Differential inequalities in multi-agent coordination and opinion dynamics modeling

Journal article (2017)

Authors

A.V. Proskurnikov Team Tamas Keviczky - Mechanical, Maritime and Materials Engineering , ITMO University
Ming Cao University Medical Center Groningen
Research Group
Team Tamas Keviczky (Mechanical, Maritime and Materials Engineering) (TU Delft)
Multi-agent systems Cooperative control Complex network Distributed algorithm
More Info
expand_more

Published Date

2017

Language

English

Reuse Rights

Other than for strictly personal use, it is not permitted to download, forward or distribute the text or part of it, without the consent of the author(s) and/or copyright holder(s), unless the work is under an open content license such as Creative Commons.

Faculty

Mechanical, Maritime and Materials Engineering

Department

Delft Center for Systems and Control

Research Group

Team Tamas Keviczky

Abstract

Many distributed algorithms for multi-agent coordination employ the simple averaging dynamics, referred to as the Laplacian flow. Besides the standard consensus protocols, examples include, but are not limited to, algorithms for aggregation and containment control, target surrounding, distributed optimization and models of opinion formation in social groups. In spite of their similarities, each of these algorithms has been studied using separate mathematical techniques. In this paper, we show that stability and convergence of many coordination algorithms involving the Laplacian flow dynamics follow from the general consensus dichotomy property of a special differential inequality. The consensus dichotomy implies that any solution to the differential inequality is either unbounded or converges to a consensus equilibrium. In this paper, we establish the dichotomy criteria for differential inequalities and illustrate their applications to multi-agent coordination and opinion dynamics modeling.