Lü混沌系统的反馈控制与动态控制方法

On feedback control and dynamical control of Lü chaotic system

通过Lyapunov第一方法对Lü混沌系统的非线性动力学行为及平衡点的稳定性进行分析.采用反馈控制方法对Lü混沌系统行为进行控制与反控制.根据霍尔维茨判据及线性化理论,选择控制参数以满足一定的特征值条件,从而把Lü混沌系统控制到指定的平衡态或周期轨道上.通过控制参数的动态调整,实现了Lü混沌系统从混沌态到稳定态,混沌态到稳定的极限环,稳定态到极限环,稳定态到混沌态的转化,实现了Lü混沌系统的动态控制.利用数值方法模拟控制结果。

Nonlinear dynamical behavior and equilibrium stability analysis were carried out for Lü chaotic system by using Lyapunov first method. Controlling and anti-controlling the Lü chaotic system were studied by using feedback controlling method. According to Hurwits Criterion and equilibrium linearizing theory, and by selecting suitable controlling parameter to adapt certain eigenvalue conditions, the Lü chaotic system was controlled to predetermine equilibrium states or cyclical trajectories. Dynamical controlling of Lü chaotic system was investigated by adjusting controlling parameters at suitable time. Different kinds of state changes are realized, which include state changing from chaos to stable state, from chaos to stable limiting circle, from stable state to limiting circle and from limiting state to chaos. Numerical simulations were carried out which verified the results.