Achieving fixed-time synchronization of the Kuramoto model via improving control techniques

This paper further analyzes the fixed-time (FxT) phase agreement (PA) and the frequency synchronization (FS) of the Kuramoto model with identical and non-identical oscillators, respectively. The non-chattering control protocol is carefully picked to overcome the deficiency of the signum function contained in the conventional finite-time (FT)/FxT controllers, which improves the synchronized performance of networked systems. Furthermore, for reducing control cost, the switching control scheme is taken into consideration. Through the utilization of FxT stability theory, several sufficient conditions are derived successively for achieving the FxT PA and FS, in which the upper bound time estimates for arriving at PA and FS are given regardless of the initial states of the Kuramoto model. Finally, some simulation results lead to the conclusion that the proposed theoretical analysis is correct and effective.