Global Predefined-Time Collective Synchronization of Coupled Kuramoto Oscillators

This paper addresses the problem of global predefined-time collective synchronization of coupled Kuramoto oscillators. Distinguished from the traditional finite-/fixed-time phase-frequency synchronization of Kuramoto oscillators, the upper-bound time estimation(UBTE) of predefined-time convergence is explicit and can be set as needed in advance, which is not related with the network information, controlling parameters, initial phases and frequencies of oscillators. Particularly, the multilayer networked switching control protocols are proposed for steering the global predefined-time phase-frequency synchronization of coupled oscillators. At the same time, the sufficient conditions are deduced by the predefined-time Lyapunov stability analysis. Finally, the correction and effectiveness of the theoretical results are verified by numerical simulation.