Simultaneous Topology Estimation and Synchronization of Dynamical Networks with Time-varying Topology

TL;DR

This paper introduces an adaptive control method for real-time estimation of changing network topology and synchronization in complex dynamical systems, leveraging an edge-agreement framework and auxiliary networks.

Contribution

It presents a novel approach transforming topology estimation into weight estimation of a complete graph, with auxiliary networks ensuring stability and bounded errors.

Findings

Effective topology and synchronization estimation demonstrated in numerical example.

Method handles unknown, time-varying network topologies.

Ensures bounded estimation and synchronization errors under specified conditions.

Abstract

We propose an adaptive control strategy for the simultaneous estimation of topology and synchronization in complex dynamical networks with unknown, time-varying topology. Our approach transforms the problem of time-varying topology estimation into a problem of estimating the time-varying weights of a complete graph, utilizing an edge-agreement framework. We introduce two auxiliary networks: one that satisfies the persistent excitation condition to facilitate topology estimation, while the other, a uniform-$\delta$ persistently exciting network, ensures the boundedness of both weight estimation and synchronization errors, assuming bounded time-varying weights and their derivatives. A relevant numerical example shows the efficiency of our methods.