Fixed-Time Synchronization and Energy Consumption for Kuramoto-Oscillator Networks With Multilayer Distributed Control

The fixed-time synchronization and energy consumption of Kuramoto-oscillator networks with multilayer distributed control are studied in this brief. In order to achieve fixed-time synchronization, multilayer networks are designed, including the proportional layer, the finite-time layer and the fixed-time layer. Then, to overcome that Kuramoto-oscillator networks cannot realize synchronization at the desired time, the sufficient conditions for Kuramoto-oscillator networks are proposed to guarantee the fixed-time synchronization. To achieve energy saving of the controller, the supremum of energy consumption is obtained when the Kuramoto-oscillator networks reach synchronization. Finally, an example for Kuramoto-oscillator networks is given to illustrate the effectiveness of the proposed synchronization and energy consumption.