Synchronization of Kuramoto-oscillator networks based on economic control strategy

This paper focuses on the fixed-time (FDT) phase agreement and frequency synchronization problem of Kuramoto-oscillator networks. Traditional controllers for FDT synchronization of Kuramoto-oscillator networks often suffer from complex structures and high costs. To address these issues, a novel FDT controller consisting of only two terms or even a single term is proposed. The simplicity of this controller allows it to adapt better to various types of Kuramoto-oscillator networks and more complex scenarios, thereby significantly expanding the application scope of FDT synchronization control. By efficiently allocating control resources and reducing unnecessary adjustments of control signals, the controller achieves cost-effective and efficient synchronization. Furthermore, the upper bound of the synchronization time and the sufficient conditions for synchronization are rigorously derived, simulation results show that the newly designed controller is effective.