Distributed Inference of the Multiplex Network Topology of Complex Systems

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.