受扰不确定混沌系统的双路组合函数投影同步  

Two-way Combined Function Projection Synchronization of Uncertain Chaotic System

作　　者：王延峰 张胤 安小宇 方洁 WANG Yan-feng;ZHANG Yin;AN Xiao-yu;FANG Jie(Zhengzhou University of Light Industry,Zhengzhou 450002,China)

机构地区：[1]郑州轻工业大学电气信息工程学院,河南郑州450002

出　　处：《数学的实践与认识》2021年第6期112-119,共8页Mathematics in Practice and Theory

基　　金：国家自然科学基金(61775198);河南省科技攻关项目(202102210317,192102210083);河南省高等学校重点科研项目(20A413012)。

摘　　要：研究了具有未知参数和外界扰动的多个混沌系统之间的双路组合函数投影同步问题.首先给出了由四个混沌驱动系统和两个混沌响应系统组成的双路组合函数投影同步系统的定义,然后以Lyapunov稳定性理论和不等式变换方法为分析依据,设计了鲁棒自适应控制器和参数自适应律,使得两路同步系统中的响应系统和驱动系统按照相应的函数比例因子矩阵实现同步,并有效克服未知有界干扰和未知参数的影响.相应的理论分析和数值仿真证明了该同步方案的可行性和有效性.This paper studies the two-way combined function projection synchronization between multiple chaotic systems with unknown parameters and external disturbances.Firstly,a two-way combined function projection synchronization system consisting of four chaotic driving systems and two chaotic response systems is defined.Then the robust adaptive controller and parameter adaptive law are designed based on Lyapunov stability theory and inequality transformation method,by which the response systems and the drive systems in the two-way synchronization system can realize synchronization according to the corresponding function scale factor matrix.The effects of unknown bounded interference and unknown parameters are effectively overcome by the controller.Theoretical analysis and numerical simulation prove the feasibility and effectiveness of the synchronization scheme.

关 键 词：混沌系统 双路组合函数投影同步 自适应控制 未知参数 干扰 

分 类 号：O415.5[理学—理论物理] O231[理学—物理]