Finite time synchronization of the high-dimensional Kuramoto model with distributed nonlinear feedback control

This paper investigates the finite time synchronization problem of the Kuramoto model on high-dimensional spheres. Unlike most existing studies focused on asymptotic or exponential convergence, we propose a novel sliding mode control strategy that ensures exact synchronization in finite time. An explicit upper bound on the convergence time is derived via a carefully constructed Lyapunov function, and global synchronization is rigorously established. The proposed method also substantially relaxes the initial condition requirements, enabling convergence from a wider set of initial states. Numerical simulations corroborate the theoretical results. This work offers a new framework for fast synchronization control in high-dimensional coupled systems.