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

Benedetto Piccoli, Francesco Rossi, Emmanuel Trelat
2015 2015 American Control Conference (ACC)  
The well-known Cucker-Smale model is a macroscopic 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
more » ... 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.
doi:10.1109/acc.2015.7170907 dblp:conf/amcc/PiccoliRT15 fatcat:gffogp5ydvaldd7prbyipi3rpa