一类四维混沌系统切换混沌同步

构建了一类可切换的四维混沌系统，通过选择器实现这类系统间的随机切换.简要地分析了四维混沌系统平衡点的性质、混沌吸引子的相图和Lyapunov指数等特性，并设计了实现四维混沌系统切换的实际电路.利用非线性反馈控制方法实现了这类系统与其中某个系统之间的切换混沌同步.根据系统稳定性理论，得到了非线性反馈控制器的结构和系统达到混沌同步时反馈控制增益的取值范围. 关键词： 非线性反馈 混沌同步 四维混沌系统     

利用锯齿非线性混沌化稳定的Takagi-Sugeno (TS) 模糊系统

研究了利用任意小幅值的状态反馈控制来混沌化稳定的Takagi-Sugeno (TS) 模糊系统问题。所用状态反馈控制器是系统状态的锯齿函数。我们应用改进的Marotto定理从数学上证明了受控系统在Li-Yorke意义下是混沌的。特别地，给出了计算混沌化参数的解析公式。最后一个数值例子被用来说明所提的理论结果。     

热对流环中混沌的控制技术

本文应用谱展开法将描述一维热对流环中流体层流自然对流循环的质量、动量和能量守恒方程化为一组无穷维的常微分方程组;其一阶模态为自封闭的Lorenz方程。应用线性与非线性反馈控制,通过数值模拟发现混饨的线性和非线性反馈控制技术可以明显改变热对流环中流体的运动特征,达到我们所希望的流型,即增强混沌或抑制混沌。     

Genesio-Tesi和Coullet混沌系统之间的非线性反馈同步

分析了Genesio-Tesi 系统和Coullet系统的特性，表明两系统拓扑不等价但奇异吸引子结构具有一定相似性，而且采用非线性反馈控制方法实现了两系统之间的混沌同步.根据系统 的稳定性理论，得到了非线性反馈控制器的结构和反馈控制增益的取值范围.数值仿真的结 果表明理论分析的正确性. 关键词： 非线性反馈控制 Genesio-Tesi系统 Coullet系统 混沌同步     

实现连续时间标量混沌信号同步的自适应控制方法

以能大范围实现连续时间标量(超)混沌信号同步控制的非线性反馈控制器为基础,在一定的假设前提下,设计了一个自适应控制器.连续时间混沌系统的标量输出在自适应控制器的控制下,不仅能大范围同步于给定参考标量混沌信号,而且解决了非线性反馈控制器中控制系数的估计问题,又使同步控制具有一定的鲁棒性.计算机模拟结果也证实了自适应控制器的有效性. 关键词： 混沌 同步 自适应控制     

半周期延迟-非线性反馈控制混沌

提出了基于稳定性准则的半周期延迟-非线性反馈控制混沌的方法，即SC(stability criterion)半周期延迟非线性反馈控制法.通过对混沌系统的适当分离，得到一个特殊的非线性函数，并利用混沌输出信号与其半周期延迟信号的非线性函数之和，构造了连续反馈输入干扰.该方法继承了延迟反馈控制方法及稳定性准则控制方法的优点，实现了有效的自控制过程；并克服了延迟反馈方法的限制，能将嵌入混沌吸引子中的自对称直接不稳周期轨稳定.控制过程可随时开始，具有简便、灵活性.数值模拟结果显示了SC半周期延迟-非线性反馈方法控制的有效性. 关键词： 稳定性准则 混沌控制 半周期延迟 非线性反馈     

用负反馈控制混沌Lorenz系统到达任意目标

研究了用非线性反馈控制混沌Lorenz系统的方法,经理论分析,给出了反馈控制函数的表达 式和混沌控制的期望结果,理论结果和数值结果一致表明,不同的控制函数可使系统稳定在不同的目标点或不同的周期轨道上. 关键词：     

Coullet混沌系统的演化和控制实验

构建了Coullet混沌系统的硬件实验电路,改变系统的参数,可以从示波器上观察系统从稳定周期状态演变到混沌状态的分岔过程.采用非线性反馈控制方法实现了对Coullet混沌系统的有效控制,改变反馈控制增益,可以将Coullet系统从混沌状态控制到稳定的周期状态.     

延迟-非线性反馈控制混沌

提出了基于稳定性准则的延迟非线性反馈控制混沌的方法，即SC延迟非线性反馈控制法. 通过对混沌系统的适当分离，得到一个特殊的非线性函数，并利用混沌输出信号与其延迟信号的非线性函数的差，构造了连续反馈输入干扰，以控制混沌轨到某一期望的不稳周期轨上. 该方法继承了延迟反馈控制方法的优点，实现了自-控制过程. 另外由于该方法基于线性系统的稳定性准则，保证了控制的有效性. 控制过程可随时开始，具有简便、灵活性. 给出耦合Duffing振子的例子，数值模拟结果显示了SC延迟反馈方法控制的有效性. 关键词： 稳定性准则 混沌控制 延迟反馈 干扰     

Liu混沌系统的非线性反馈同步控制

研究了新型混沌系统——Liu系统的同步控制问题.基于Lyapunov稳定性理论，采用非线性反馈控制方法，给出了Liu系统实现自同步的充分条件以及控制律参数的取值范围；结合参数自适应控制方法，实现了Liu混沌系统与统一混沌系统的异结构系统快速同步.数值仿真证明了该方法的有效性. 关键词： Liu混沌系统 混沌同步 非线性反馈控制 参数自适应控制     

Chaotifying a stable linear controllable system by single input state feedback

In this paper, an approach for chaotifying a stable controllable linear system via single input state-feedback is presented. The overflow function of the system states is designed as the feedback controller, which can make the fixed point of the closed-loop system to be a snap-back repeller, thereby yields chaotic dynamics. Based on the Marotto theorem, it proves theoretically that the closed-loop system is chaotic in the sense of Li and Yorke. Finally, the simulation results are used to illustrate the effectiveness of the proposed method.     

