共查询到20条相似文献,搜索用时 155 毫秒
1.
Control of chaos via an unstable delayed feedback controller 总被引:7,自引:0,他引:7
Pyragas K 《Physical review letters》2001,86(11):2265-2268
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. 相似文献
2.
3.
非线性反馈控制单模激光Haken-Lorenz混沌系统 总被引:1,自引:1,他引:0
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. 相似文献
4.
5.
We present a control mechanism for tuning a fast-slow dynamical system undergoing a supercritical Hopf bifurcation to be in the canard regime, the tiny parameter window between small and large periodic behavior. Our control strategy uses continuous feedback control via a slow control variable to cause the system to drift on average toward canard orbits. We apply this to tune the FitzHugh-Nagumo model to produce maximal canard orbits. When the controller is improperly configured, periodic or chaotic mixed-mode oscillations are found. We also investigate the effects of noise on this control mechanism. Finally, we demonstrate that a sensor tuned in this way to operate near the canard regime can detect tiny changes in system parameters. 相似文献
6.
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. 相似文献
7.
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. 相似文献
8.
9.
10.
Y.-C. HSIAOP.C. TUNG 《Journal of sound and vibration》2002,254(1):163-174
This study describes a global approach of controlling chaos to reduce tedious waiting time caused by using conventional local controllers. With Euler's method, a non-autonomous system is approximated by a non-linear difference system and then an approximate global Poincaré map function is derived from the difference system by iterating one or more periods of a periodic excitation. Based on the map function, unstable periodic orbits embedded in a chaotic motion can be detected and a global controller for a targeted unstable periodic orbit is designed. The global controller makes all the unstable periodic orbits vanish except a targeted periodic orbit. Furthermore, a Lyapunov's direct method is applied to confirm that the global controller can asymptotically stabilize the unique periodic orbit. For practical applications, system models are usually unknown. To obtain a mathematical model, non-linear system identification based on the harmonic balance principle is applied to an unknown chaotic system of a noisy environment. Simulation results demonstrate that the global controller successfully regularizes a chaotic motion even if the chaotic trajectory is far from the targeted periodic orbit. 相似文献
11.
提出了自适应脉冲微扰控制混沌系统的方法.在参量脉冲微扰中引入自适应控制策略,设计出可以产生合适的脉冲强度的自适应控制器来实现混沌控制.采取这种方法对混沌的Rssle r连续系统和Hnon离散映射实施仿真控制,能够将系统稳定到不同的周期轨道或不动点上 ;并且,数值仿真结果还表明该控制方法具有较强的鲁棒性.
关键词:
自适应
脉冲微扰
混沌控制
鲁棒性 相似文献
12.
光学二次谐波浑沌控制 总被引:1,自引:1,他引:0
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. 相似文献
13.
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. 相似文献
14.
A method for stabilizing periodic orbits and steady states of chaotic systems is presented using specifically filtered feedback signals. The efficiency of this control technique is illustrated with simulations (R?ssler system, laser model) and a successful experimental application for stabilizing intensity fluctuations of an intracavity frequency-doubled Nd:YAG laser. 相似文献
15.
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. 相似文献
16.
This Letter is concerned with bifurcation and chaos control in scalar delayed differential equations with delay parameter τ. By linear stability analysis, the conditions under which a sequence of Hopf bifurcation occurs at the equilibrium points are obtained. The delayed feedback controller is used to stabilize unstable periodic orbits. To find the controller delay, it is chosen such that the Hopf bifurcation remains unchanged. Also, the controller feedback gain is determined such that the corresponding unstable periodic orbit becomes stable. Numerical simulations are used to verify the analytical results. 相似文献
17.
This Letter deals with the problem of designing time-delayed feedback controllers (TDFCs) to stabilize unstable equilibrium points and periodic orbits for a class of continuous time-delayed chaotic systems. Harmonic balance approach is used to select the appropriate controller parameters: delay time and feedback gain. The established theoretical results are illustrated via a case study of the well-known Logistic model. 相似文献
18.
Chaotic behaviors of the tent map (a piecewise-linear, continuous map with a unique maximum) are studied analytically throughout its chaotic region in terms of the invariant density and the power spectrum. As the height of the maximum is lowered, successive band-splitting transitions occur in the chaotic region and accumulate to the transition point into the nonchaotic region. The timecorrelation function of nonperiodic orbits and their power spectrum are calculated exactly at the band-splitting points and in the vicinity of these points. The method of eigenvalue problems of the Frobenius-Perron operator is used. 2 m?1 critical modes, wherem = 1,2, 3, ..., are found which exhibit the critical slowing-down near the 2 m?1-band to 2 m -band transition point. After the transition these modes become periodic modes which represent the cycling of nonperiodic orbits among 2 m bands together with the periodic modes generated by the preceding band splittings. Scaling laws near the transition point into the nonchaotic region are investigated and a new scaling law is found for the total intensity of the periodic part of the spectrum. 相似文献
19.