Robustness of Synchronization in Heterogeneous Multi-Agent Systems

This paper studies robustness of synchronization in heterogeneous multi-agent systems, which is gained by interactions with other agents through the network. In order to effectively deal with the heterogeneous cases, 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 the group behavior against differences among agents. First, we show that strong coupling among heterogeneous agents makes the trajectories of all agents remain in an arbitrarily small neighborhood of the trajectory of the averaged dynamics. Second, we observe that the amount of individual variation of each agent, that contributes to the averaged dynamics, gets smaller as the number of agents increases, and thus, the averaged dynamics becomes more robust to the differences among agents. Simulation results confirm our claim that a large number of agents with strong couplings have robust synchronization.