TY - GEN
T1 - Control of the 1D continuous version of the Cucker-Smale model
AU - Piccoli, Benedetto
AU - Rossi, Francesco
AU - Trélat, Emmanuel
N1 - Publisher Copyright:
© 2015 American Automatic Control Council.
PY - 2015/7/28
Y1 - 2015/7/28
N2 - 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.
AB - 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.
KW - Cucker-smale model
KW - PDEs with nonlocal terms
KW - collective behavior
KW - control of transport PDEs
UR - http://www.scopus.com/inward/record.url?scp=84940936736&partnerID=8YFLogxK
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U2 - 10.1109/ACC.2015.7170907
DO - 10.1109/ACC.2015.7170907
M3 - Conference contribution
AN - SCOPUS:84940936736
T3 - Proceedings of the American Control Conference
SP - 1264
EP - 1269
BT - ACC 2015 - 2015 American Control Conference
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 2015 American Control Conference, ACC 2015
Y2 - 1 July 2015 through 3 July 2015
ER -