IEEE Paper, 18 Apr 05

Present: Fax, Murray, Olfati-Saber

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

Viscek This 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 Early example of a protocol Focused on alignment (common problem)	Related papers Jadbabaie Blondel et al (incorrect citation?)
Tabuada Currently 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 Might not cite this; Action (Demetri): look for follow up work (if any). If we can't find something more recent that is significant, probably won't include Effects of dynamics (especially nonlinear)	Related papers Naomi Leonard Action (Richard): look for other papers on this topic
Fax Would be nice to see more work in the area of performance and observer structure. Various follow-on 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 Starting point for Laplacian	Related papers Double graph model by Zhipu?
Olfati-Saber We 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 Basic problem definition Initial setting for switching, time delays Role of balanced graphs?	Related papers Switching: Jadbabaie, Moreau, Beard Time delays: Moreau (recent)
Jadbabaie One 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.	Takeaways for our paper: Eventual connectivity is sufficient for consensus in presence of switching and time delays Different approach from Moreau	Related papers: Moreau
Moreau Extends the results of Jadbabie: Admits nonlinear update laws Makes use of properties of stochastic matrices to get very short proof (for undirected graphs) Proof for directed graphs is harder Basic point is to define a disagreement metric in a Laplacian-like 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.	Takeaways for our paper: Shows how to extend most of the things we have done to nonlinear case, with switching	Related papers Jadbabaie
Olfati-Saber, Flocking	Takeaways for our paper:	Related papers:
Mesbahi Results 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.	Takeaways for our paper: May not play a major role in our paper, but reference in flocking	Related papers:
Xiao and Boyd Showed 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.	Takeaways for our paper: Initial results for optimizing lambda_2	Related papers: Olfati-Saber, small world
	Takeaways for our paper:	Related papers:
	Takeaways for our paper:	Related papers:
	Takeaways for our paper:	Related papers:

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

Continuous versus Discrete

• Are they solving the same problem?

Role of Consensus in Distributed Estimation

• Tie to distributed Kalman Filtering
• Might also talk about role of observers/predictors here

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: