参数不确定混沌系统的自适应同步

针对参数未知的混沌系统，提出了一种基于参数估计和黎卡提不等式的自适应混沌同步方法.利用
李雅普若夫稳定性理论，证明了混沌同步的问题可以转化为黎卡提不等式的求解.用状态观测器方法构造
同步混沌接收系统，根据最速下降法辨识未知参数.结合严格正实函数的概念，分析了实现混沌同步保密
通信的条件，构造并求解相应的黎卡提不等式和等式组得到目标矩阵，实现混沌系统的同步和参数的自适
应估计.并通过对蔡氏电路的同步及双通道保密通信的仿真研究，结果表明，该同步方法可以实现两个系
统参数未知的混沌系统的快速同步，及信息信号得以复杂的加密和正确地接收.

Adaptive synchronization of parameter uncertain chaotic systems

Aimed at chaotic systems with unknown parameters,an adaptive chaotic synchronization method based on parameters identification and Riccati inequality was proposed. By using Lyapunov stability theory,the rule that chaotic synchronization could be transformed into the resolution of a Riccati inequality was proved.A synchronous chaotic receive system was constructed by a state observer method,and the unknown parameters were identified by steepest descend method.The condition of chaotic synchronous secure communication realization was analyzed by applying the concept of severe positive real function.The corresponding Riccati inequality and equality group was constructed and resolved to obtain the object matrix,and the chaotic system synchronization and the parameter adaptive identification were achieved.Chua's synchronous circuit and two-channel secure communication were simulated.The results show that the proposed method can rapidly realize the synchronization of two chaotic systems with unknown parameters,and can encrypt complexly and received accurately the information signal.