具有可变系数的三维混沌系统与五维超混沌系统的同步问题研究

On Synchronization of 5D Hyperchaotic System and 3D Chaotic System with Variable Coefficient

本文基于中心平移同步法,研究非线性部分具有可变系数,即非线性部分系数具有不确定性的三维混沌系统与五维超混沌系统的同步问题。通过将响应三维混沌系统状态变量的中心平移至驱动五维超混沌系统的指定状态变量,将异结构系统的状态同步问题转化为与响应系统模型相同的误差系统的稳定性控制问题。该方法可有效简化同步控制器的设计过程,并可应用于驱动系统模型具有不确定性但其需同步状态及其导数已知或可通过状态观测器估算的同步问题研究中。

In this paper, the 3D chaotic system and the 5D hyperchaotic system are synchronized via the center translation method, where the variable coefficient in the nonlinear part of the 3D chaotic system is taken as the uncertainty in the synchronization. The center of the state variables of the response 3D chaotic system is translated to the assigned state variables of the drive 5D hyper-chaotic system, such that the model of the error system is the same as that of the response system. Thus, synchronization of different systems is converted to stability control of the error system. This method can effectively simplify the design procedure for synchronization controller, and it can be applied to the study of drive system with uncertainty, so long as the synchronized state variables of the drive system and their derivatives are known or can be estimated by state observer.