A Leader-following Rendezvous Control Design for the Cucker-Smale Model on the Infinite Cylinder

The collective behavior of multi-agent systems on Riemannian manifolds have attracted increasing interest. In this paper, we consider a leader-following rendezvous problem for the Cucker-Smale model on the infinite cylinder, which is a special kind of Riemannian manifold. By using the covariant derivative, the parallel transport, and the geodesic on the infinite cylinder, we design a feedback control law for the Cucker-Smale model such that the positions of all followers asymptotically track the trajectory of the moving leader. We also provide a numerical simulation to verify and illustrate the theoretical results.