On the alternating target tracking of a point cloud on Riemannian manifolds

We study finite-time and asymptotic tracking of a given moving target configuration. For this, we proposed two multi-agent systems on Riemannian manifolds based on Filippov's framework. For asymptotic tracking, we adopt a piecewise C1-vector field on Riemannian manifolds resulting from switching moving targets, whereas for finite-time tracking, we use a piecewise C0 and non-Lipschitzian vector field on Euclidean space. For both multi-agent systems, we provide several sufficient frameworks for the desired asymptotic or finite-time tracking that are formulated in terms of system parameters, a preassigned switching moving target configuration, kernel functionals, and initial data.