Dynamic event-triggered control for fixed-time synchronization of Kuramoto-oscillator networks with and without a pacemaker

In this paper, an improved fixed-time dynamic event-triggered control scheme is developed for solving the synchronization problem of Kuramoto-oscillator network models with and without a pacemaker. First, a set of multiplex control strategies are designed to achieve the phase agreement for Kuramoto networks connected to a pacemaker. Then, the developed strategies are employed to address the phase agreement and frequency synchronization of Kuramoto networks without a pacemaker. For the triggering function, a dynamic variable is introduced to filter out massive unnecessary triggering instants, which significantly reduces the update frequency of the controllers. Moreover, through theoretical analysis, the fixed-time synchronization is guaranteed when the initial phase of nodes are unknown and the coupling strength between nodes are weak. It is also proved that there is no Zeno behavior in the network control dynamics. Finally, three numerical simulation experiments are given to demonstrate the validity of the proposed dynamic event-triggered control scheme.