Consensus problem in multi-agent systems with physical position neighbourhood evolving network

In multi-agent system (MAS), the communication topology of agent network plays a very important role in its consensus problem. To describe the communication topologies of MAS, a class of evolving network models with the concept of physical position neighbourhood connectivity are proposed and studied in this paper. The analysis and simulation results for network parameters such as the first nonzero eigenvalue and maximal eigenvalue of graph Laplacian matrix, clustering coefficients, average distances and degree distributions for different evolving parameters of these models are presented. The dynamical behaviour of each node on the consensus problem is also studied. It was found that the time to reach consensus becomes shorter sharply with the increasing of neighbourhood depth of the nodes in these models. And it was also found that for the maximal distance preferential attachment model (Model 3), the synthetic characteristic, such as robustness to communication delay, as well as convergence speed in consensus problem, is the best in all these models.