Prescribed-Time Synchronization of Kuramoto Oscillators Over Undirected Network

The prescribed-time synchronization of both homogeneous and heterogeneous Kuramoto-oscillator network are studied respectively in this paper. Two distributed control schemes based on a scaling function are designed to solve the phase and frequency synchronization of homogeneous and heterogeneous Kuramoto oscillators, respectively. Different from finite-time synchronization process, where the convergence time is dependent on initial conditions, and fixed-time synchronization, where the synchronization time cannot be preassigned, the actual converging time of proposed prescribed-time synchronization is independent of initial states and can be preassigned arbitrarily. In order to achieve phase and frequency synchronization of Kuramoto-oscillator network in a prescribed-time, some sufficient conditions based on Lyapunov stability theory are proposed. Finally, numerical examples further verify the effectiveness of the control schemes.