Network Identification for Diffusively-Coupled Systems with Minimal Time Complexity
It provides a theoretically optimal and practical solution for identifying interaction topologies in nonlinear diffusively-coupled networks, addressing a gap in existing methods that rely on dynamics linearization.
This paper presents a network identification method for nonlinear agents with non-smooth or discontinuous dynamics by linearizing steady-state equations, achieving a sub-cubic time algorithm that is proven optimal in 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 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.