自适应线性反馈与自适应微分反馈控制混沌  

Control chaos with the adaptive linear feedback and the adative differential feedback method

作　　者：黄报星[1] 

机构地区：[1]江汉大学物理与信息工程学院,湖北武汉430056

出　　处：《中国计量学院学报》2003年第2期140-143,共4页Journal of China Jiliang University

摘　　要：　构造自适应线性反馈控制混沌Chen系统到达平衡点.应用Lyapunov第二方法证明受控系统可渐近稳定收敛到三个平衡点.将控制参数p看作第4个变量构成与受控系统等价的自治系统,数值仿真结果验证了受控系统(2)对指定平衡点的稳定收敛.构造自适应微分反馈控制混沌Chen系统,应用Ruoth Hurwitz定理证明受控系统(4)可稳定收敛到平衡点S+,S-,而不能收敛到平衡点S0.自适应方法的优点是控制信号微小简单,可在任意时刻加入,可以迅速将混沌系统控制到系统的平衡点,且在系统收敛到平衡点时,控制扰动u(t)也迅速趋于0.A adaptive linear feedback is constructed to control the chaotic Chen system to the desired equilbrums. It is verified by the second Lyapunov method that the controlled system (2) can be asymptotically stabilized to three equilbrums with the adaptive control. A autonomous system equivalent to the controlled system(2) is constructed by treating the control parameter as the 4th variate.The controllability and the stability of the controlled system at the equilbrums are verified in the numerical simulation in Matlab.A adative differential feedback is constructed to control Chen system.It is verified by Routh-Hurwitz theorem that the controlled system(4) can be asymptotically stabilized to the equilbrums \$S\-+\$ and \$S\--\$ but not to \$S\-0\$. The advantages of the adaotive method are that the collect of the control signals are simple and can put on any time and the chaotic system can be asymptotically stabilized to equilbrums with small control and the control disturbance will tend to zero at the same time.

关 键 词：自适应线性反馈 自适应微分反馈 混沌控制 混沌吸引子 LORENZ系统 CHEN系统 稳定性 平衡点 

分 类 号：O231[理学—运筹学与控制论] O415.5[理学—数学]