Achieving Prescribed-Time Synchronization in Noisy Kuramoto Networks: A Distributed Control Approach

This paper addresses the problem of global prescribed-time stochastic synchronization for networked Kuramoto oscillators subject to diffusive noise. A novel distributed control strategy, incorporating a time-varying scaling function, is proposed to ensure synchronization in a prescribed time for both identical and nonidentical oscillators operating in noisy environments. By combining stochastic Lyapunov theory with graph-theoretic properties, we derived sufficient conditions for global synchronization that explicitly depend on network topology, coupling strength, and noise intensity. The analytical results show that synchronization can be achieved within the prescribed time, regardless of initial phase conditions. Furthermore, the effectiveness and robustness of the proposed controllers are validated through numerical simulations across a range of noise intensities.