The Impact of Multi-group Multi-layer Network Structure on the Performance of Distributed Consensus Building Strategies

Multi-group multi-layer (MGML) structure is common to distributed sensor networks (DSNs) in many natural and engineered applications. Although network structure plays a crucial role in the performance of consensus building strategies in such networks, little work is done to establish the precise connection between the two. In this paper, we consider a structural approach to the consensus building problem in MGML DSNs that have wide applications in e.g., multi-vehicle systems. From among the possible network structures, we focus on bipartite graph structures and briefly discuss hierarchical structures due to their wide applicability in similar applications. We show that the consensus building dynamics in MGML structure can be easily mapped to canonical discrete-time first-order dynamics. We establish the exact conditions for consensus and derive a precise relationship between the consensus value and the degree distribution of the nodes in the bipartite graph. We also demonstrate that for subclasses of connectivity patterns, convergence time and simple characteristics of network topology can be captured by explicit algebra. Direct inference of the convergence behavior of consensus strategies from MGML DSN structure is the main contribution of this paper. The insights gained from our analysis facilitate the design and development of large-scale DSNs that meet specific performance criteria. ∗Assistant Professor, Department of Electrical Engineering, and AIAA Member. †Associate Professor, Department of Electrical Engineering. ‡Masters Student, Department of Electrical Engineering. §Professor, Department of Electrical Engineering.