Synchronization of Diverse Agents via Phase Analysis

TL;DR

This paper develops phase-based synchronization conditions for heterogeneous agents in dynamical networks, providing scalable criteria and controller design methods to manage agent diversity and achieve synchronization.

Contribution

It introduces novel phase-based synchronization conditions and controller design algorithms for heterogeneous agents, extending existing methods with scalable and diversity-aware criteria.

Findings

New phase-based synchronization conditions derived

Conditions scale well with network size

Controller algorithms for diverse agents provided

Abstract

In this paper, the synchronization of heterogeneous agents interacting over a dynamical network is studied. The edge dynamics can model the inter-agent communications which are often heterogeneous by nature. They can also model the controllers of the agents which may be different for each agent or uniform for all the agents. Novel synchronization conditions are obtained for both cases from a phase perspective by exploiting a recently developed small phase theorem. The conditions scale well with the network and reveal the trade-off between the phases of node dynamics and edge dynamics. We also study the synchronizability problem which aims to characterize the allowable diversity of the agents for which controllers can be designed so as to achieve synchronization. The allowable diversity is captured in terms of phase conditions engaging the residue matrices of the agents at their persistent modes. Controller design algorithms are provided for the cases of agent-dependent and uniform controllers, respectively.