On Chaotification of Discrete Lagrange Systems

This paper is concerned with chaotification of discrete Lagrange systems in one dimension, via feedback control techniques. A chaotification theorem for discrete Lagrange systems is established. The controlled systems are proved to be chaotic 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.     

基于部分变量反馈的混沌系统控制

提出了混沌系统部分变量逆序反馈控制器的定义，并以陈氏系统为例对该类控制器进行了研究，得出了部分变量正序和逆序控制器存在的条件，应用该条件扩展了有关文献的研究成果，得到了混沌系统的多种形式的反馈控制器.仿真结果显示，基于部分变量的混沌系统的控制是简单而有效的. 关键词： 部分变量反馈控制 逆序控制器 混沌系统     

Design of output feedback controller for a unified chaotic system

In this paper, the synchronization of a unified chaotic system is investigated by the use of output feedback controllers; a two-input single-output feedback controller and single-input single-output feedback controller are presented to synchronize the unified chaotic system when the states are not all measurable. Compared with the existing results, the controllers designed in this paper have some advantages such as small feedback gain, simple structure and less conservation. Finally, numerical simulations results are provided to demonstrate the validity and effectiveness of the proposed method.     

The design and artificial realization of a controller of pulse coupling feedback

In this paper a controller of pulse coupling feedback (PCF) is designed to control chaotic systems. Control principles and the technique to select the feedback coefficients are introduced. This controller is theoretically studied with a three dimensional (3D) chaotic system. The artificial simulation results show that the chaotic system can be stabilized to different periodic orbits by using the PCF method, and the number of the periodic orbits are 2ⁿ× 3^mp (n and m are integers). Therefore, this control method is effective and practical.     

Design of output feedback controller for a unified chaotic system

In this paper, the synchronization of a unified chaotic system is investigated by the use of output feedback controllers; a two-input single-output feedback controller and single-input single-output feedback controller are presented to synchronize the unified chaotic system when the states are not all measurable. Compared with the existing results, the controllers designed in this paper have some advantages such as small feedback gain, simple structure and less conservation. Finally, numerical simulations results are provided to demonstrate the validity and effectiveness of the proposed method.     

A nonlinear controller design for permanent magnet motors using a synchronization-based technique inspired from the Lorenz system

The dynamic behavior of a permanent magnet synchronous machine (PMSM) is analyzed. Nominal and special operating conditions are explored to show that the PMSM can experience chaos. A nonlinear controller is introduced to control these unwanted chaotic oscillations and to bring the PMSM to a stable steady state. The designed controller uses a pole-placement approach to force the closed-loop system to follow the performance of a simple first-order linear system with zero steady-state error to a desired set point. The similarity between the mathematical model of the PMSM and the famous chaotic Lorenz system is utilized to design a synchronization-based state observer using only the angular speed for feedback. Simulation results verify the effectiveness of the proposed controller in eliminating the chaotic oscillations while using a single feedback signal. The superiority of the proposed controller is further demonstrated by comparing it with a conventional PID controller. Finally, a laboratory-based experiment was conducted using the MCK2812 C Pro-MS(BL) motion control kit to confirm the theoretical results and to verify both the causality and versatility of the proposed controller.     

Neural networks and chaos: construction, evaluation of chaotic networks, and prediction of chaos with multilayer feedforward networks

Many research works deal with chaotic neural networks for various fields of application. Unfortunately, up to now, these networks are usually claimed to be chaotic without any mathematical proof. The purpose of this paper is to establish, based on a rigorous theoretical framework, an equivalence between chaotic iterations according to Devaney and a particular class of neural networks. On the one hand, we show how to build such a network, on the other hand, we provide a method to check if a neural network is a chaotic one. Finally, the ability of classical feedforward multilayer perceptrons to learn sets of data obtained from a dynamical system is regarded. Various boolean functions are iterated on finite states. Iterations of some of them are proven to be chaotic as it is defined by Devaney. In that context, important differences occur in the training process, establishing with various neural networks that chaotic behaviors are far more difficult to learn.     

Passive control of chaotic system with multiple strange attractors

In this paper we present a new simple controller for a chaotic system, that is, the Newton--Leipnik equation with two strange attractors: the upper attractor (UA) and the lower attractor (LA). The controller design is based on the passive technique. The final structure of this controller for original stabilization has a simple nonlinear feedback form. Using a passive method, we prove the stability of a closed-loop system. Based on the controller derived from the passive principle, we investigate three different kinds of chaotic control of the system, separately: the original control forcing the chaotic motion to settle down to the origin from an arbitrary position of the phase space; the chaotic intra-attractor control for stabilizing the equilibrium points only belonging to the upper chaotic attractor or the lower chaotic one, and the inter-attractor control for compelling the chaotic oscillation from one basin to another one. Both theoretical analysis and simulation results verify the validity of the suggested method.