随机干扰下拓扑时变Kuramoto网络事件触发固定时间同步

Fixed-time event-triggered synchronization of Kuramoto network under time-varying topology and stochastic perturbation

本文针对一类网络拓扑时变且耦合通道存在随机干扰的Kuramoto型振子网络的同步问题,设计了事件触发机制下的固定时间控制算法.针对耦合网络的拓扑在切换中保持连通的假设,给出了一种具有多层结构的事件触发分布式控制策略,并能够抵消随机干扰对同步性能带来的负面影响.利用随机Lyapunov稳定理论和固定时间稳定性理论给出了达到实际固定时间相位同步的控制参数条件和同步调节时间的上界.另外,证明了所使用的事件触发机制在引入双曲正切函数之后不会产生Zeno现象,并给出了触发间隔的下界.同时,在推论中给出了本文提出的控制方法也可以应对振子耦合拓扑图不连通情况的结论.最后,通过两组具有不同噪声强度的仿真实验验证了理论分析结果.

This paper studies a phase synchronization problem of the Kuramoto oscillator network model with timevarying coupling topology and stochastic interference,and proposes a fixed-time control method under event-triggered mechanism.A multi-layer event-triggered distributed control strategy is proposed for the coupling network under the assumption that the topology is connected,and the negative effect of random disturbance on synchronization performance is addressed.The control parameter conditions for realizing practical fixed-time phase synchronization and the upper bound of the settling time are presented by the stochastic Lyapunov stability theory and fixed-time stability theory.Moreover,it is proved that the proposed event-triggered mechanism with hyperbolic tangent function does not produce Zeno behavior.The lower bound of the triggered time interval is given.At the same time,the conclusion that the proposed control can also deal with the unconnected topology of oscillator is given in corollary.Finally,the validity of the theoretical analysis results are verified by two sets of experiments with different noise intensities.