A feedback control design for rendezvous of the Cucker-Smale model on the unit circle

In this paper, we consider a leader-following rendezvous problem for the Cucker-Smale model on the unit circle. With the help of the covariant derivative, parallel transport, and geodesic on the unit circle, a feedback control law is designed such that all followers will converge to a moving leader. Furthermore, some numerical simulations are provided to verify and illustrate the theoretical result.