Controllability and data-driven identification of bipartite consensus on nonlinear signed networks

TL;DR

This paper investigates the controllability of nonlinear signed networks with negative weights, revealing how structural balance and symmetries affect controllability, and proposes data-driven methods to identify bipartite structures using Koopman operator approximation.

Contribution

It identifies the role of structural balance and symmetries in uncontrollability and introduces a data-driven approach to extract bipartite structures in nonlinear signed networks.

Findings

Structural balance leads to uncontrollability under certain symmetries.

Extended Dynamic Mode Decomposition can extract bipartite structures from data.

Controllability is influenced by network structure and symmetries.

Abstract

Nonlinear networked systems are of interest in several areas of research, such as multi-agent systems and social networks. In this paper, we examine the controllability of several classes of nonlinear networked dynamics on which the underlying graph admits negative weights. Such signed networks exhibit bipartite clustering when the underlying graph is structurally balanced. We show that structural balance is the key ingredient inducing uncontrollability when combined with a leader-node symmetry and a certain type of dynamical symmetry. We then examine the problem of extracting the bipartite structure of such graphs from data using Extended Dynamic Mode Decomposition to approximate the corresponding Koopman operator.