EECI08: Information Flow and Consensus - Revision history

Murray at 20:26, 1 March 2009

2009-03-01T20:26:26Z

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	{{eeci-sp08 header\|next=[[~~NCS~~: Distributed Estimation and Control\|Distributed Control]]\|prev=[[~~NCS~~: Packet-Based Estimation and Control\|Packet-Based Control]]}}		{{eeci-sp08 header\|next=[[EECI08: Distributed Estimation and Control\|Distributed Control]]\|prev=[[EECI08: Packet-Based Estimation and Control\|Packet-Based Control]]}}

	{{righttoc}}		{{righttoc}}

Murray: EECI: Information Flow and Consensus moved to EECI08: Information Flow and Consensus

2009-03-01T20:16:45Z

EECI: Information Flow and Consensus moved to EECI08: Information Flow and Consensus

← Older revision		Revision as of 20:16, 1 March 2009
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Murray: /* Lecture Materials */

2008-03-30T23:50:58Z

Lecture Materials

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	== Lecture Materials ==		== Lecture Materials ==
	* Lecture slides: {{eeci-sp08 pdf\|L8_graphtheory.pdf\|An Introduction to Graph Theory}}		* Lecture slides: {{eeci-sp08 pdf\|L8_graphtheory.pdf\|An Introduction to Graph Theory}}
			** Some students had troubles print these due to font issues. Here is a {{eeci-sp08 pdf\|L8_graphtheory-scan.pdf\|scan}} of the notes in case you can't get them to print.

	== Reading ==		== Reading ==

Murray at 01:03, 29 March 2008

2008-03-29T01:03:18Z

← Older revision		Revision as of 01:03, 29 March 2008
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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.		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-sp08 pdf\|L8_graphtheory.pdf\|An Introduction to Graph Theory}}		* Lecture slides: {{eeci-sp08 pdf\|L8_graphtheory.pdf\|An Introduction to Graph Theory}}

	==~~== Additional Information ====~~		== Reading ==

	~~==== Further~~ Reading ====
	*<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.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>

Murray: /* Further Reading */

2008-03-29T00:39:37Z

Murray at 00:38, 29 March 2008

2008-03-29T00:38:00Z

← Older revision		Revision as of 00:38, 29 March 2008
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	{{righttoc}}		{{righttoc}}
			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 ====

Murray at 15:59, 28 March 2008

2008-03-28T15:59:15Z

← Older revision		Revision as of 15:59, 28 March 2008
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	==== Additional Information ====		==== Additional Information ====

	\|}

	==== Further Reading ====		==== Further Reading ====

Murray: NCS: Information Flow and Consensus moved to EECI: Information Flow and Consensus

2008-03-28T15:21:48Z

NCS: Information Flow and Consensus moved to EECI: Information Flow and Consensus

← Older revision		Revision as of 15:21, 28 March 2008
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Murray at 10:06, 21 March 2008

2008-03-21T10:06:20Z

← Older revision		Revision as of 10:06, 21 March 2008
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	{{righttoc}}		{{righttoc}}
	This lecture describes how to extend results in estimation and control to the case where the information between sensing, actuation and computation flows across a network with possible packet loss and time delay. We begin with the estimation problem, summarizing the results on Sinopoli et al on Kalman filtering with intermittent data, which uses average convergence as a stability metric. An alternative formulation is to use almost sure convergence, which gives improved results for lossy networks. Finally, we extend the results on estimation to the control setting, summarizing approaches in the cases where receipt of packets are acknowledge (TCP-like) or not acknowledged (UDP-like).

	==== Lecture Materials ====		==== Lecture Materials ====

Murray at 10:06, 21 March 2008

2008-03-21T10:06:10Z

New page

{{eeci-sp08 header|next=[[NCS: Distributed Estimation and Control|Distributed Control]]|prev=[[NCS: Packet-Based Estimation and Control|Packet-Based Control]]}}

{{righttoc}}
This lecture describes how to extend results in estimation and control to the case where the information between sensing, actuation and computation flows across a network with possible packet loss and time delay. We begin with the estimation problem, summarizing the results on Sinopoli et al on Kalman filtering with intermittent data, which uses average convergence as a stability metric. An alternative formulation is to use almost sure convergence, which gives improved results for lossy networks. Finally, we extend the results on estimation to the control setting, summarizing approaches in the cases where receipt of packets are acknowledge (TCP-like) or not acknowledged (UDP-like).

==== Lecture Materials ====
* Lecture slides: {{eeci-sp08 pdf|L8_graphtheory.pdf|An Introduction to Graph Theory}}

==== Additional Information ====

|}

==== Further Reading ====

← Older revision		Revision as of 00:39, 29 March 2008
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	==== Further Reading ====		==== Further Reading ====
			*<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>

			*<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>