EECI09: Graph theory: Difference between revisions
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{{eeci-sp09 header|prev= | {{eeci-sp09 header|prev=Information patterns|next=Distributed control}} | ||
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This lecture gives an introduction to some concepts and tools in graph theory. After giving the basic definitions of graphs and properties of graphs, we introduce the Laplacian of a matrix and discuss its properties and uses. Special emphasis is placed on the eigenvalues of the Laplacian, including the bounding of those eigenvalues using the Gershgorin disk theorem. The consensus problem is introduced as an example of the use of the basic concepts. | |||
== Lecture Materials == | == Lecture Materials == | ||
* Lecture slides: {{eeci-sp09 pdf| | * Lecture slides: {{eeci-sp09 pdf|L4_graphtheory.pdf|An Introduction to Graph Theory}} | ||
== Further Reading == | == Further Reading == | ||
* <p>[http://www. | *<p>[http://www.amazon.com/exec/obidos/ASIN/0387952209/drgordonroyle/002-0302673-7388830 Algebraic Graph Theory] G. Royle and C. Godsil, Springer, Graduate Texts in Mathematices, 2001. </p> | ||
*<p>[http://www.cds.caltech.edu/~murray/papers/2003f_om04-tac.html Consensus problems in networks of agents with switching topology and time-delays], R. Olfati-Saber and R. M. Murray, IEEE Transactions on Automatic Control, vol. 49, 1520-1533, Sept. 2004. A good reference for continuous time consensus algorithms. </p> | |||
* [http:// | |||
* [[EECI08: | *<p>[http://www.seas.upenn.edu/~jadbabai/papers/JadLiMorseTAC_June03.pdf Coordination of groups of mobile autonomous agents using nearest neighbor rules], A. Jadbabaie, J. Lin, and A. S. Morse, IEEE Transactions on Automatic Control, Vol. 48, No. 6, June 2003, pp. 988-1001. A good reference for discrete time consensus algorithms and theoretical explanation for consensus of multi-agent systems using nearest neighbor rules.</p> | ||
== Additional Information == | |||
* [[EECI08: Information Flow and Consensus|2008 lecture page]] | |||
Latest revision as of 00:21, 8 March 2009
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This lecture gives an introduction to some concepts and tools in graph theory. After giving the basic definitions of graphs and properties of graphs, we introduce the Laplacian of a matrix and discuss its properties and uses. Special emphasis is placed on the eigenvalues of the Laplacian, including the bounding of those eigenvalues using the Gershgorin disk theorem. The consensus problem is introduced as an example of the use of the basic concepts.
Lecture Materials
- Lecture slides: An Introduction to Graph Theory
Further Reading
Algebraic Graph Theory G. Royle and C. Godsil, Springer, Graduate Texts in Mathematices, 2001.
Consensus problems in networks of agents with switching topology and time-delays, R. Olfati-Saber and R. M. Murray, IEEE Transactions on Automatic Control, vol. 49, 1520-1533, Sept. 2004. A good reference for continuous time consensus algorithms.
Coordination of groups of mobile autonomous agents using nearest neighbor rules, A. Jadbabaie, J. Lin, and A. S. Morse, IEEE Transactions on Automatic Control, Vol. 48, No. 6, June 2003, pp. 988-1001. A good reference for discrete time consensus algorithms and theoretical explanation for consensus of multi-agent systems using nearest neighbor rules.
