Limitations and improvements on potential-based connectivity preservation of multi-agent systems

In multi-agent cooperative control, consensus result often relies on the connectivity of the underlying communication network. This paper studies the problem of preserving connectivity with bounded control inputs for agent network with fixed and time-varying topologies. Firstly, a general potential based control law is investigated and sufficient conditions for preserving connectivity are presented. Then, a necessary condition for preserving connectivity with bounded control inputs is obtained. Based on this condition, a novel control law with bounded inputs is proposed and the selection of appropriate parameters for the corresponding control law is also discussed. The effectiveness of the proposed control law and the boundedness of the inputs are illustrated by numerical examples.