Optimal Design for Synchronization of Kuramoto Oscillators in Tree Networks

Mahyar Fazlyab, Florian Dörfler, Victor M. Preciado

Published 2015-03-25Version 1

In this paper, we develop an optimization framework to optimize phase synchronization in tree networks of coupled Kuramoto oscillators. We consider the \emph{phase cohesiveness} metric, that accounts for the maximum phase difference across all the edges in the network. we address three different optimization problems: (\emph{i}) The \emph{optimal critical coupling problem} in which we design the natural frequency of each oscillator to minimize the required coupling for synchronization (\emph{ii}) the \emph{nodal-frequency design problem}, in which we design the natural frequencies to optimize the phase cohesiveness, and (\emph{iii}) the \emph{edge-weight design problem}, in which we design the link weights. We assume that tuning the natural frequencies and/or modifying the link weights have an associated cost and develop an optimization framework to find the optimal allocation of resources under certain assumptions. We illustrate the effectiveness of our approach via numerical simulations.