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.     

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.     

光学二次谐波浑沌控制

用变量延时反馈控制法对光学二次谐波系统的浑沌进行了有效的控制.通过对系统的最大李雅普诺夫指数分析,给出了确定可控参数区的方法.证明适当的延时量和反馈强度可以使浑沌得到稳定的控制,被控制系统的轨道是初始系统浑沌吸引子中的不稳定周期轨道.     

On a simple recursive control algorithm automated and applied to an electrochemical experiment

We review a simple recursive proportional feedback (RPF) control strategy for stabilizing unstable periodic orbits found in chaotic attractors. The method is generally applicable to high-dimensional systems and stabilizes periodic orbits even if they are completely unstable, i.e., have no stable manifolds. The goal of the control scheme is the fixed point itself rather than a stable manifold and the controlled system reaches the fixed point in d+1 steps, where d is the dimension of the state space of the Poincare map. We provide a geometrical interpretation of the control method based on an extended phase space. Controllability conditions or special symmetries that limit the possibility of using a single control parameter to control multiply unstable periodic orbits are discussed. An automated adaptive learning algorithm is described for the application of the control method to an experimental system with no previous knowledge about its dynamics. The automated control system is used to stabilize a period-one orbit in an experimental system involving electrodissolution of copper. (c) 1997 American Institute of Physics.     

Stability transformation: a tool to solve nonlinear problems

We present an analysis of the properties as well as the diverse applications and extensions of the method of stabilisation transformation. This method was originally invented to detect unstable periodic orbits in chaotic dynamical systems. Its working principle is to change the stability characteristics of the periodic orbits by applying an appropriate global transformation of the dynamical system. The theoretical foundations and the associated algorithms for the numerical implementation of the method are discussed. This includes a geometrical classification of the periodic orbits according to their behaviour when the stabilisation transformations are applied. Several refinements concerning the implementation of the method in order to increase the numerical efficiency allow the detection of complete sets of unstable periodic orbits in a large class of dynamical systems. The selective detection of unstable periodic orbits according to certain stability properties and the extension of the method to time series are discussed. Unstable periodic orbits in continuous-time dynamical systems are detected via introduction of appropriate Poincaré surfaces of section. Applications are given for a number of examples including the classical Hamiltonian systems of the hydrogen and helium atom, respectively, in electromagnetic fields. The universal potential of the method is demonstrated by extensions to several other nonlinear problems that can be traced back to the detection of fixed points. Examples include the integration of nonlinear partial differential equations and the numerical determination of Markov-partitions of one-parametric maps.     

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.     

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.     

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     

Local control of chaotic motion

On the basis of the Ott, Grebogi and Yorke method (OGY) of controlling chaotic motion by stabilizing unstable periodic orbits we propose a control method which allows a nearly continuous adjusting of the control parameter and which therefore is capable also for controlling noisy systems. Any motion which is a solution of the system's equation of motion can be stabilized, unstable periodic orbits as well as chaotic trajectories. We demonstrate the feasibility of the method by stabilizing experimentally arbitrarily chosen chaotic trajectories of a driven damped pendulum affected by noise.     

状态反馈控制声光双稳系统的倍周期分岔和混沌

设计了一种动力学状态反馈(DSF)方法控制非线性混沌系统.介绍了DSF方法的控制原理,并用此方法控制声光双稳(AOB)系统的混沌,以此验证其有效性.仿真模拟显示,通过选择恰当的控制参数,有效地实现了声光双稳(AOB)系统中倍周期分岔的延迟控制和混沌吸引子中原不稳定周期轨道的稳定控制,同时,还可以将系统控制在2np、3mp 和2np×3mp这样其它任意所需的周期轨道上.