Overview
- Organizes and refocusses the latest studies in an important approach to networked and multi-agent systems
- Self-contained treatment requires only general undergraduate mathematics to make use of the content
- Extensive use of examples and exercises allow readers to practice their abilities and explore related problems
- Includes supplementary material: sn.pub/extras
Part of the book series: Lecture Notes in Control and Information Sciences (LNCIS, volume 472)
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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, the authors 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.
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Keywords
Table of contents (5 chapters)
Reviews
“This book gives a nice, conscientious introduction to the theory of averaging dynamics over networks. … The book is essentially self-contained. In particular, it does not assume any knowledge of Perron-Frobenius theory, or Markov chain convergence. Every chapter of the book is complemented by numerous exercises and bibliographical notes.” ( Jiřì Černý, Mathematical Reviews, February, 2019)
Authors and Affiliations
About the authors
Dr. Frasca has served in the Conference Editorial Boards of several events, including IEEE CDC, ACC, ECC, MTNS, IFAC NecSys, and is currently serving as Associate Editor for the International Journal of Robust and Nonlinear Control, the Asian Journal of Control, and the IEEE Control Systems Letters.
Bibliographic Information
Book Title: Introduction to Averaging Dynamics over Networks
Authors: Fabio Fagnani, Paolo Frasca
Series Title: Lecture Notes in Control and Information Sciences
DOI: https://doi.org/10.1007/978-3-319-68022-4
Publisher: Springer Cham
eBook Packages: Engineering, Engineering (R0)
Copyright Information: Springer International Publishing AG 2018
Hardcover ISBN: 978-3-319-68021-7Published: 12 November 2017
Softcover ISBN: 978-3-319-88532-2Published: 25 August 2018
eBook ISBN: 978-3-319-68022-4Published: 09 November 2017
Series ISSN: 0170-8643
Series E-ISSN: 1610-7411
Edition Number: 1
Number of Pages: XII, 135
Number of Illustrations: 19 b/w illustrations, 3 illustrations in colour
Topics: Control and Systems Theory, Systems Theory, Control, Computer Communication Networks, Robotics and Automation, Communications Engineering, Networks, Graph Theory