不确定时滞复杂网络的自适应控制同步  

Adaptive control synchronization for uncertain complex networkswith time-varying delays

作　　者：乔天宇 潘浩天 邵林芳 庞光鹏 张川 QIAO Tianyu;PAN Haotian;SHAO Linfang;PANG Guangpeng;ZHANG Chuan(School of Mathematical Sciences,Qufu Normal University,273165,Qufu,Shandong,PRC)

机构地区：[1]曲阜师范大学数学科学学院,山东省曲阜市273165

出　　处：《曲阜师范大学学报（自然科学版）》2023年第1期18-23,共6页Journal of Qufu Normal University(Natural Science)

基　　金：国家自然科学基金(62003189);中国博士后科学基金(2020M672024);国家级大学生创新训练项目(S202010446015).

摘　　要：文章研究了一类复杂网络的同步问题,其中网络模型中考虑了时变节点时滞和多重时变耦合时滞,系统参数未知并且节点间的耦合是不确定的.通过设计自适应控制器,实现了复杂网络的完全同步和反同步.基于Lyapunov稳定性理论和不等式方法,得到了网络同步的充分条件.上述结果同时适用于确定网络和无时滞网络的情形,结果具有一般性.仿真例子验证了控制方法的有效性.This paper investigates the synchronization of a class of complex networks,in which time-varying node delay and multiple time-varying coupling delays are both considered,and meanwhile the system parameters are unknown and the coupling between nodes are uncertain.By designing an adaptive controller,this paper realizes the complete synchronization and anti-synchronization of complex networks.By utilizing Lyapunov stability theory and inequality method,sufficient conditions for network synchronization are obtained.The above results are applicable to the deterministic networks and networks without delay,and the results are more general.Simulation examples verify the effectiveness of controllers.

关 键 词：复杂网络 LYAPUNOV函数 时变时滞 自适应控制 完全同步 反同步 

分 类 号：O157.5[理学—数学] O231[理学—基础数学]