Nonlinear feedback synchronisation control between fractional-order and integer-order chaotic systems

This paper focuses on the synchronisation between fractional-order and integer-order chaotic systems. Based on Lyapunov stability theory and numerical differentiation, a nonlinear feedback controller is obtained to achieve the synchronisation between fractional-order and integer-order chaotic systems. Numerical simulation results are presented to illustrate the effectiveness of this method.

H_∞ Synchronization of Chaotic Systems via Delayed Feedback Control

The H∞ synchronization problem for a class of delayed chaotic systems with external disturbance is investigated. A novel delayed feedback controller is established under which the chaotic master and slave systems are synchronized with a guaranteed H∞ performance. Based on the Lyapunov stability theory, a delay-dependent condition is derived and formulated in the form of linear matrix inequality （LMI）. A numerical simulation is also presented to validate the effectiveness of the developed theoretical results.

The feedback control of fractional order unified chaotic system

This paper studies the stability of the fractional order unified chaotic system. On the unstable equilibrium points, the equivalent passivity＇＇ method is used to design the nonlinear controller. With the definition of fractional derivatives and integrals, the Lyapunov function is constructed by which it is proved that the controlled fractional order system is stable. With Laplace transform theory, the equivalent integer order state equation from the fractional order nonlinear system is obtained, and the system output can be solved. The simulation results validate the effectiveness of the theory.

Hybrid Synchronization of a Chen Hyper-Chaotic System with Two Simple Linear Feedback Controllers

This paper brings attention on the hybrid synchronization of the Chen hyper-chaotic system by using some simple controllers. We give the sufficient conditions for achieving the goal by using the Lyapunov stability theory, and we verify our conclusion by numerical simulations.

Theoretical and experimental study of Chen chaotic system with notch filter feedback control

Since the past two decades, the time delay feedback control method has attracted more and more attention in chaos control studies because of its simplicity and efficiency compared with other chaos control schemes. Recently, it has been proposed to suppress low-dimensional chaos with the notch filter feedback control method, which can be implemented in a laser system. In this work, we have analytically determined the controllable conditions for notch filter feedback controlling of Chen chaotic system in terms of the Hopf bifurcation theory. The conditions for notch filter feedback controlled Chen chaoitc system having a stable limit cycle solution are given. Meanwhile, we also analysed the Hopf bifurcation direction, which is very important for parameter settings in notch filter feedback control applications. Finally, we apply the notch filter feedback control methods to the electronic circuit experiments and numerical simulations based on the theoretical analysis. The controlling results of notch filter feedback control method well prove the feasibility and reliability of the theoretical analysis.

Time-delay feedback control in a delayed dynamical chaos system and its applications

The feedback control of a delayed dynamical system, which also includes various chaotic systems with time delays, is investigated. On the basis of stability analysis of a nonautonomous system with delays, some simple yet less conservative criteria are obtained for feedback control in a delayed dynamical system. Finally, the theoretical result is applied to a typical class of chaotic Lorenz system and Chua circuit with delays. Numerical simulations are also given to verify the theoretical results.

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 2^n×3^m p （n and m are integers）. Therefore, this control method is effective and practical.

Equilibrium points and bifurcation control of a chaotic system

Based on the Routh-Hurwitz criterion, this paper investigates the stability of a new chaotic system. State feedback controllers are designed to control the chaotic system to the unsteady equilibrium points and limit cycle. Theoretical analyses give the range of value of control parameters to stabilize the unsteady equilibrium points of the chaotic system and its critical parameter for generating Hopf bifurcation. Certain nP periodic orbits can be stabilized by parameter adjustment. Numerical simulations indicate that the method can effectively guide the system trajectories to unsteady equilibrium points and periodic orbits.

Adaptive stabilization of an incommensurate fractional order chaotic system via a single state controller

In this paper, we investigate the stabilization of an incommensurate fractional order chaotic systems and propose a modified adaptive-feedback controller for the incommensurate fractional order chaos control based on the Lyapunov stability theory, the fractional order differential inequality and the adaptive control theory. The present controller, which only contains a single state variable, is simple both in design and in implementation. The simulation results for several fractional order chaotic systems are provided to illustrate the effectiveness of the proposed scheme.

三阶三次幂非线性混沌电路的自适应反馈控制和H_(∞)控制

针对三阶三次幂非线性混沌电路,研究其控制问题.首先,给出系统的Lyapunov指数和混沌吸引子,验证系统存在复杂的混沌现象;其次,用自适应反馈控制方法和H_(∞)状态反馈控制方法,设计参数已知和参数未知的自适应反馈控制器以及H_(∞)状态反馈控制器,将混沌系统状态稳定到平衡点上;最后,通过MATLAB软件进行数值仿真验证控制器的有效性,并对两种控制器的控制效果进行比较.

基于全光混沌注入双环电光相位反馈环的混沌保密通信系统研究

针对现有混沌保密光通信系统时延特征隐藏所需反馈增益系数较大这一问题,设计了一种基于全光混沌注入双环电光相位反馈环的混沌保密通信系统。首先,由全光反馈产生光混沌并将其耦合至2个电光相位混沌反馈环中。然后,通过相位调制的方式实现信息与混沌载波的非线性耦合并参与混沌载波的生成。最后,在检测端通过光混沌同步实现信号的解密。借助MATLAB软件仿真分析了系统中混沌信号的复杂度、时延特征隐藏、同步性、鲁棒性和通信性能。仿真结果表明,所设计的混沌保密通信系统在较小的反馈系数时具有较高的复杂度且时延特征得到较好的隐藏。

