Adaptive flocking with a virtual leader of multiple agents governed by locally Lipschitz nonlinearity

This paper investigates adaptive flocking of multi-agent systems (MASs) with a virtual leader. All agents and the virtual leader share the same intrinsic nonlinear dynamics, which satisfies a locally Lipschitz condition and depends on both position and velocity information for the agent itself. Under the assumption that the initial network is connected, an approach to preserving the connectivity of the network is proposed. On the basis of the Lyapunov stability theory, an adaptive flocking control law is derived, for making the MASs track the virtual leader without collision. Finally, a numerical example is presented to illustrate the effectiveness of the theoretical results.