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Diffusionless Lorenz equations (DLE) are a simple one-parameter version of the well-known Lorenz model, which was obtained in the limit of high Rayleigh and Prandtl numbers, physically corresponding to diffusionless convection. A simple control method is presented to control chaos by using periodic parameter perturbation in DLE. By using the generalized Melnikov method, the parameter conditions could be obtained to guide the controlled DLE to a low-periodic motion. Moreover, the existence conditions of periodic orbits and homoclinic orbits in the system are given. Some results of the numerical simulation are also explained clearly by a rigorous analysis. 相似文献
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The Lorenz system is well known for its ability to produce chaotic motion and the control problem of this system has attracted much attention in recent years. In this paper, control of the Lorenz chaotic systems based on a nonlinear feedback technique is presented. The objective of control is two-fold: one is to drive the system to one of equilibrium points associated with uncontrolled chaotic motion and the other is to let one of the closed-loop system states track a given signal. The controllers designed here are based on exact linearization theory of nonlinear systems and can regulate the closed-loop system states globally to a given point. Finally, illustrative examples show the effectiveness of the proposed design method. 相似文献
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Copyright by Science in China Press 2005 1 Introduction In the 1960s, American scientist E. N. Lorenz discovered the first chaotic attractorwhen he worked on some numerical experiments of meteorology. Since then, studies of chaos have been greatly developed in many areas[1?4]. Professor J. Ford, a famous physi-cist, named the discovery of chaos “the third revolution of physics”. As the first chaotic system, the Lorenz system indicates the essential phenomenon of the complexity of non-li… 相似文献
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在考虑温度对圆柱壳材料性能影响的基础上,建立了圆柱壳在扰动外压作用下的几何非线性动力控制方程.并采用伽辽金原理及 Melnikov 法研究了圆柱壳在热载荷及微扰外压作用下的分岔,进一步讨论分析了温度、Batdorf 参数等因素对圆柱壳发生混沌运动区域的影响,得出了随温度、Batdorf 参数的增大,混沌运动区域将越来越大的结论. 相似文献
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针对延迟反馈法参数较难确定的问题,给出了一种自适应调节反馈系数方法来控制非线性Lorenz混沌系统的方案.数值仿真结果表明,选择适当的延迟时间和反馈系数能够控制系统的不稳定周期轨道、消除混沌,并能使系统从失稳状态进入稳定状态.由于不需要外加参考信号,可以在混沌态的任意时刻施加控制,所以该方法简单易行.同时将以上控制效果应用于动画的控制中,对指定动画角色行为进行控制,使其可以运动到混沌的轨道上或者某一个特殊的轨迹上. 相似文献
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Control of a chaotic system 总被引:9,自引:0,他引:9
The Lorenz equations are well known for their ability to produce chaotic motion. We investigate here the Lorenz system subject to a control input. Two different controllers are the designed for this system, one based on linear methods and one based on nonlinear methods. The objective of the controller is to drive the system to one of the unstable equilibrium points associated with uncontrolled chaotic motion. Each controller is able to produce stable motion. However, the character of this motion may differ considerably, depending on adjustment of gains used in the controller. In particular, the motion may contain chaotic transients. It is possible to create a system with intermediate-term-senstive dependence on initial conditions, but with no such long-term dependence.
Recommended by W.J. Grantham 相似文献
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采用基于误差线性系统稳定性准则的混沌控制方法,控制具有结构内阻尼的磁性刚体航天器在重力场与磁场共同作用下在圆形轨道的混沌姿态运动.讨论了航天器姿态运动方程中部分参数的取值对于运动姿态的影响,给出了这些参数通过倍周期分岔或逆倍周期分岔通往混沌的途径.当参数使系统做混沌姿态运动时,采用上述方法将混沌运动控制至周期-4轨道,并实现周期-1、2、4轨道之间转换的灵活控制.此外,分析了控制参数的变化对于控制效果的影响,并分别给出了控制至不同轨道时的输入扰动范围及控制参数范围.仿真结果表明,该方法能够实现混沌姿态运动在预定周期轨道间的灵活控制,且输入扰动量小、控制速度快、具有高精度,从而验证了该方法在航天器混沌姿态运动控制方面的有效性. 相似文献
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以Lorenz时滞混沌系统为研究对象,基于Lyapunov-Krasovskii泛函理论,设计了一组线性控制器实现混沌同步. 所设计的控制律简单,鲁棒性强并且易于实现. 为验证所提出的控制算法的有效性,基于DSPbuilder设计了时滞混沌系统的数字电路,并在数字电路上完成了混沌系统的同步仿真. 仿真结果表明所设计的控制器取得了很好的控制效果. 相似文献
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Her-Terng Yau Cheng-Chi Wang Chin-Tsung Hsieh Ching-Chang Cho 《Computers & Mathematics with Applications》2011,61(8):1912-1916
This study analyzes the chaotic behavior of a micromechanical resonator with electrostatic forces on both sides and investigates the control of chaos. A phase portrait, maximum Lyapunov exponent and bifurcation diagram are used to find the chaotic dynamics of this micro-electro-mechanical system (MEMS). To suppress chaotic motion, a robust fuzzy sliding mode controller (FSMC) is designed to turn the chaotic motion into a periodic motion even when the MEMS has system uncertainties. 相似文献
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为了分析行星齿轮系统的混沌特性,基于集中参数理论,考虑时变啮合刚度、齿隙和综合啮合误差等非线性因素,建立行星齿轮系统扭转振动模型.采用Runge-Kutta数值解法求解振动方程,利用分岔图和最大Lyapunov指数图分析系统随各种参数变化的分岔与混沌特性.数值仿真得出:随激励频率的增加,系统首先从周期运动进入阵发性混沌,再通过逆倍化分岔由混沌回到周期运动,之后再次通过跳跃激变和倍化分岔由周期运动进入混沌运动,最后通过逆倍化分岔稳定到1周期运动.随阻尼比的增加,系统通过逆倍化分岔由混沌运动进入周期运动.随综合啮合误差幅值、齿隙和刚度幅值分别增加的三种情况下,系统都是通过倍化分岔由周期运动进入混沌运动.随荷载的增加,系统通过跳跃激变和逆倍化分岔由混沌运动进入周期运动.以上分析结果可为行星齿轮系统参数设计提供理论依据. 相似文献
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利用广义Hamilton系统理论的Melnikov方法,严格分析了延迟反馈方法控制混沌Lorenz系统到周期解的机理,揭示了延迟时间与控制混沌的关系.延迟反馈项实际上是一个作用明显的扰动项,通过选择合适的参数,使得系统的稳定流形与不稳定流形不再横截相交,Smale意义下的混沌受到抑制,将Lorenz混沌系统引导到各种不同的周期轨道;可见,延迟时间关系到控制扰动量的大小,但不必是混沌吸引子内嵌不稳定周期轨道的周期整数倍.另外,通过数值仿真,其结果与理论分析相符,从而表明了该分析方法的有效性. 相似文献
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《国际计算机数学杂志》2012,89(6):1255-1280
This paper investigates the synchronization of coupled chaotic systems with many equilibrium points. By addition of an external switching piecewise-constant controller, the system changes to a new one with several independent chaotic attractors in the state space. Then, by addition of a nonlinear state feedback control, the chaos synchronization is presented. This method can be used in many couples of chaotic systems characterized by the same equilibrium point or by two different equilibrium points, even they are the same systems (Lorenz, Jerk, Van der Pol) or two chaotic systems with different structures (Lorenz modified). 相似文献