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Abstract:
This paper investigates the prescribed-time tracking synchronization (PTS) of Kuramoto oscillator networks (KONs) with directed graphs. Existing control protocols for achieving KONs’ synchronization within a finite time are based on linear or power functions of phase differences, but they ignore the -periodicity of phase oscillators. This leads to desynchronization and dramatic phase changes, increasing system load, failure rates, and control costs. To overcome these drawbacks, we propose a sine function-based protocol, incorporating the periodicity of oscillators, to achieve tracking synchronization within a prescribed time. Then a new cosine-based error variable is introduced to characterize the degree of tracking synchronization. By leveraging the error variable and constructing an ingenious Lyapunov function, we establish relaxed criteria for achieving PTS of KONs with the proposed protocol. The condition of the graph containing a directed spanning tree is the weakest, and the initial phases can be almost global. Moreover, we demonstrate the boundedness of the protocol. Finally, numerical simulations validate our results’ effectiveness and superiority compared in others.
