用截面映象非线性延时反馈控制混沌

提出了利用相空间Poincare截面上的非线性延时反馈稳定微分动力系统混沌吸引子中不稳定周期轨道的新方法.以Henon映象和带注入信号的双光子激光系统为例，给出了理论分析和数值模拟结果．这种方法的主要特点是不需要获取混沌系统中不稳定周期轨道的任何信息，并且可以在混沌态的任意时刻施加控制作用．     

一种基于系统变量的线性和非线性变换实现混沌控制的方法

提出了一种通过系统变量的线性和非线性变换实现混沌控制的方法,以Henon映象和Lorenz系统作为两个典型的例子,验证了这种控制方法的有效性.结果表明,通过改变系统变量之间的线性变换矩阵,可以实现混沌系统中各种不稳定周期轨道的稳定控制.将这种方法推广到非线性(神经网络)变换,可以获得稳定的新的动力学行为.同时,从信息熵的角度,讨论了这种混沌控制方法的物理机制. 关键词：     

利用相空间压缩实现混沌与超混沌控制

提出一种通过压缩非线性系统轨道的相空间实现混沌和超混沌控制的方法-以Henon映象、Lorenz系统和Rossler超混沌系统为例,进行了数值研究-结果表明：该方法能有效地控制非线性系统中的混沌和超混沌行为,并获得98P的高周期稳定轨道- 关键词：     

混沌系统的辅助参考反馈控制

研究了保守系统混沌运动的控制问题．在线性反馈控制方法的基础上提出了一种新的控制方法——辅助参考反馈法,给出了控制参数的选择原则,适当调整反馈系数和参考项即可以得到不同的周期轨道．数值研究证明了该方法能够有效地控制耗散混沌系统和保守系统,同时周期窗口在弱噪声干扰下具有很强的鲁棒性． 关键词：     

随机性参数自适应的混沌同步

对两个不同参数的混沌系统进行随机性参数自适应控制，选取合适的控制律和反馈系数，导致其同步.以Henon映射为例进行数值模拟，结果表明，由于控制周期和反馈系数的随机变化，具有一定的实用意义. 关键词： Henon映射 混沌同步 随机性自适应控制     

用数字有限脉冲响应滤波器控制混沌

利用数字有限脉冲响应滤波器稳定微分动力系统和二维离散映象混沌吸引子中不稳定周期轨道的方法，实现了高周期轨道的稳定控制.分别研究了Lorenz系统和Henon映象，给出了初步的分析和数值模拟结果.这种方法的主要特点是不需要获取混沌系统中不稳定周期轨道的任何信息，控制参数的选择与被控混沌系统无关. 关键词：     

状态反馈和参数调整控制离散非线性系统的倍周期分岔和混沌

利用系统的状态反馈和参数调节的方法，有效地实现了离散非线性动力系统的倍周期分岔的延迟控制和混沌吸引子中不稳定周期轨道的控制.同时，通过选择合适的调控参数，可以将系统从一个2n周期轨道控制到2m(m关键词： 状态反馈 参量调节 混沌控制 分岔控制     

对称混沌系统的非线性动力学行为及控制

基于线性反馈控制思想，提出了一种对称动力学系统及其控制混沌的方法，给出了预期各周期轨道反馈系数的选择原则，适当选择反馈系数，即可得到不同的周期轨道.将此方法应用 到Logistic映射中，取得了良好的控制效果. 关键词： 反馈控制 周期转道 对称系统     

利用凹槽滤波引导混沌系统到周期解

通过对混沌动力系统增加一个线性的反馈控制器——凹槽滤波器,引导一大类系统从混沌运动转化为期望的低周期运动.基于混沌的微扰判据——Melnikov方法,解释了该方法实现混沌控制的数学物理机理.控制仿真结果表明,该方法简单而实用,具有良好的应用前景,并能控制超混沌系统 关键词： 混沌控制 凹槽滤波 Melnikov方法     

平移法控制离散系统的倍周期分岔和混沌

利用平移系统的方法,实现了对离散非线性动力学系统的倍周期分岔的控制和混沌吸引子不稳定周期轨道的控制.只要选择适当的平移参数,使系统平移到不同位置,就可将系统控制在不同的预期轨道.将此方法应用到Logistic映射和Henon映射中取得了很好的控制效果.     

