Second-order consensus for multi-agent systems with limited communication range

This paper studies the second-order consensus problem for multi-agent systems with a limited communication range where two agents can communicate with each other only when they are within a certain distance. Second-order consensus means that the agents asymptotically gather to a point and move in the same velocity. Different form most existing works where the change of network topology is independent of the system evolution, we construct a Cuker-Smale type model to formulate the relation between the network topology and the system state. The main result of this paper provides a sufficient condition on the initial velocities, positions and the communication range which can guarantee the multi-agent system to asymptotically achieve the second-order consensus. We prove it using the Lyapunov functional approach. Finally, simulation examples are given to verify the theorem.