Control of the 1D continuous version of the Cucker-Smale model

Benedetto Piccoli, Francesco Rossi, Emmanuel Trélat

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

1 Scopus citations


The well-known Cucker-Smale model is a microscopic system reproducing the alignment of velocities in a group of autonomous agents. Here, we focus on its mean-field limit, which we call the continuous Cucker-Smale model. It is a transport partial differential equation with nonlocal terms. For some choices of the parameters in the Cucker-Smale model (and the continuous one), alignment is not ensured for some initial configurations, therefore it is natural to study the enforcing of alignment via an external force. We provide a control strategy enforcing alignment for every initial data and acting only on a small portion of the crowd at each time. This is an adapted version of the sparse control for a finite number of agent, that is the constraint of acting on a small number of agents at each time.

Original languageEnglish (US)
Title of host publicationACC 2015 - 2015 American Control Conference
PublisherInstitute of Electrical and Electronics Engineers Inc.
Number of pages6
ISBN (Electronic)9781479986842
StatePublished - Jul 28 2015
Event2015 American Control Conference, ACC 2015 - Chicago, United States
Duration: Jul 1 2015Jul 3 2015

Publication series

NameProceedings of the American Control Conference
ISSN (Print)0743-1619


Other2015 American Control Conference, ACC 2015
Country/TerritoryUnited States

All Science Journal Classification (ASJC) codes

  • Electrical and Electronic Engineering


  • Cucker-smale model
  • PDEs with nonlocal terms
  • collective behavior
  • control of transport PDEs


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