# Consensus equation, help please.

1. Nov 3, 2007

### l46kok

I am having the most trouble understanding this equation. Why is the limit of summation, declared as a node j in a member of the neighbors of agents i (Which is a set of nodes and links, taken from disk graphs)? Why is it that by the term $$x_j(t)$$, a derivative of X(of the i index) must be taken? Can anyone explain how this equation works?

I am sure that this is a very difficult question and may take time to answer it, but I would heavily appriciate it if anyone can explain it well, as my research is at stake here.

http://www.piaggio.ccii.unipi.it/Bertinoro 2007/Materiale Didattico/EgerstedtTalk.pdf

2. Nov 3, 2007

### HallsofIvy

Staff Emeritus
If i=1, N1= {1} so $\overdot{x}$1= x1- x1= 0.
If i= 2, N2= {1, 2} so $\overdot{x}$2= (x32- x1)+ (x2- x2= x2- x1
If i= , N3= {1,2,3} so $\overdot{x}$= (x3- x1)+ (x3)+ (x3- x2)+ x3- x1)= 2x3- x1-x2.
etc.

Last edited: Nov 6, 2007
3. Nov 3, 2007

### l46kok

Ok, I stared at what you said for 10 minutes but failed to understand it. Can you please provide additional details?

4. Nov 5, 2007

anyone?

5. Nov 7, 2007

### l46kok

:( anyone?

6. Nov 11, 2007