Network Identification for Diffusively-Coupled Systems with Minimal Time Complexity
Miel Sharf, Daniel Zelazo
TL;DR
This work tackles the problem of identifying the topology and edge weights of diffusively-coupled networks with nonlinear, potentially non-smooth dynamics by exploiting steady-state responses to constant exogenous inputs. It introduces a sub-cubic identification algorithm that linearizes the steady-state relation around a chosen operating point, enabling recovery of the incidence structure and weights from multiple input-output pairs. The authors establish that their approach is time-optimal under a discretized complexity framework and provide robustness results under noise, disturbances, and partial actuator availability, complemented by two numerical case studies with discontinuous dynamics. The findings extend network identification to broad nonlinear settings, with practical implications for scalable and energy-efficient probing in large multi-agent systems.
Abstract
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.