【作者】 胡满峰；

【导师】 徐振源；

【作者基本信息】 江南大学 ， 轻工信息技术与工程， 2008， 博士

【摘要】 由于其在不同科学领域,特别是在混沌保密通信领域的广泛潜在应用,混沌同步吸引了越来越多的科学家和工程技术人员的广泛重视。本文主要研究和混沌投影同步相关的一些问题,包括控制方法,在混沌保密通信系统、系统参数辨识等方面的应用,主要工作和成果如下:简单介绍了混沌的四个发展阶段,描述了常用的混沌同步方法,简要说明了混沌同步技术在混沌保密通信中的关键性。线性自适应反馈控制技术用来实现预期投影因子的投影同步。自适应反馈控制技术首次用来控制具有部分线性结构的耦合混沌系统的投影因子,从而达到控制投影同步最终状态的目的。应用这种控制方法实现的投影同步技术来设计混沌保密通信系统,对所提方案作了理论上的严格证明。脉冲控制技术用来实现两个混沌系统的完全同步和投影同步。首先,应用已有的脉冲微分方程理论结果,对脉冲控制系统进行分析和设计,提出了一个新的混沌同步方法并应用到Lorenz混沌系统。然后,应用脉冲微分方程理论里的比较系统方法,首次用来研究部分线性系统的投影同步问题。提出了驱动-响应复杂动力学网络模型,并研究了其上的网络投影同步。理论上给出了实现网络投影同步的充分条件,并且应用牵制控制方法实现对网络投影同步的控制。提出了网络投影聚类同步的概念。在驱动-响应复杂动力学网络模型里研究了实现网络投影聚类同步的充分条件,并且应用牵制控制方法实现对网络投影聚类同步的控制。提出了全状态混合投影同步的概念。利用Lyapunov第二方法,理论上给出了连续型混沌系统之间的全状态混合投影同步实现的判别条件、离散混沌映射之间的全状态混合投影同步控制器设计的一般形式。值得一提的是全状态混合投影同步的概念包含了完全同步、反同步,全状态投影同步,部分同步,错位同步作为其特例。应用全状态混合投影同步方法辨识混沌系统未知参数。理论上给出了驱动系统参数未知情况下两个混沌系统实现全状态混合投影同步的自适应控制器,该控制器同时保证可以正确辨识出未知参数,并具有一定的抗噪能力。研究了两个混沌系统参数皆未知的情况下全状态混合投影同步问题。两个混沌系统的维数可以相同,也可以不同。对于不同维数的两个混沌系统,提出了降阶全状态混合投影同步、增阶全状态混合投影同步的概念。理论上给出了一般的自适应控制器的表达式。数值研究证实了混合投影同步的存在性。针对一个具体的具有部分线性结构的混沌系统,数值实验发现了混合投影同步现象是存在的,从而支持了全状态混合投影同步概念的合理性。研究了更一般的Q-S同步问题。利用矩阵的广义逆理论和Lyapunov稳定性理论,给出了实现更一般的Q-S混沌同步的控制器设计方法,所涉及到的驱动-响应系统可以具有不同的结构,甚至可以具有不同的维数。该方法的特点在于可以实现事先给定的系统状态可观测变量之间的同步。以上所有的理论方法都做了相应的数值实验,给出了相应的数值结果,验证了理论方法的正确性和有效性。更多还原

【Abstract】 Due to its wide-scope potential applications in various scientific fields, especially in chaotic secure communication, the problem of chaos synchronization has attracted increased attention from scientists and engineers. This dissertation is devoted to study on the related problem of projective synchronization, including the control scheme and some application in chaotic security communication and parameters identification. The author’s main research work and contributions are as follows:In this dissertation, the four stages of development in chaos theory are briefly introduced, some existing chaos control approaches are surveyed and the key role of chaos synchronization played in chaotic communication scheme is described.Linear adaptive feedback controller is first designed to direct the scaling factor, characterized the synchronized dynamics of projective synchronization in partially linear chaotic systems, onto a desired value. Based on the adaptive projective synchronization, a secure communication scheme is proposed and proved rigorously.Impulsive control approach is adopted to realize the chaossynchronization and projective synchronization, respectively. First, we derive some conditions for (asymptotic) stability of impulsive control systems with impulses at fixed times based on a existing theory result of impulsive differential equations, and the results are used to design impulsive synchronization for Lorenz systems. Then, we first use the impulsive control approach to control the scaling factor of projective synchronization onto any desired scale.A drive-response dynamical networks model is presented and its projective synchronization is investigated. The sufficient condition of projective synchronization in drive-response network is derived. Because the scaling factor is difficult to be estimated, pinning control techniques are used to direct the scaling factor onto the desired value.The definition of projective cluster synchronization in drive-response dynamical networks is introduced and the sufficient condition on this novel synchronization scheme is derived. For the same reason, we use pinning control methods to control the scaling factors onto the desired values.The definition of full state hybrid projective synchronization is first presented. Based on the Lyapunov stability theory, a general controller is designed for full state hybrid projective synchronization of continuous-time chaotic systems and discrete-time chaotic maps, respectively. It is worthy noting that our full state hybrid projective synchronization includes complete synchronization, anti-synchronization, full state projective synchronization, partial synchronization and mismatched synchronization as special cases.Estimating the model parameters of the drive system based on the full state hybrid projective synchronization scheme is presented. The adaptive controller is designed to realize the full state projective synchronization and to identify the unknown parameters, simultaneously. In addition, the proposed adaptive controller is quite robust against the effect of noise.The full state hybrid projective synchronization of chaotic and hyper-chaotic systems with fully unknown parameters is further investigated. A unified adaptive controller and parameters update law is designed for achieving full state hybrid projective synchronization between two chaotic systems with the same and different order based on the Lyapunov stability theory. Especially, for the case of two chaotic systems with different order, two new concepts, reduced order full state hybrid projective synchronization and increased order full state hybrid projective synchronization, are also studied.The existence of hybrid projective synchronization in a five dimensional chaotic systems is experimentally found, which shows that the definition of full state hybrid projective synchronization presented before is reasonable.The general problem of Q-S synchronization between chaotic and/or hyper-chaotic systems is studied. We propose a general controller for Q-S synchronization of chaotic and/or hyper-chaotic systems based on the Lyapunov stability theorem and the theory of generalized inverse matrix. The drive and response systems studied in this part can be strictly different dynamical systems (including different dimensional systems). In addition, the proposed controller can realize the Q-S synchronization with respect to the freely selected observable variables Qi and S_i.For each proposed theory result, we give numerical simulations to illustrate the effectiveness in this dissertation.更多还原