Introduction to Averaging Dynamics over Networks

  • Fabio Fagnani
  • Paolo Frasca

Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 472)

Table of contents

  1. Front Matter
    Pages i-xii
  2. Fabio Fagnani, Paolo Frasca
    Pages 1-30
  3. Fabio Fagnani, Paolo Frasca
    Pages 31-67
  4. Fabio Fagnani, Paolo Frasca
    Pages 69-92
  5. Fabio Fagnani, Paolo Frasca
    Pages 93-108
  6. Fabio Fagnani, Paolo Frasca
    Pages 109-131
  7. Back Matter
    Pages 133-135

About this book


This book deals with averaging dynamics, a paradigmatic example of network based dynamics in multi-agent systems. The book presents all the fundamental results on linear averaging dynamics, proposing a unified and updated viewpoint of many models and convergence results scattered in the literature.

Starting from the classical evolution of the powers of a fixed stochastic matrix, the text then considers more general evolutions of products of a sequence of stochastic matrices, either deterministic or randomized. The theory needed for a full understanding of the models is constructed without assuming any knowledge of Markov chains or Perron–Frobenius theory. Jointly with their analysis of the convergence of averaging dynamics, theauthors derive the properties of stochastic matrices. These properties are related to the topological structure of the associated graph, which, in the book’s perspective, represents the communication between agents. Special attention is paid to how these properties scale as the network grows in size.

Finally, the understanding of stochastic matrices is applied to the study of other problems in multi-agent coordination: averaging with stubborn agents and estimation from relative measurements. The dynamics described in the book find application in the study of opinion dynamics in social networks, of information fusion in sensor networks, and of the collective motion of animal groups and teams of unmanned vehicles. Introduction to Averaging Dynamics over Networks will be of material interest to researchers in systems and control studying coordinated or distributed control, networked systems or multiagent systems and to graduate students pursuing courses in these areas.


Coordinated Control Consensus Dynamics Averaging Dynamics Graph-theoretic Methods in Control Multi-agent Systems Networked Systems Autonomous-vehicle Networks Opinion Dynamics

Authors and affiliations

  • Fabio Fagnani
    • 1
  • Paolo Frasca
    • 2
  1. 1.Dipartimento di Scienze Matematiche “Giuseppe Luigi Lagrange”Politecnico di TorinoTurinItaly
  2. 2.GIPSA-labCNRSGrenobleFrance

Bibliographic information

  • DOI
  • Copyright Information Springer International Publishing AG 2018
  • Publisher Name Springer, Cham
  • eBook Packages Engineering Engineering (R0)
  • Print ISBN 978-3-319-68021-7
  • Online ISBN 978-3-319-68022-4
  • Series Print ISSN 0170-8643
  • Series Online ISSN 1610-7411
  • Buy this book on publisher's site