IEEE Paper, 18 Apr 05
Present: Fax, Murray, OlfatiSaber
Contents
 1 Agenda
 2 Discussion of papers
 3 New papers to consider
 4 Common themes
 4.1 "Protocols" for concensus and cooperation
 4.2 Laplacians and Graph Theory
 4.3 From Consensus to Cooperation: Closing the Loop
 4.4 Continuous versus Discrete
 4.5 Switching and TimeDelays
 4.6 Role of Consensus in Distributed Estimation
 4.7 Relationship to Distributed Computation
 4.8 Performance
 4.9 Open Problems
 5 Agenda for next meeting
Agenda
 Discuss papers we came up with last time
 Add new papers to the list that we think we should read
 Include papers from ACC 2005
 Discuss common themes
 Set agenda for next meeting
Discussion of papers
ViscekThis is the paper that Ali cites and so everyone cites it. In the physics community, this is cited correctly. In controls, this paper is often credited with things that aren't really in the paper. Deals with alignment in flocking behavior. Position of agenda matters (who are your neighbors). Uses a completely nonlinear protocol as his alignment rule. Agents move with velocity v in the plane. Looks at effects of change in density and change in noise. Some further work on crowd control (published in Nature) using similar tools (purely computational). 
Takeaways for our paper

Related papers

TabuadaCurrently at Notre Dame. Alex cited this in this thesis. Was done in the context of nonholonomic vehicle. What graphs would you set up to enable meaningful controls. Started with acyclic graphs. Paper was never accepted into a journal. 
Takeaways for our paper

Related papers

FaxWould be nice to see more work in the area of performance and observer structure. Various followon results have not yet been followed up. Getting information from different sources (potentially at different times). Action (Alex): look at papers that cite this one (google scholar) and make sure we understand what further results have been achieved. 
Takeaways for our work

Related papers

OlfatiSaberWe can use this paper for the basic definitions that we want to include. This paper also highlights the role of balanced graphs (and more generally the difference between directed and undirected). For balanced graphs, we can solve average consensus for any linear function. 
Takeaways for our work

Related papers

JadbabaieOne of the early papers to look at switching and the stability properties in this case. We might be able to say this in a bit more consistent terminology with current work. First order linear process (so it doesn't quite apply to Viscek's model). Relies on undirected tools, makes use of tools from matrix theory. 
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Related papers:

MoreauExtends the results of Jadbabie:
Basic point is to define a disagreement metric in a Laplacianlike framework, you can show that disagreement metric contracts. Then look for conditions underwhich is reaches zero. Doesn't care about directed versus undirected. Shows that almost everything converges; we should point out that speed of convergence is not discussed. 
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Related papers

OlfatiSaber, Flocking 
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MesbahiResults didn't see that useful. Might be bad presentation of a good set of ideas. Should reference in some of the flocking work that Reza did. Looks at state dependent connectivity, which is different than many other papers. 
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Xiao and BoydShowed how to select the weights (under fixed topology) to optimize lambda_2. Solution is highly centralized. Solves the average consensus problem. Only gives a slight improvement over sparse connectivity. 
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Ren and BeardCan be viewed as an extension of Ali's results where weighted graphs are used. Requires spanning trees. 
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LeonardProbably too orthogonal to what we want to talk about. Focuses on rigidity, potential functions, etc. 
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SpanosAverage consensus algorithm can be used to calculate two central sums in a Kalman filter in a sensor network. Basically a way to do distributed sensor fusion 
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TsitsiklisThis paper shows how previous results can be used to study this problem. Difference between this paper and Ali's paper:

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New papers to consider
 Distribute computation (Action (RMM): read Bertsekes and Tsitsiklis book)
 Technical results in graph theory in Moreau's paper. Reza has gone through this a bit. Related to this: we should include as part of a review of relevant results in graph theory.
 Bullo results on consensus (w/ Cortes). Claim consensus papers are special case. Action (Reza): summarize this for the group next time
Common themes
"Protocols" for concensus and cooperation
 Distributed setting (doesn't require complete connectivity)
Laplacians and Graph Theory
 Introduce Laplacian by average consensus example
 Role of lamba_2 in performance
 Try to summarize some of the main threads of results that are relevant to consensus and cooperation
From Consensus to Cooperation: Closing the Loop
 Possible way to organize sections of the paper
Continuous versus Discrete
 Are they solving the same problem?
 Discussion of time delays and what they mean/imply
Switching and TimeDelays
 Large collection of results looking at the impact of switching and different sorts of time delays
Role of Consensus in Distributed Estimation
 Tie to distributed Kalman Filtering
 Might also talk about role of observers/predictors here
Relationship to Distributed Computation
 How do the results we cite here relate to older results in distributed computation
 One difference is that we close the loop around the consensus
 Another difference is the way switching topologies are handled
 Action (Richard): We need to do a careful review of the work in that field
Performance
 Current results are mainly tied to lambda_2
Open Problems
 Performance
Agenda for next meeting
Original plan:
 List tools
 Open problems
 Outline paper
Revised plan:
 Focus on outlining the paper at the section, subsection level
 Action items out of next meeting will be to come back with outline of contents for each subsection
 Action (Demetri): put links up to papers