A Sharp Bound on the $s$-Energy and Its Applications to Averaging Systems
Multiagent Systems
2018-12-31 v2 Optimization and Control
Abstract
The {\em -energy} is a generating function of wide applicability in network-based dynamics. We derive an (essentially) optimal bound of on the -energy of an -agent symmetric averaging system, for any positive real , where~ is a lower bound on the nonzero weights. This is done by introducing the new dynamics of {\em twist systems}. We show how to use the new bound on the -energy to tighten the convergence rate of systems in opinion dynamics, flocking, and synchronization.
Cite
@article{arxiv.1802.01207,
title = {A Sharp Bound on the $s$-Energy and Its Applications to Averaging Systems},
author = {Bernard Chazelle},
journal= {arXiv preprint arXiv:1802.01207},
year = {2018}
}