噪声扰动下时滞复杂网络动力学参数及拓扑结构辨识

卫亭1，杨晓丽1，孙中奎2

(1.陕西师范大学数学与信息科学学院,西安710062；2.西北工业大学应用数学系，西安710072)

摘要：针对随机噪声及时间滞后普遍存在于耦合网络，且其结构往往未知或部分未知问题，基于网络间随机广义投影滞后同步原理，通过合理设计控制器与自适应更新规则，构建辨识网络模型未知动力学参数及拓扑结构的识别方案；结合随机时滞微分方程LaSalle型不变性原理，从数学上严格证明识别方案的准确性。通过具体网络模型，借助计算仿真验证识别方案的有效性。数值模拟结果表明，网络未知动力学参数及拓扑结构不但能准确辨识，且识别方案不依赖耦合时滞、更新增益及网络拓扑结构等选取。

关键词：网络结构识别；网络同步；耦合时滞；随机噪声

中图分类号:O322文献标志码：A

基金项目：国家自然科学基金资助项目(11372081)

收稿日期：2014-09-22修改稿收到日期：2014-11-06

基金项目：国家自然科学基金重大研究计划重点支持项目“古建木构的状态评估、安全极限与性能保持”(51338001)；北京交通大学人才基金项目(2014RC011)

收稿日期：2014-07-29修改稿收到日期：2014-10-17

Identification of system parameters and network topology of delay-coupled complex networks under circumstance noise

WEITing1,YANGXiao-Li1,SUNZhong-kui2(1. Shanxi Normal University, Xi’an 710062, China; 2. Northwestern Polytechnical University, Xi’an 710072, China)

Abstract:Noting that the random noise and time delay are prevalent in complex networks and the topology of a network is often unknown or partially unknown, based on the principle of random generalized projective lag synchronization, an approach was proposed to estimate the system parameters and topological structure of delay-coupled complex networks under circumstance noise. By constructing an appropriate controller and adaptive updating rules, the unknown network parameters and topological structure of the concerned networks were identified simultaneously. The accuracy of the method was rigorously proved by the LaSalle-type theorem for stochastic differential delay equations．An example of network with chaotic oscillator was provided to illustrate the method. The numerical results indicate that the unknown network parameters and topological structure can be accurately identified, and yet the proposed method is robust against the time delay, the update gain and the network topology.

Key words:topology identification; network synchronization; coupled delay; random noise

在网络结构已知条件下，有关其统计特征(如平均路径长度、度分布、聚类系数)的动力学行为及控制、网络结构对动力学影响等获得广泛研究[1-7]。然而，由于各种因素的不确定性，诸多(如蛋白质相互作用、生物神经、电力等)网络动力学参数或拓扑结构往往未知或部分未知，因此，辨识网络模型的动力学参数及拓扑结构在复杂动力网络研究中具有重要的理论意义与应用价值。……