Multilayer proportional-integral consensus of heterogeneous multi-agent systems

A distributed proportional-integral multilayer strategy is proposed, to achieve consensus in networks of heterogeneous first-order linear systems. The closed-loop network can be seen as an instance of so-called multiplex networks currently studied in network science. The strategy is able to guarantee consensus, even in the presence of constant disturbances and heterogeneous node dynamics. Contrary to previous approaches in the literature, the proportional and integral actions are deployed here 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.