Flocking And Consensus Of Multiple Agents Governed By Nonlinear Dynamics

During with the development of network technology, the scale of the network is getting larger and larger, and more and more people are devoting to the research of the network science. As a new research direction of network science, complex network attracts a lot of researchers. The research of multi-agent systems whose communication networks are complex networks is getting a research hot spot because of it’s widely application value in many areas such as multi-robot systems, multi-UAV (unmanned aerial vehicle) systems, multi-satellite systems.Based on complex network knowledge and the knowledge of flocking and consensus of multi-agent systems, this paper firstly investigates adaptive flocking control of multi-agent systems of complex dynamical network 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 of the agent itself. Under the assumption that the initial network is connected, an approach to preserving the connectivity of the network is proposed. Based on the Lyapunov stability theory, an adaptive flocking control law is derived to make the multi-agent systems track the virtual leader without collision. A numerical example is presented to illustrate the effectiveness of the theoretical results.Then, this paper investigates second-order consensus of multi-agent systems with time-varying delays and 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 of the agent itself. Under the assumption that the communication network is fixed, based on the Lyapunov stability theory, an approach is proposed to let the position and velocity of each agent in the systems converge to the virtual leader’s position and velocity respectively. Then, the approach is proofed to be appropriate for two conditions that the weighted coupling configuration matrix is symmetric and asymmetric. Finally, two numerical examples are presented to illustrate the effectiveness of the theoretical results.