Quick Relaxation in Collective Motion

Bernard Chazelle, Kritkorn Karntikoon

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Scopus citations


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.

Original languageEnglish (US)
Title of host publication2022 IEEE 61st Conference on Decision and Control, CDC 2022
PublisherInstitute of Electrical and Electronics Engineers Inc.
Number of pages6
ISBN (Electronic)9781665467612
StatePublished - 2022
Externally publishedYes
Event61st IEEE Conference on Decision and Control, CDC 2022 - Cancun, Mexico
Duration: Dec 6 2022Dec 9 2022

Publication series

NameProceedings of the IEEE Conference on Decision and Control
ISSN (Print)0743-1546
ISSN (Electronic)2576-2370


Conference61st IEEE Conference on Decision and Control, CDC 2022

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Modeling and Simulation
  • Control and Optimization


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