时滞复杂动态网络的有限时间随机广义外部同步  

Finite-time stochastic generalized outer synchronization of time-delayed complex dynamical networks

作　　者：李望[1,2] 马志才[2] 侍红军[2] LI Wang MA Zhicai SHI Hongjun(Basic Department, Jiangsu Xuzhou Medical College, Xuzhou 221008, Jiangsu, China School of Mathematics, China University of Mining and Technology, Xuzhou 221008, Jiangsu, China)

机构地区：[1]江苏徐州医药高等职业学校基础部,江苏徐州221116 [2]中国矿业大学数学学院,江苏徐州221116

出　　处：《山东大学学报（工学版）》2017年第3期1-7,78,共8页Journal of Shandong University（Engineering Science）

基　　金：国家自然科学基金资助项目(61403393);中央高校基本科研业务费资助项目(2015XKMS076)

摘　　要：基于有限时间控制技术以及开环控制技术,研究具有噪声干扰的时滞复杂动态网络的有限时间广义外部同步问题。设计新的有限时间控制器,利用随机微分方程的稳定性理论得到网络实现有限时间随机广义外部同步的充分条件。研究表明:设计的控制器对于噪声干扰具有较强的鲁棒性,且网络同步时间与控制强度密切相关。在其他条件不变的情况下,网络同步时间随着控制强度的增大而减小。数值模拟中分别选择R?ssler-like系统和Hindmarsh-Rose系统作为驱动网络与响应网络的节点动力学,给出了网络同步误差和总同步误差的演化轨迹。数值模拟结果验证了理论结果的有效性与可行性。Based on the finite-time control technology and the open-loop control method, the generalized outer synchro- nization between two complex dynamical networks with time delay and noise perturbation was investigated. A new fi- nite-time controller was designed and the sufficient condition for the finite-time stochastic generalized outer synchroniza- tion was obtained based on the finite-time stability theory of stochastic differential equations. The results showed that the synchronization scheme was robust to the noise perturbation. The theoretical results showed that the synchronization time depended on the control strength. Under the same conditions, the synchronization time decreased with the increasing of the control strength. In the numerical examples, the R6ssler-like system and Hindmarsh-Rose system were chosen as the node dynamics of the drive and response networks, respectively. The time evolution trajectories of synchronization error and total synchronization error were given. The effectiveness and feasibility of the theoretical result was confirmed by the numerical results.

关 键 词：复杂网络 同步 噪声 时滞 

分 类 号：TP13[自动化与计算机技术—控制理论与控制工程]