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Control to flocking of the kinetic Cucker-Smale model

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TypeOfResource
Text
TitleInfo
Title
Control to flocking of the kinetic Cucker-Smale model
Name (type = personal)
NamePart (type = family)
Piccoli
NamePart (type = given)
Benedetto
Affiliation
Mathematical Sciences, Rutgers University
Role
RoleTerm (authority = marcrt); (type = text)
author
Name (type = personal)
NamePart (type = family)
Rossi
NamePart (type = given)
Francesco
Affiliation
Aix Marseille Universit´e, Universit´e de Toulon
Role
RoleTerm (authority = marcrt); (type = text)
author
Name (type = personal)
NamePart (type = family)
Trélat
NamePart (type = given)
Emmanuel
Affiliation
Sorbonne Universit´es
Role
RoleTerm (authority = marcrt); (type = text)
author
Name (authority = RutgersOrg-Department); (type = corporate)
NamePart
Mathematical Sciences
Name (authority = RutgersOrg-School); (type = corporate)
NamePart
Camden College of Arts and Sciences
Genre (authority = RULIB-FS)
Article, Refereed
Genre (authority = NISO JAV)
Accepted Manuscript (AM)
OriginInfo
Publisher
SIAM
DateIssued (encoding = w3cdtf); (keyDate = yes); (qualifier = exact)
2015
Abstract (type = Abstract)
The well-known Cucker-Smale model is a macroscopic system reflecting flocking, i.e. the alignment of velocities in a group of autonomous agents having mutual interactions. In the present paper, we consider the meanfield limit of that model, called the kinetic Cucker-Smale model, which is a transport partial differential equation involving nonlocal terms. It is known that flocking is reached asymptotically whenever the initial conditions of the group of agents are in a favorable configuration. For other initial configurations, it is natural to investigate whether flocking can be enforced by means of an appropriate external force, applied to an adequate time-varying subdomain. In this paper we prove that we can drive to flocking any group of agents governed by the kinetic Cucker-Smale model, by means of a sparse centralized control strategy, and this, for any initial configuration of the crowd. Here, “sparse control” means that the action at each time is limited over an arbitrary proportion of the crowd, or, as a variant, of the space of configurations; “centralized” means that the strategy is computed by an external agent knowing the configuration of all agents. We stress that we do not only design a control function (in a sampled feedback form), but also a time-varying control domain on which the action is applied. The sparsity constraint reflects the fact that one cannot act on the whole crowd at every instant of time. Our approach is based on geometric considerations on the velocity field of the kinetic Cucker-Smale PDE, and in particular on the analysis of the particle flow generated by this vector field. The control domain and the control functions are designed to satisfy appropriate constraints, and such that, for any initial configuration, the velocity part of the support of the measure solution asymptotically shrinks to a singleton, which means flocking.
Language
LanguageTerm (authority = ISO 639-3:2007); (type = text)
English
PhysicalDescription
InternetMediaType
application/pdf
Extent
32 p.
Subject (authority = local)
Topic
Cucker-Smale model
Subject (authority = local)
Topic
Transport PDEs with nonlocal terms
Subject (authority = LCSH)
Topic
Collective behavior
Subject (authority = local)
Topic
Control
Subject (authority = LCSH)
Topic
Differential equations, Partial--Numerical solutions
Extension
DescriptiveEvent
Type
Citation
AssociatedObject
Name
SIAM Journal on Mathematical Analysis
Type
Journal
Relationship
Has part
Identifier (type = volume and issue)
47(6)
Reference (type = url)
https://dx.doi.org/10.1137/140996501
Detail
4685–4719
DateTime (encoding = w3cdtf)
2015
Note (type = version identification)
First published in SIAM Journal on Mathematical Analysis, 47(6), 2015, published by the Society of Industrial and Applied Mathematics (SIAM). Copyright © by SIAM. Unauthorized reproduction of this article is prohibited.
Note (type = peerReview)
Peer reviewed
RelatedItem (type = host)
TitleInfo
Title
Piccoli, Benedetto
Identifier (type = local)
rucore30182700001
Location
PhysicalLocation (authority = marcorg); (displayLabel = Rutgers, The State University of New Jersey)
NjNbRU
Identifier (type = doi)
doi:10.7282/T3D50PXX
Genre (authority = ExL-Esploro)
Accepted Manuscript
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Copyright
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Copyright protected
Availability
Status
Open
Reason
Permission or license
RightsEvent
Type
Permission or license
AssociatedObject
Type
License
Name
Multiple author license v. 1
Detail
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RightsEvent
Type
Publication notice
Detail
First published in SIAM Journal on Mathematical Analysis, 47(6), 2015, published by the Society of Industrial and Applied Mathematics (SIAM). Copyright © by SIAM. Unauthorized reproduction of this article is prohibited.
RightsHolder (type = corporate)
Name
Society for Industrial and Applied Mathematics
Role
Copyright holder
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RULTechMD (ID = TECHNICAL1)
ContentModel
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