LEADER-FOLLOWING RENDEZVOUS CONTROL FOR GENERALIZED CUCKER-SMALE MODEL ON RIEMANNIAN MANIFOLDS

This paper studies a leader-following rendezvous problem for the generalized CuckerSmale model, a double -integrator multiagent system, on some Riemannian manifolds. By using intrinsic properties of the covariant derivative, logarithmic map, and parallel transport on the Riemannian manifolds, we design a feedback control law and prove that this feedback control law enables all followers to track the trajectory of the moving leader when the Riemannian manifold is compact or flat. As concrete examples, we consider the leader-following rendezvous problem on the unit sphere, in Euclidean space, on the unit circle, and infinite cylinder and present the corresponding feedback control laws. Meanwhile, numerical examples are given for the aforementioned Riemannian manifolds to illustrate and verify the theoretical results.