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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通过平滑控制方法的复杂网络的预指定时间群集同步

大多数现有的有限/固定时间同步控制方案都是不平滑或不连续的，建立时间是保守估计的。这是由于使用了信号函数或小数功率状态反馈。本文简要介绍了使用平滑控制协议对复杂网络进行预定时间群集同步的问题。同步时间与任何控制参数或任何系统的初始条件无关，而这些条件实际上是根据任务要求统一规定的，而无需进行任何估算。此外，集群同步可以在指定的时间后保持，并且平滑控制输入也始终可以在无限的时间间隔内保持均匀的边界。最后，提供了一个数值示例来说明所提出的协议和设计方法的有效性。