TY - GEN
T1 - Quick Relaxation in Collective Motion
AU - Chazelle, Bernard
AU - Karntikoon, Kritkorn
N1 - Publisher Copyright:
© 2022 IEEE.
PY - 2022
Y1 - 2022
N2 - We establish sufficient conditions for the quick relaxation to kinetic equilibrium in the classic Vicsek-Cucker-Smale model of bird flocking. The convergence time is polynomial in the number of birds as long as the number of flocks remains bounded. This new result relies on two key ingredients: exploiting the convex geometry of embedded averaging systems; and deriving new bounds on the s-energy of disconnected agreement systems. We also apply our techniques to bound the relaxation time of certain pattern-formation robotic systems investigated by Sugihara and Suzuki.
AB - We establish sufficient conditions for the quick relaxation to kinetic equilibrium in the classic Vicsek-Cucker-Smale model of bird flocking. The convergence time is polynomial in the number of birds as long as the number of flocks remains bounded. This new result relies on two key ingredients: exploiting the convex geometry of embedded averaging systems; and deriving new bounds on the s-energy of disconnected agreement systems. We also apply our techniques to bound the relaxation time of certain pattern-formation robotic systems investigated by Sugihara and Suzuki.
UR - http://www.scopus.com/inward/record.url?scp=85147006676&partnerID=8YFLogxK
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U2 - 10.1109/CDC51059.2022.9992475
DO - 10.1109/CDC51059.2022.9992475
M3 - Conference contribution
AN - SCOPUS:85147006676
T3 - Proceedings of the IEEE Conference on Decision and Control
SP - 6472
EP - 6477
BT - 2022 IEEE 61st Conference on Decision and Control, CDC 2022
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 61st IEEE Conference on Decision and Control, CDC 2022
Y2 - 6 December 2022 through 9 December 2022
ER -