Stochastic synchronization of Kuramoto-oscillator network with pinning control

The issue of time cost for the Kuramoto-oscillator network synchronization has received widespread attention. However, there is no relevant research on the stochastic synchronization of the Kuramoto-oscillator network with partial uncontrollable oscillators. This article investigates the synchronization problem of the Kuramoto-oscillator network in noisy environments using the pinning control strategy and multilayer distributed control. Previous research requires control of all oscillators, which implies a great control cost. To reduce the control cost, the finite/fixed time pinning controllers are designed to provide the conditions for synchronization in noisy environments, and then the upper bounds on the convergence time of the network are estimated. Finally, numerical simulations are performed to justify the theoretical conclusions.