Rendezvous analysis and control design for multiple mobile agents with preserved network connectivity on hyperboloid

This paper studies the rendezvous problem for a second-order multi-agent system on the hyperboloid under a proximity-based communication topology. Using the Riemannian geometrical structure on the hyperboloid, we design a nonlinear feedback control law in which each agent has a limited sensing range. By analyzing the switching behavior of the communication topology, we show that the switching time of the resulting closed-loop system is finite, and the connectivity of the communication topology is preserved if the initial network is connected. In addition, we also provide an analysis of the asymptotic behavior of the second-order closed-loop system on the hyperboloid and prove that the proposed feedback control law enables all agents to converge to the same position.