  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 non-smooth or discontinuous dynamics. We use
global convergence properties of the network, which can be assured 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.

Systems and Control;Optimization and Control