynchronization.(3) To study the universal synchronization control method, the robust H_∞fuzzysynchronization method is proposed for generalized Lorenz systems.With the noise disturbance and uncertain parameters, the robust H_∞fuzzy synchronization method for generalized Lorenz systems keep satisfiedsynchronization performance. The synchronization strategy and control models are fitfor all continuous chaotic systems which satisfy GLCF format.(4) Backstepping synchronization and Active synchronization methods are proposedfor different structure chaotic systems: Liu-Genesio systems and hyperchaotic Liu-R(?)ssler systems.Firstly, the Backstepping method is put forward to synchronize Liu system andGenesio system, which designs the single driving and multi-driving controllers aredesigned, receives Q-S synchronization format and simplifies the structures ofcontrollers. Secondly, the active synchronization method is presented for hyperchaoticLiu system and hyperchaotic R(?)ssler system. Moreover this method establishes theunified control models for completed synchronization, generalized synchronizationand delayed synchronization.(5) Feedback synchronization method based on LMI is proposed for a new piecewiselinear chaotic system.After analyzing the structure characteristics of the new piecewise linear chaoticsystem, studying linear feedback synchronization method and investigating stateobserver synchronization method, the feedback synchronization method based onLMI is proposed. The global format of transformed piecewise chaotic systems onlyneeds seek feasible solutions by LMI. So the method provides a new thought forsynchronizing a class piecewise chaotic systems.Finally, some open issues on synchronization control of chaotic systems as wellas the future work are pointed out.