TY - JOUR
T1 - A sharp bound on the s-energy and its applications to averaging systems
AU - Chazelle, Bernard
N1 - Funding Information:
Manuscript received July 21, 2018; revised January 2, 2019; accepted February 3, 2019. Date of publication February 14, 2019; date of current version September 25, 2019. Recommended by Associate Editor B. De Schutter. This work was supported by the Army Research Office and the Defense Advanced Research Projects Agency and was accomplished under Grant W911NF-17-1-0078. The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the official policies, either expressed or implied, of the Army Research Office, the Defense Advanced Research Projects Agency, or the U.S. Government. The U.S. Government is authorized to reproduce and distribute reprints for Government purposes notwithstanding any copyright notation herein.
Funding Information:
This work was supported by the Army Research Office and the Defense Advanced Research Projects Agency and was accomplished under Grant W911NF-17-1-0078. The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the official policies, either expressed or implied, of the Army Research Office, the Defense Advanced Research Projects Agency, or the U.S. Government. The U.S. Government is authorized to reproduce and distribute reprints for Government purposes notwithstanding any copyright notation herein.
PY - 2019/10
Y1 - 2019/10
N2 - 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.
AB - 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.
KW - S-energy
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U2 - 10.1109/TAC.2019.2899509
DO - 10.1109/TAC.2019.2899509
M3 - Article
AN - SCOPUS:85075546547
VL - 64
SP - 4385
EP - 4390
JO - IEEE Transactions on Automatic Control
JF - IEEE Transactions on Automatic Control
SN - 0018-9286
IS - 10
M1 - 8642407
ER -