arXiv
Open Access
2018
A Sharp Bound on the $s$-Energy and Its Applications to Averaging Systems
Bernard Chazelle
Abstrak
The {\em $s$-energy} is a generating function of wide applicability in network-based dynamics. We derive an (essentially) optimal bound of $(3/ρs)^{n-1}$ on the $s$-energy of an $n$-agent symmetric averaging system, for any positive real $s\leq 1$, where~$ρ$ 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 $s$-energy to tighten the convergence rate of systems in opinion dynamics, flocking, and synchronization.
Penulis (1)
B
Bernard Chazelle
Akses Cepat
Informasi Jurnal
- Tahun Terbit
- 2018
- Bahasa
- en
- Sumber Database
- arXiv
- Akses
- Open Access ✓