Multilayer PI Control for Consensus in Heterogeneous Multi-Agent Networks

In this paper, a distributed proportional-integral multilayer control strategy is proposed, for reaching consensus in networks of heterogeneous first-order linear node dynamics. The resulting closed-loop network can be seen as an instance of multiplex networks currently studied in network science. The strategy is able to guarantee consensus, even in the presence of constant disturbances and heterogeneity. The proportional and integral actions are deployed on two different layers across the network, each with its own topology. Explicit expressions for the consensus values are obtained together with sufficient conditions guaranteeing convergence. The effectiveness of the theoretical results are illustrated via numerical simulations using a power network example.