Uniform global asymptotic synchronization of Kuramoto oscillators via hybrid coupling

Riccardo Bertollo (1) , Elena Panteley (2) , Romain Postoyan (3) , Luca Zaccarian (1, 4)

1 UNITN - Università degli Studi di Trento = University of Trento
2 L2S - Laboratoire des signaux et systèmes
3 CRAN - Centre de Recherche en Automatique de Nancy
4 LAAS-MAC - Équipe Méthodes et Algorithmes en Commande

Using a hybrid framework, we propose a generalized version of the well-known Kuramoto model for interconnected oscillators. The proposed model does not modify the classical model close to the synchronization set, but avoids the typical non-uniform convergence phenomenon. For the two-oscillators case, we prove the uniform global asymptotic stability of the consensus set by using a hybrid Lyapunov function whose generality promises possible extension of the result to higher order dynamics. We comparatively illustrate the achieved uniform convergence properties by simulating both the case with two and multiple oscillators, thus confirming the effectiveness of our approach.

Mots clés: networked oscillators; nonlinear control; hybrid systems; Kuramoto model; synchronization

Domaines: Automatique; Systèmes et contrôle [cs.SY]

Riccardo Bertollo, Elena Panteley, Romain Postoyan, Luca Zaccarian. Uniform global asymptotic synchronization of Kuramoto oscillators via hybrid coupling. IFAC 2020 - 21st IFAC World Congress, Jul 2020, Berlin, Germany. ⟨10.1016/j.ifacol.2020.12.1626⟩. ⟨hal-02562689⟩