A connectivity-preserving flocking algorithm for nonlinear multi-agent systems with bounded potential function

Without assuming that the communication topology can maintain its connectivity frequently enough during the evolution of agents, the flocking problem of multi-agent systems with second-order nonlinear dynamics is investigated in this paper. By combining the ideas of collective potential functions and velocity consensus, a connectivity-preserving flocking algorithm with bounded potential function is proposed. Using tools from algebraic graph theory and matrix analysis, it is shown that the present algorithm can enable the group of multiple agents to move with the same velocity while preserving the connectivity of the whole network if the the algebraic connectivity of the initial network is larger than a threshold value. Furthermore, the flocking algorithm is used to solve the flocking problem of multi-agent systems with a virtual leader by adding a navigation feedback term. In this case, each informed agent only has partial velocity information about the leader, yet the present algorithm not only can guarantee the velocity of the whole group to track that of the leader asymptotically, and also can preserve the connectivity of the network. Finally, simulation results are provided to valid the effectiveness of the theoretical results.