Group Synchronization of Heterogeneous Multiagent System With Hierarchical Structure and Beyond Pairwise Interactions

Systems of different types of agents coupled with high-order interactions can emerge complex synchronization patterns. This article presents an analysis framework to study the group synchronization of heterogeneous multiagent systems with hierarchical structure and directed interactions of arbitrary order. First, directed hypergraph is introduced to describe the arbitrary-order interactions among the agents. Then, to explore the possible group synchronization patterns, the agent partition methods commonly used in dyadic graphs are extended to the directed hypergraph. Meanwhile, to verify the admissibility of the group synchronization patterns, two equitable partition types of agent partition are defined from the perspective of hyperedge partition. Next, using the simultaneous block diagonalization method, the stability problem of the group synchronous solution is decoupled into several independent subblocks. These subblocks are associated with the perturbations along and transverse to the synchronous manifold, with transverse subblocks related to loss of synchronization. Therefore, the stability of the group synchronous solution can be investigated by evaluating the stability of each transverse subblock via the master stability function method, thus significantly reducing the stability calculation complexity. Finally, the effectiveness of the analysis framework is illustrated via the simulation.