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Introduction to Synchronization in Nature and Physics and Cooperative Control for Multi-Agent Systems on Graphs Read chapter Read first chapter

2014 | OriginalPaper | Chapter

7. Graph Laplacian Potential and Lyapunov Functions for Multi-Agent Systems

Authors : Frank L. Lewis, Hongwei Zhang, Kristian Hengster-Movric, Abhijit Das

Published in: Cooperative Control of Multi-Agent Systems

Publisher: Springer London

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Abstract

In this chapter we show that for networked multi-agent systems, there is an energy-like function, called the graph Laplacian potential, that depends on the communication graph topology. The Laplacian potential captures the notion of a virtual potential energy stored in the graph. We shall study the Laplacian potential for both undirected graphs and directed graphs. The Laplacian potential is further used here to construct Lyapunov functions that are suitable for the analysis of cooperative control systems on graphs. These Lyapunov functions depend on the graph topology, and based on them a Lyapunov analysis technique is introduced for cooperative multi-agent systems on graphs. Control protocols coming from such Lyapunov functions are distributed in form, depending only on information about the agent and its neighbors.

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previous chapter Graphical Games: Distributed Multiplayer Games on Graphs
next chapter Cooperative Adaptive Control for Systems with First-Order Nonlinear Dynamics
Literature
1.
Astrom KJ, Wittenmark B (2008) Adaptive Control, 2nd edn. Dover, Mineola
2.
Bernstein D (2009) Matrix Mathematics: Theory, Facts, and Formulas, 2nd edn. Princeton University Press, Princeton
3.
Chopra N, Spong M (2006) Passivity-based control of multi-agent systems. In: Kawamura S, Svinin M (eds) Advances in Robot Control: From Everyday Physics to Human-Like Movements. Springer-Verlag, Berlin
4.
5.
Horn R, Johnson C (1990) Matrix Analysis. Cambridge University Press, New YorkMATH
6.
Igarashi Y, Hatanaka T, Fujita M, Spong M (2008) Passivity-based output synchronization and flocking algorithm in SE (3). In: Proc. Amer. Control Conf., Seattle, WA, pp. 723–728
7.
Ioannou P, Fidan B (2006) Adaptive Control Tutorial. SIAM Press, Philadelphia
8.
Jadbabaie A, Lin J, Morse A (2003) Coordination of groups of mobile autonomous agents using nearest neighbor rules. IEEE Trans Automat Contr 48(6):988–1001CrossRefMathSciNet
9.
Khalil H (2002) Nonlinear Systems, 3rd edn. Prentice Hall, Upper Saddle River
10.
11.
Olfati-Saber R, Murray R (2003) Consensus protocols for networks of dynamic agents. In: Proc. Amer. Control Conf., Denver, CO, pp. 951–956
12.
Olfati-Saber R, Murray R (2004) Consensus problems in networks of agents with switching topology and time-delays. IEEE Trans Automat Contr 49(9):1520–1533CrossRefMathSciNet
13.
Qu Z (2009) Cooperative Control of Dynamical Systems: Applications to Autonomous Vehicles. Springer-Verlag, London
14.
Ren W, Beard R (2008) Distributed Consensus in Multi-Vehicle Cooperative Control: Theory and Applications. Springer-Verlag, London
15.
Ren W, Beard R, Atkins E (2007) Information consensus in multivehicle cooperative control. IEEE Contr Systs Mag 27(2):71–82CrossRef
16.
Spong M, Hutchinson S, Vidyasagar M (2006) Robot Modeling and Control. Wiley, New York
17.
Zhang H, Lewis FL, Qu Z (2012) Lyapunov, adaptive, and optimal design techniques for cooperative systems on directed communication graphs. IEEE Trans Ind Elec 59(7):3026–3041CrossRef
Metadata
Title
Graph Laplacian Potential and Lyapunov Functions for Multi-Agent Systems
Authors
Frank L. Lewis
Hongwei Zhang
Kristian Hengster-Movric
Abhijit Das
Copyright Year
2014
Publisher
Springer London
Book
Cooperative Control of Multi-Agent Systems

Print ISBN: 978-1-4471-5573-7

Electronic ISBN: 978-1-4471-5574-4

Copyright Year: 2014

DOI
https://doi.org/10.1007/978-1-4471-5574-4_7