Graph Laplacian Potential and Lyapunov Functions for Multi-Agent Systems

Frank L. Lewis; Hongwei Zhang; Kristian Hengster-Movric; Abhijit Das

doi:10.1007/978-1-4471-5574-4_7

Graph Laplacian Potential and Lyapunov Functions for Multi-Agent Systems

Frank L. Lewis^*
, Hongwei Zhang
, Kristian Hengster-Movric
, Abhijit Das

^*Corresponding author for this work

University of Texas at Arlington
Southwest Jiaotong University
Danfoss AS

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

19 Scopus citations

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.

Original language	English
Title of host publication	Communications and Control Engineering
Publisher	Springer International Publishing
Pages	221-234
Number of pages	14
Edition	9781447155737
DOIs	https://doi.org/10.1007/978-1-4471-5574-4_7
State	Published - 2014
Externally published	Yes

Publication series

Name	Communications and Control Engineering
Number	9781447155737
ISSN (Print)	0178-5354
ISSN (Electronic)	2197-7119

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10.1007/978-1-4471-5574-4_7

Cite this

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title = "Graph Laplacian Potential and Lyapunov Functions for Multi-Agent Systems",

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.",

author = "Lewis, \{Frank L.\} and Hongwei Zhang and Kristian Hengster-Movric and Abhijit Das",

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Graph Laplacian Potential and Lyapunov Functions for Multi-Agent Systems. / Lewis, Frank L.; Zhang, Hongwei; Hengster-Movric, Kristian et al.
Communications and Control Engineering. 9781447155737. ed. Springer International Publishing, 2014. p. 221-234 (Communications and Control Engineering; No. 9781447155737).

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

TY - CHAP

T1 - Graph Laplacian Potential and Lyapunov Functions for Multi-Agent Systems

AU - Lewis, Frank L.

AU - Zhang, Hongwei

AU - Hengster-Movric, Kristian

AU - Das, Abhijit

PY - 2014

Y1 - 2014

N2 - 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.

AB - 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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PB - Springer International Publishing

ER -

Graph Laplacian Potential and Lyapunov Functions for Multi-Agent Systems

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