Most existing finite-/fixed-time synchronization control schemes are nonsmooth or discontinuous, and the settling time is estimated with conservatism. It is due to the utilization of signum function or fraction power state feedback. This brief considers the problem of prespecified-time cluster synchronization of complex networks with a smooth control protocol. The synchronization time is independent of any control parameters or any systems' initial conditions, which is actually uniformly prescribed according to task requirements without any estimations. Moreover, the cluster synchronization can maintain after the specified time, and the smooth control input can always keep uniformly bounded in an infinite time interval as well. Finally, one numerical example is provided to illustrate the effectiveness of the proposed protocol and design method.

中文翻译：

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通过平滑控制方法实现复杂网络的预定时间集群同步


大多数现有的有限/固定时间同步控制方案都是非平滑或不连续的，并且稳定时间的估计较为保守。这是由于使用了正负号函数或分数功率状态反馈。本简介考虑了具有平滑控制协议的复杂网络的预定时间集群同步问题。同步时间与任何控制参数或任何系统的初始条件无关，实际上是根据任务要求统一规定的，无需任何估计。此外，集群同步可以在指定时间后保持，并且平滑控制输入也可以在无限时间间隔内始终保持一致有界。最后，提供了一个数值例子来说明所提出的协议和设计方法的有效性。