超混沌Liu系统的控制研究

Control of Hyperchaotic Liu System

研究了超混沌Liu系统的自适应反馈控制和基于微分几何理论的状态反馈精确线性化方法控制的问题.首先利用Matlab软件计算了系统的平衡点以及该平衡点处系统的特征值,对系统进行了耗散性分析,确定了系统中混沌吸引子的存在,利用Wolf方法计算了系统的Lyapunov指数,绘制了超混沌Liu系统的相轨迹图和时域波形图,验证了该超混沌系统中蕴含的复杂动力学行为,然后分别采用自适应反馈控制方法和状态反馈精确线性化方法对超混沌Liu系统中出现的混沌现象进行控制,通过设计合适的控制器使超混沌Liu系统均能收敛于系统的惟一一个不稳定平衡点,最后通过数值仿真验证以上两种方法,仿真结果力证了控制方法的有效性.

The adaptive feedback control and the precise linearization control of state feedback based on differential geometry theory were studied for hyperchaotic Liu systems.Firstly,the equilibrium point of the system and its eigenvalue at the equilibrium point were calculated by using Matlab software,the dissipation of the system was analyzed,and the existence of chaotic attractors in the system was confirmed.The Lyapunov exponent of the system was calculated by using Wolf method,the phase trajectories and time domain waveform diagram of the hyperchaotic Liu system were drawn,and its complex dynamic behavior was verified.Then the adaptive feedback control method and and the precise linearization method of state feedback were used to control the chaotic phenomena in the hyperchaotic Liu system respectively.By designing appropriate controllers,the hyperchaotic Liu system can converge to its sole unstable equilibrium point.Finally,the above two methods were verified by numerical simulation,and the simulation results prove the effectiveness of the control method.