非线性反馈控制单模激光Haken-Lorenz混沌系统

提出一种变量非线性反馈（VNF）方法控制混沌系统.介绍了该方法的控制原理以及反馈系数的选取原则,以单模激光Haken-Lorenz系统为例对非线性反馈控制方法进行了理论研究.仿真结果显示,通过恰当的选择反馈系数k,使系统的最大李雅普诺夫（Lyapunov）指数由正值转变为负值,相图中系统的轨迹由混沌吸引子转变为周期数为2n×3mp(n、m为整数)的周期轨道.通过与线性反馈控制结果对比发现,非线性反馈控制方法简便有效,控制速度快.     

Global view on a nonlinear oscillator subject to time-delayed feedback control

We apply time-delayed feedback control to stabilise unstable periodic orbits of an amplitude-phase oscillator. The control acts on both, the amplitude and the frequency of the oscillator, and we show how the phase of the control signal influences the dynamics of the oscillator. A comprehensive bifurcation analysis in terms of the control phase and the control strength reveals large stability regions of the target periodic orbit, as well as an increasing number of unstable periodic orbits caused by the time delay of the feedback loop. Our results provide insight into the global features of time-delayed control schemes.     

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.     

New control methodology of microcantilevers in atomic force microscopy

We apply an external feedback control technique to vibrating microcantilevers in atomic force microscopy. Here we have no difficulty in getting information on periodic orbits required for application of the external feedback control unlike controlling chaos since stable orbits are used as reference ones. This approach enables us not only to control vibrations of the cantilevers but also to measure the sample surfaces (surface topographies) simultaneously. The efficiency and validity of our approach is demonstrated by numerical simulations and a theoretical analysis with the assistance of numerical computations.     

Act-and-wait time-delayed feedback control of autonomous systems

Recently an act-and-wait modification of time-delayed feedback control has been proposed for the stabilization of unstable periodic orbits in nonautonomous dynamical systems (Pyragas and Pyragas, 2016 [30]). The modification implies a periodic switching of the feedback gain and makes the closed-loop system finite-dimensional. Here we extend this modification to autonomous systems. In order to keep constant the phase difference between the controlled orbit and the act-and-wait switching function an additional small-amplitude periodic perturbation is introduced. The algorithm can stabilize periodic orbits with an odd number of real unstable Floquet exponents using a simple single-input single-output constraint control.     

A new hyperchaotic system and its linear feedback control

This paper reports a new hyperchaotic system by adding an additional state variable into a three-dimensional chaotic dynamical system, studies some of its basic dynamical properties, such as the hyperchaotic attractor, Lyapunov exponents, bifurcation diagram and the hyperchaotic attractor evolving into periodic, quasi-periodic dynamical behaviours by varying parameter k. Furthermore, effective linear feedback control method is used to suppress hyperchaos to unstable equilibrium, periodic orbits and quasi-periodic orbits. Numerical simulations are presented to show these results.     

Control of chaos via an unstable delayed feedback controller

Delayed feedback control of chaos is well known as an effective method for stabilizing unstable periodic orbits embedded in chaotic attractors. However, it had been shown that the method works only for a certain class of periodic orbits characterized by a finite torsion. Modification based on an unstable delayed feedback controller is proposed in order to overcome this topological limitation. An efficiency of the modified scheme is demonstrated for an unstable fixed point of a simple dynamic model as well as for an unstable periodic orbit of the Lorenz system.     

Beyond the odd number limitation of time-delayed feedback control of periodic orbits

We discuss the stabilization of odd-number orbits by time-delayed feedback control. In particular, we review the stabilization of odd-number orbits born in a subcritical Hopf bifurcation or a saddle-node bifurcation of periodic orbits. These examples refute the often invoked odd-number theorem.     

晶闸管混沌行为的延迟反馈控制与尖峰电流抑制

应用延迟反馈控制法(time-delayed feedback control,TDFC),有效地控制了晶闸管中出现的混沌行为,由此提出一种基于Floquet定理的延迟反馈控制法的优化设计方法.为进一步抑制延迟反馈控制出现的尖峰电流现象,根据相空间压缩原理对反馈信号进行相空间压缩,从而很好地抑制尖峰电流.