Stochastic finite-time synchronization and energy consumption for Kuramoto-oscillator networks

This article studies stochastic finite-time synchronization, energy consumption, and trade-off analysis of Kuramoto-oscillator networks. First, according to Lyapunov theory, the stochastic finite-time PA and frequency synchronization criteria of Kuramoto-oscillator networks under identical and nonidentical natural frequencies are obtained. Simultaneously, based on the stochastic theory, the upper bound of the setting-time of Kuramoto-oscillator networks is obtained. Subsequently, to evaluate the runtime of the controller, the corresponding upper bound on the energy consumption required for system synchronization is developed. In addition, to meet the needs of different industries, the optimal equilibrium point is obtained by conducting a trade-off analysis, and an appropriate evaluation index function is introduced, which will further enrich the application scenarios of the obtained theory. Finally, the simulation results show that the results obtained in this article are correct and effective.