The 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 ≤ 1, where ρ is a lower bound on the nonzero weights. This is done by introducing the new dynamics of twist systems. We show how to use the new bound on the s-energy to tighten the convergence rates of systems in opinion dynamics, flocking, and synchronization.
All Science Journal Classification (ASJC) codes
- Control and Systems Engineering
- Computer Science Applications
- Electrical and Electronic Engineering