【作者】 段朝锋；

【导师】 王兴元；

【作者基本信息】 大连理工大学 ， 计算机应用技术， 2005， 硕士

【摘要】 本文利用理论推导和数值模拟相结合的方法研究了混沌控制理论及混沌应用中的相关问题,取得了如下成果: 利用受控Chen系统,基于镜像操作的方法,发现Chen吸引子是由左、右两个吸引子组成的复合结构,且左、右吸引子均可由极限环生成。采用一维时间序列相空间重构技术和系统混沌的定量判据准则,揭示出Chen系统从规则运动转化到混沌运动所具有的普适特征:Chen系统可通过Pomeau-Manneville途径走向混沌,且其间歇性与Hopf分岔和倍周期分岔有关,在这些途径上可观察到类Chen吸引子、Chen系统和Lorenz系统之间的过渡吸引子和类Lorenz吸引子。 设计了识别不确定Lorenz系统和R(o|¨)ssler系统未知参数的观测器,提出了控制这两个系统的线性反馈控制策略。数值模拟结果表明:观测器可以有效地标识未知参数;选取不同的目标参数,既可以使Lorenz系统和R(o|¨)ssler系统稳定在不同周期轨道上,也可以稳定在任意目标点上。 提出了一类基于线性状态观测器的混沌或超混沌同步方案,并将其应用到保密通信中。对观测器的理论分析表明,该方案的同步误差收敛速率是由观测器的增益参数θ来决定的;θ越大,同步误差的收敛速率越快。通过对R(o|¨)ssler系统的仿真研究,验证了该方案的有效性。 对E.Alvarez在1999年提出的混沌密码方案进行了改进:以混沌系统的控制参数和初始状态为密钥,迭代混沌系统产生一比特链C_i,在该比特链中搜索明文分组,记下迭代次数n_i作为密文分组。改进算法避免了原密码方案中的若干弱点,增强了原密码系统的安全性。更多还原

【Abstract】 The relative problems of chaos control theory and chaos application are studied in this thesis using the methods of theoretical derivation and numerical simulation. The main achievements contained in the research are as follows:Utilizing the controlled Chen system, and according to the method of the mirror operation, the fact is found that Chen attractor is a compound structure which is obtained by merging together two simple attractors, i.e. the left-attractor and the right-attractor. By using phase space reconstruct technique from a time series, the general features of Chen system transforming from regularity to chaos are found: chaotic patterns of Chen system may emerge out of Pomeau-Manneville route and its intermittence have something to do with Hopf bifurcation and period-doubling bifurcation.Two effective observers are produced to identify the unknown parameters of uncertain Lorenz and Rossler systems respectively. Moreover, two linear feedback control strategies are proposed for controlling the two uncertain systems. Numerical simulations show that the observer can identify the unknown parameters effectively, and the proposed controllers can enable the controlled chaotic system to approach any desired points or periodic orbits.A linear state observer based synchronization scheme for a class of chaotic systems is presented, and this scheme is applied to secure communication. The analysis result shows that the system’s convergence rate of the synchronization error depends on the parameter 0 of observer gain, in the sense that the larger the value of θis the faster the convergence.The chaotic encryption scheme presented by E.Alvarez in 1999 is improved: select the control parameters and the initial condition of chaotic system as the secret key, generate a bit chain Ci from the chaotic orbit, find the position at which a plaintext block appears in the Ci. Then record the number of the iterations of the chaotic map ni as the cipher block. Several weaknesses are voided in the improved scheme, which strengthens the security of the E.Alvarez cryptosystem.更多还原