Achieving Consensus and Synchronization by Adapting the Network Topology

In this paper, we present a novel control strategy for achieving consensus via network evolution. Namely, we associate to each edge a multi-dimensional dynamical system forced by the state mismatch of its nodes. We consider the case in which the network evolution is driven by a multi-well potential, whose wells define the possible asymptotic levels of interactions between each pair of nodes. We show that the proposed network evolution supports asymptotic consensus while leading to an emerging steady-state weighted topology. Moreover, we illustrate how a proper tuning of the potential parameters can be used to tailor the properties of this emerging topology. Finally, numerical simulations confirm the theoretical predictions as well as the viability of this approach for synchronizing nonlinear dynamical systems.