Topology Identification of Dynamical Signed Graphs

TL;DR

This paper introduces an adaptive control method for identifying the topology of dynamical signed networks, ensuring simultaneous network identification and synchronization with proven stability.

Contribution

It presents a novel adaptive control protocol that guarantees topology identification and synchronization in signed networks modeled with a repelling Laplacian.

Findings

Guarantees simultaneous network identification and synchronization.

Establishes uniform semiglobal practical asymptotic stability of estimation errors.

Numerical simulations validate the theoretical results.

Abstract

We propose an adaptive control protocol for identifying the topology of dynamical networks interconnected over undirected graphs with cooperative and antagonistic interactions. The signed network is modeled using a repelling Laplacian. Topology identification relies on an edge-based formulation of the network and adaptive control protocols through the design of a persistently excited auxiliary network. Our approach guarantees the simultaneous identification and synchronization of the unknown signed network and establishes uniform semiglobal practical asymptotic stability of the estimation errors. Numerical simulations validate our theoretical results.