Network Identification for Diffusively Coupled Networks with Minimal Time Complexity

The theory of network identification, namely, identifying the (weighted) interaction topology among a known number of agents, has been widely developed for linear agents. However, the theory for nonlinear agents using probing inputs is far less developed, relying on dynamics linearization and, thus, cannot be applied to networks with nonsmooth or discontinuous dynamics. In this article, we use global convergence properties of the network, which can be ensured using passivity theory, to present a network identification method for nonlinear agents. We do so by linearizing the steady-state equations rather than the dynamics, achieving a sub-cubic time algorithm for network identification. We also study the problem of network identification from a complexity theory standpoint, showing that the presented algorithms are optimal in terms of time complexity. We demonstrate the presented algorithm in two case studies with discontinuous dynamics.