Step-size analysis in discrete-time dynamic average consensus

Eduardo Montijano, Juan Ignacio Montijano, Carlos Sagüés, and Sonia Martínez
Proceedings of the 2014 American Control Conference, Portland, OR, USA, June 2014

Abstract:

In this paper we deal with the problem of reaching the average consensus of a set of time-varying reference signals in a distributed manner. We analyze the approach initially presented in Zhu and Martinez, giving an alternative proof of the convergence that leads to larger, more realistic bounds on the step sizes that guarantee a steady-state error upper-bounded by a given constant. The interest of the new results appear when the algorithm is used in real networks, where there are constraints in the communication rate between the nodes. We derive the bounds for the cases of a fixed and a time varying communication topology, as well as for different orders of the consensus algorithm. We demonstrate that our bounds always allow bigger step sizes independently of the number of nodes or the network topology. Moreover, for fixed step size and steady-state error, we show how the corresponding algorithm can guarantee that the error is no larger than the desired one, using that step-size. Finally, simulation results corroborates the theoretical findings of the paper.

File: main.pdf

Bib-tex entry:

@InProceedings{EM-JIM-CS-SM:14-acc},
author = {E. Montijano and J.I. Montijano and C. Sagu\'es and S. Mart{\'\i}nez},
booktitle = {2014 American Control Conference},
title = { Step-size analysis in discrete-time dynamic average consensus },
year = {2014},
address ={Portland, OR},
pages = {5127--5132}
}