Cluster partitioning of heterogeneous multi-agent systems

This paper investigates the collective behaviors induced by the network interconnection of heterogeneous input-affine single-input nonlinear systems through a constant but general directed graph. In this sense, we prove that the dynamics of all agents cluster into as many subgroups as the number of cells of the almost equitable partition induced by the communication graph. All agents belonging to the same cell are equally influenced by a new mean-field dynamics which is paradigmatic of the network. The case of a network of pendula illustrates the results through simulations.