Global Frequency Synchronization over Networks of Uncertain Second-Order Kuramoto Oscillators via Distributed Adaptive Tracking

In this work, we consider the problem of global frequency synchronization of a network of second-order Kuramoto oscillators, cast as a distributed tracking problem, in the sense that the reference synchronization frequency for the network is generated by an autonomous leader. The main contribution of this paper is to develop a novel control strategy for the problem of leader-follower frequency synchronization, by exploiting the adaptive control framework to cope with parametric uncertainties in the oscillators. These adaptive controllers (one for each system) are interconnected with a distributed observer, used to reconstruct the reference signal for the systems not directly connected to the leader. Adopting the Lie Groups formalism for the unit circle to globally characterize the phase dynamics, we show that synchronization is not hindered if the physical couplings are in part preserved. Stability of the closed-loop interconnection is analyzed with Lyapunov-like arguments and verified in a numerical simulation.