超混沌系统的间歇同步与控制

Hyperchaos synchronization and control using intermittent feedback

基于稳定性理论,采用间歇反馈控制研究了四维连续超混沌R ssler和LC振子系统.通过选择恰当的控制周期Ts、自治周期Ta以及反馈系数k来设计控制器.数值计算表明所设计的控制器使系统经过大约8到35个时间单位达到了稳定点,两个系统之间经过大约15到50个时间单位实现了全局同步.通过求解系统Jacobi矩阵的特征值来确定Ts与Ta的关系,获得间歇控制下控制器稳定的条件.数值计算结果与理论分析一致.

Based on the stability theory, intermittent feedback scheme is proposed to synchronize and control the four-dimensional continuous hyperehaotic Rǒssler and LC systems. The systems are directed to reach arbitrary desired target within about 8 to 35 time units and realize complete synchronization within about 15 to 50 time units under this scheme by selecting right autonomous period Ta, controlling period Ts and gain coefficient k. The advantage of this scheme is that the controller is designed analytically in detail, not only relying on the common numerical simulation. The controller works only on certain period and the system develops freely in other periods. The numerical simulation results confirmed its effectiveness and gave evidence that shorter transient period before reaching desired target requires bigger feedback coefficient k, and it is consistent with the theoretical analysis.