一种三维混沌系统的混沌同步研究

混沌同步在保密通信领域有着广阔的应用前景,但要实现混沌保密通信,位于接收端和发送端的两个混沌系统必须达到混沌同步。为此,采用简单的线性反馈控制实现了一个新三维混沌系统的混沌同步控制,并应用Lyapunov稳定性理论,证明了两个混沌系统在线性反馈控制下实现混沌同步的条件。根据这些同步条件,只要给定系统参数值,就能够判断两个混沌系统是否能够达到混沌同步;另一方面,也可以根据这些判据来选取实现混沌同步的系统参数。最后,进行了计算机仿真,验证了所得到的同步条件是有效的。

AFM-TM微悬臂梁系统混沌运动及控制算法分析

针对轻敲式原子力显微镜微(AFM-TM)悬臂梁系统的混沌运动会严重影响到AFM-TM的测量精度的问题,对该系统动力学特性及控制算法进行了分析。首先,通过数值仿真,综合利用Lyapunov指数、分岔图、Poincaré截面和相位图分析了外部激励幅值变化时AFM-TM微悬臂梁系统运动特性的演化;然后,提出将延时反馈控制和模糊自适应延时反馈,用于控制系统的混沌运动;最后,对两种控制算法进行了比较。研究结果表明,当无量纲外部激励幅值在[0.65,0.85]等取值区间内取值时,系统表现出明显的混沌运动特性;延时反馈控制和模糊自适应延时反馈控制均能有效的将系统的混沌运动拉回到周期轨道,但模糊自适应延时反馈更适用于AFM-TM被测样品变化的复杂情况。结果对AFM-TM微悬臂梁外部激励参数选择、非线性系统复杂动力学特性分析和混沌运动控制提供有意义的理论参考。

基于混沌映射的抗机器学习攻击强物理不可克隆函数

物理不可克隆函数(PUF)在硬件安全领域具有广阔的应用前景,然而易受到基于机器学习等建模攻击。通过对强PUF电路结构和混沌映射机理的研究,该文提出一种可有效抵御机器学习建模攻击的PUF电路。该电路将原始激励作为混沌映射初始值,利用PUF激励响应映射时间与混沌算法迭代深度之间的内在联系产生不可预测的混沌值,并采用PUF中间响应反馈加密激励,进一步提升激励与响应映射的复杂度,增强PUF的抗机器学习攻击能力。该PUF采用Artix-7 FPGA实现,测试结果表明,即使选用的激励响应对数量高达106组,基于逻辑回归、支持向量机和人工神经网络的攻击预测率仍接近50%的理想值,并具有良好的随机性、唯一性和稳定性。

一类非自治混沌系统的时滞反馈控制

针对一类非自治混沌系统,提出一种时滞反馈控制方法,通过构造特殊的Lyapunov函数,利用时滞微分方程稳定性理论,分析和证明了受控系统的全局指数稳定性.最后将理论结果应用到典型的洛仑兹(Lorenz)系统和约瑟夫森(Josephson)系统,并给出数值模拟来验证结论的正确性.

新分段分数阶混沌系统的同步控制

通过改变修正的Lorenz-Stenflo(modified Lorenz-Stenflo,MLS)混沌系统的分段函数项,得到了一个新的四维分段混沌系统。新系统较MLS混沌系统具有更低的分数阶维数,在3.44阶时仍具有混沌特性。根据分数阶系统的线性稳定性理论和非线性反馈控制方法,提出了新分数阶系统的状态同步方法。通过理论推导,得到了两个混沌系统的同步稳定条件。控制器能够自适应地根据误差大小调节反馈系数,缩短同步时间。最后对3.6阶的分数阶系统进行了同步仿真实验,仿真结果验证了改进算法能够加快同步速度。

一个新混沌系统的非线性反馈同步控制

提出三维连续自治混沌系统,该系统含有4个参数,3个非线性乘积项,并且每个方程均具有不同的非线性乘积项.利用理论推导、数值仿真、分岔图等对系统的基本动力学特性进行了分析.研究表明,该系统存在着复杂的混沌吸引子,系统具有5个平衡点,与以往研究的Lorenz,Chen等混沌系统是非拓扑等价的;在不同的参数范围下系统可以由混沌态转为稳定的周期轨道,系统由倍周期序列通向混沌.基于Lyapunov稳定性理论,采用非线性反馈控制方法,给出系统在不同初值下实现自同步的充分必要条件及控制律参数的选取范围,数值仿真证明了该方法的有效性.

经济混沌模型中一种改进的反馈控制方法

就经济系统中的一类多参数混沌模型 ,应用非线性动力学理论 ,在OGY方法的基础上 ,对反馈控制方法进行了改进 ,提出了基于预测的反馈控制方法 .该方法成功地进行了多参数混沌控制 ,并通过两例具体的经济混沌模型 。

新型Liu混沌系统的模糊反馈同步方法

论文研究了新近提出的Liu混沌系统(2004)的模糊反馈同步方法。Liu混沌系统结构不同于以往的连续混沌系统,本文基于T-S(Takagi-Sugeno)模糊模型重构了Liu混沌系统;然后用Lyapunov理论和反馈同步的思想推导了两个重构的Liu系统同步的稳定性条件,并给出了误差系统以衰减率α全局渐近稳定的充分条件;最后基于LMI方法进行了仿真实验。良好的仿真结果验证了本文算法的有效性和快速性。

Liu混沌系统的线性反馈和状态观测器同步

Liu混沌系统是新近提出的三维混沌系统。文章分析Liu混沌系统的结构特点,设计了线性反馈同步方法和基于状态观测器的同步方法。线性反馈同步法结构简单;通过误差系统的分析,从理论上推导了系统实现同步的充分条件。基于状态观测器的同步方法对原系统结构没有特殊要求,无需求解Lyapunov函数;通过设定不同的控制参量,分析了控制参量和同步速度之间的关系。实验结果证明了两种同步方法的有效性和正确性。