Robustness of synchronization of heterogeneous agents by strong coupling and a large number of agents

This technical note studies robustness of synchronization against heterogeneity of multi-agent systems. Here, heterogeneity also includes uncertainties and external disturbances in each agent. In order to effectively deal with the heterogeneous agents, we introduce the concept of the averaged dynamics which is the average of all agents' dynamics, and then claim that two sources enhance the robustness of synchronized behavior against heterogeneity of agents' dynamics. First, in spite of the heterogeneity of agents' dynamics, we show that strong coupling among agents makes the trajectories of all agents arbitrarily close to the averaged dynamics. Second, in the averaged dynamics, the effect of variations in each agent gets smaller as the number of agents increases. Simulation results confirm the claim that a large number of agents with strong couplings have robust synchronization.