超混沌系统的控制研究

On the Control of Hyperchaotic System

采用自适应控制方法对一个新的超混沌系统进行控制.当系统参数未知时,通过对原超混沌系统进行坐标变换,将原超混沌系统状态控制到系统的任意一个不稳定的平衡点的控制问题转换为变换后系统在坐标原点的镇定问题.基于Lyapunov稳定性定理,设计合适的控制器以及参数自适应律对系统进行控制,借助巴巴拉特引理,通过理论推导证明了在所设计的控制器及参数自适应律作用下经坐标变换后的超混沌系统在原点是渐近稳定的,从而实现了将原超混沌系统控制到任意一个不稳定平衡点的目标,仿真结果力证了该方法的有效性.

An adaptive control method was used to control a new hyperchaotic system.When the system parameters are unknown,by means of coordinating transformation of the original hyperchaotic system,the control problem of the original hyperchaotic system state to any unstable equilibrium point of the system was transformed into the stabilization problem of the transformed system at the coordinate origin.Based on Lyapunov stability theorem,a suitable controller and parameter adaptive law was designed to control the system.With the help of babarat lemma,the hyperchaotic system after coordinate transformation is asymptotically stable at the origin under the action of the designed controller and parameter adaptive law,so that the original hyperchaotic system can be controlled to any instability.The simulation results showed the effectiveness of the method.