具有不确定链接的大规模非线性网络的均方同步
Mean sqaure synchronization in large scale nonlinear networks with uncertain links
摘要：
在本文中，我们研究了网络组件之间的随机相互作用的同步问题。网络组件的动态是非线性的，并在网络组件之间的线性随机相互作用的Lure形式建模。为了研究这个问题，我们首先证明了随机版本的正实引理（PRL）。然后利用随机PRL结果给出了随机网络系统同步的充分条件。同步的充分条件是标称（平均）耦合拉普拉斯特征值和色散系数（CoD）形式的链路不确定性统计的函数。与现有文献中关于网络同步的研究结果相反，我们的研究结果表明平均拉普拉斯算子的最大和次小特征值在随机网络的同步中起着重要的作用.鲁棒控制为基础的小增益的解释推导出的充分条件，使我们能够定义的同步裕度。同步裕度用于理解组件动态、网络拓扑和不确定性特性之间的重要权衡。对于一类特殊的环拓扑网络系统，我们给出了环维数与邻域个数之间的折衷关系的解析表达式。同样地，利用元件动力学的相同性质，对于一般类型的网络系统，给出了计算效率与网络大小无关的充分条件。对具有随机链路不确定性的耦合振子网络的仿真结果验证了所提出的理论框架。
英文摘要：
In this paper, we study the problem of synchronization with stochastic interaction among network components. The network components dynamics is nonlinear and modeled in Lure form with linear stochastic interaction among network components. To study this problem we first prove the stochastic version of Positive Real Lemma (PRL). The stochastic PRL result is then used to provide sufficient condition for synchronization of stochastic network system. The sufficiency condition for synchronization, is a function of nominal (mean) coupling Laplacian eigenvalues and the statistics of link uncertainty in the form of coefficient of dispersion (CoD). Contrary to the existing literature on network synchronization, our results indicate that both the largest and the second smallest eigenvalue of the mean Laplacian play an important role in synchronization of stochastic networks. Robust control-based small-gain interpretation is provided for the derived sufficiency condition which allow us to define the margin of synchronization. The margin of synchronization is used to understand the important tradeoff between the component dynamics, network topology, and uncertainty characteristics. For a special class of network system connected over torus topology we provide an analytical expression for the tradeoff between the number of neighbors and the dimension of the torus. Similarly, by exploiting the identical nature of component dynamics computationally efficient sufficient condition independent of network size is provided for general class of network system. Simulation results for network of coupled oscillators with stochastic link uncertainty are presented to verify the developed theoretical framework.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
