Network Identification: A Passivity and Network Optimization Approach

TL;DR

This paper introduces a novel method for identifying the interaction topology among nonlinear agents using passivity and network optimization, extending existing linear theories to more complex systems.

Contribution

It develops a network identification approach for nonlinear agents based on MEIP and optimization, including a distributed cubic-time algorithm for linear agents.

Findings

The method successfully identifies network topology in nonlinear systems.

A distributed cubic-time algorithm is derived for linear agents.

An example demonstrates application to neural network models.

Abstract

The theory of network identification, namely identifying the interaction topology among a known number of agents, has been widely developed for linear agents over recent years. However, the theory for nonlinear agents remains less extensive. We use the notion maximal equilibrium-independent passivity (MEIP) and network optimization theory to present a network identification method for nonlinear agents.We do so by introducing a specially designed exogenous input, and exploiting the properties of networked MEIP systems. We then specialize on LTI agents, showing that the method gives a distributed cubic-time algorithm for network reconstruction in that case. We also discuss different methods of choosing the exogenous input, and provide an example on a neural network model.