Constructing hyperchaotic systems at will

Over the last two decades, chaotification has received increasing attention from various communities of science and engineering. This paper aims at developing a unified chaotification framework for generating desired higher‐dimensional dissipative hyperchaotic systems by using a single‐parameter controller. The main idea is to use a block diagonal matrix in the design of the nominal system, so as to construct a desired hyperchaotic system. Specifically, the proposed scheme is to assign desired closed‐loop poles to the controlled system, allocating the corresponding numbers of eigenvalues with positive real parts at two types of saddle‐focus equilibria. For the non‐degenerate case, the number of positive Lyapunov exponents of the controlled system is given by the largest number of positive Lyapunov exponents of the desired hyperchaotic system. Two representative examples are given to illustrate and verify the proposed design method. Finally, the digital signal processor is employed to implement the above 10‐dimensional hyperchaotic systems, and the experimental observation is also given. Copyright © 2015 John Wiley & Sons, Ltd.     

基于直流电机系统的广义同步混沌化

本文对非同构系统的混沌状态同步问题进行了讨论,并对单变量单向及双向耦合和多变量耦合对各自系统动力学行为产生的影响进行了对比分析.基于广义同步混沌化的驱动控制原理,利用经典的Lorenz系统产生混沌信号去驱动永磁直流电机,使电机转速工作在混沌状态,并得到了同步控制器的解析表达式.最后,进行系统数值仿真,验证了同步控制的有效性.     

On Chaotification of Discrete Hamilton Systems

The chaotification problem of discrete Hamilton systems in one dimensional space is investigated and corresponding chaotification theorem is established. Feedback control techniques is used to make arbitrary discrete Hamilton systems chaotic, or enhance its existing chaotic behaviors. By designing a universal controller and combining anti-integrable limit it is proved that chaos of the controlled systems is in the sense of Devaney. In particular, the systems corresponding to the original systems and designed controllers are only required to satisfy some mild assumptions. Moreover, the range of the coefficient of the controller is given.     

基于时延反馈的Boost变换器混沌化控制

时延反馈是一种混沌或混沌化控制的有效方法,本文建立了电流模式控制DC-DC Boost变换器输出电压时延反馈混沌化模型,以非线性微分方程时延反馈混沌化理论为基础,研究了控制策略中不同控制参数对变换器混沌化的影响,并给出了控制参数的选择依据.时延反馈混沌化方法控制范围宽,结构简单且设计过程系统性强.同时,验证了变换器系统的混沌化对EMI的有效抑制,为相关混沌研究的工程应用提供了实现思路.     

两自由度非线性隔振系统线谱混沌化控制技术研究

线谱混沌化是提高潜艇声隐身性能的主要手段,但难以实现小振幅下的持续混沌化;同时,非线性隔振系统由于多个吸引子共存,混沌化品质依赖于初始条件和系统参数。为此,利用开环加非线性闭环方法研究两自由度非线性隔振系统的吸引子迁移和线谱混沌化。建立两自由度非线性隔振系统的动力学方程并分析其全局性态,得到系统的全局分岔特性及吸引子共存规律;通过开环加非线性闭环方法实现不同吸引子之间的迁移控制,使系统在不同初始条件下始终运行于基础振动最小的混沌吸引子上;利用开环加非线性闭环耦合方法实现驱动系统和响应系统之间的广义混沌同步,使系统在不同参数下始终处于小振幅持续混沌运动。仿真结果表明该方法具有可行性和稳定性,能实现隐匿线谱信息和保持隔振性能的双重功能。     

模糊双曲模型的混沌反控制

针对模糊双曲模型(FHM)的混沌反控制问题，提出一种新的反控制方法，即采用非线性反馈与脉冲控制相结合的方法使其混沌化．从理论上严格地证明了使用该方法产生的混沌满足Devaney的定义．进而，研究了系统模型未知时的混沌反控制方法，并通过计算机仿真验证了理论分析的正确性．     

机械振动系统混沌化控制

根据混沌的本质,对工程中一类在周期激励力作用下的振动问题,将其动力字方程进行无量纲化后,采用传统的跟踪控制的方法,使其跟踪一种During系统从而混沌化。根据出现混沌的必要条件（M6lnikov判据）设计控制参数,对共振频率下和最大转速情况进行仿真计算,实现了在一定的频率范围内对振动系统进行混沌化的过程。将无控制和经过混沌化控制2种情况进行比较发现：在共振频率下,无控制情况下输出振幅是混沌化后输出振幅的近60倍,说明了这种混沌化控制方法对控制共振的有效性。     

基于逻辑斯蒂映射的电机混沌反控制

为了提高工业搅拌的搅拌效率,本文以应用在工业搅拌实验中的永磁直流电机为例,提出了一种基于逻辑斯蒂(Logistic)映射的混沌反控制方法,通过转速反馈,诱导电机进入混沌运行.计算机仿真表明,在这种控制下的工业搅拌装置,可以有效地提高搅拌效率,降低搅拌时间等.同时,本文分析了混沌搅拌中的混沌特性,为进一步的实际应用打下了理论基础.     

Chaotifying a stable map via smooth small‐amplitude high‐frequency feedback control

In this paper, the problem of making a stable map chaotic by using smooth small‐amplitude high‐frequency feedback control is studied. The controlled map is mathematically proven to be chaotic in the sense of Li and Yorke. To demonstrate the practical usefulness of the proposed method, it is applied to a feedback boost switching regulator model operating in discontinuous mode. Copyright © 2000 John Wiley & Sons, Ltd.     

基于跟踪的混沌反控制

为了实现连续系统的混沌反控制,研究了基于跟踪已知混沌系统的混沌反控制方法,设计了非线性控制器使连续系统跟踪混沌输入信号,从而使非混沌系统产生与混沌输入信号拓扑共轭的混沌现象。采用的方法中控制器的参数选择比较灵活,为控制器的设计带来很大方便。同时,该法无需计算被控系统的Lyapunov指数,大大减少了混沌反控制的复杂计算。通过跟踪Lorenz混沌系统和超混沌Chen系统说明了该方法的设计过程,仿真结果表明了该方法的有效性和快速性。