Synchronization of kuramoto oscillators with non-identical natural frequencies: a quantum dynamical decoupling approach

This paper proposes a method to counter the drift associated to unknown non-identical natural frequencies in the Kuramoto model of coupled oscillators. Inspired by the quantum dynamical decoupling technique, it builds on a time-varying variant of the dynamics to effectively bring the oscillator phases closer to the same value. This allows effective synchronization despite arbitrarily large differences in natural frequencies. For two agents admitting instantaneous position exchanges, we exactly compute how the relative phase converges to a stable periodic fixed point. The latter tends to zero when the dynamics switches at a faster rate. With continuous state evolutions, using a related dynamic controller instead of instantaneous jumps, we show with a Lyapunov function that exact phase synchronization is obtained. We generalize the method to multiple oscillators with instantaneous state exchanges, that can be implemented by cycling through a predefined or random sequence of exchanges. Simulation results illustrate the effectiveness of the algorithms.