一类参数不确定混沌系统特殊的线性广义同步

Specific Linear Generalized Synchronization for A Class of Chaotic System with Unknown Parameters

研究了一类参数不确定混沌系统特殊的线性广义同步问题。实际系统受到干扰时,参数失真,使得这类混沌系统,在参数不匹配的情况下,根据线性广义函数与驱动系统系数矩阵的相关性,设计了非线性反馈控制器以及参数自适应律,实现了主从系统的线性广义同步。借助Lyapunov稳定性定理与Barbalat引理,严格证明了定理的正确性。对于具体的混沌系统,控制器还可以进一步简化,以Lorenz系统为例,计算机仿真结果证实了方法的正确性与有效性。

The problem of linear generalized synchronizdtion of a class of chaotic systems with unkown parame- ters, is investigated based on a single adaptive control. For the class of chaotic systems, on the basis of the corelation between linearly generalized function and the drive＇s coefficient matrix, the linear control and the adaptive principle of parameters make the master - slave system linear generalized synchronization under the condition of uncertain param- eters. By the Lyapunov stability theory and Barbalat lemma, the theory of the chaotic system proves to be right. Take specific chaotic system such as Lorenz system for an example, the controllers are able to be more simplified, and nu- merical simulation illustrates the feasibility of the technique.