Many natural and engineered systems can be modeled as a set of nonlinear units interacting with each other over a network of interconnections. Often, such interactions occur through different types of functions giving rise to so-called multiplex networks. As an example, two masses can interact through both a spring and a damper. In many practical applications, the multiplex network topology is unknown, and global information is not available. In this paper, we propose a novel distributed approach to infer the network topology for a class of networks with both nonlinear node dynamics and multiplex couplings. In our strategy, the estimators measure only local network states but cooperate with their neighbors to fully infer the network topology. Sufficient conditions for stability and convergence are derived using appropriate Lyapunov functions. Applications to networks of chaotic oscillators and multirobot manipulation are presented to validate our theoretical findings and illustrate the effectiveness of our approach.

中文翻译：

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复杂系统的复用网络拓扑的分布式推理

许多自然和工程系统可以建模为一组通过互连网络相互交互的非线性单元。通常，这种相互作用是通过不同类型的功能发生的，从而产生了所谓的多路复用网络。例如，两个质量块可以通过弹簧和阻尼器相互作用。在许多实际应用中，复用网络拓扑是未知的，并且全局信息不可用。在本文中，我们提出了一种新颖的分布式方法来推断一类同时具有非线性节点动力学和多重耦合的网络的网络拓扑。在我们的策略中，估算器仅测量本地网络状态，但与邻居协作以完全推断网络拓扑。使用适当的Lyapunov函数可以得出稳定和收敛的充分条件。