本文讨论了通过粘贴控制实现复杂网络固定时间集群同步问题。固定时间同步意味着网络可以在有限时间内达到同步，且 settling time 由常数有界。为实现固定时间集群同步，设计了一个简单的分布式协议，其有效性被严格证明，并获得了固定时间集群同步的充分条件。特别地，当集群数为一时，集群同步变为完全同步问题；当每个节点的内在动力学缺失时，固定时间集群同步变为固定时间集群（或完全）一致性问题；当网络只有一个节点时，节点间的耦合项消失，同步问题变为最简单的主从情况，这也包括神经网络等非线性系统的稳定性问题。所有这些情况都被讨论。最后，通过数值模拟展示了所获得理论结果的正确性。
英文摘要：
In this paper, the fixed-time cluster synchronization problem for complex networks via pinning control is discussed. Fixed-time synchronization has been a hot topic in recent years, which means that the network can achieve synchronization in finite-time and the settling time is bounded by a constant for any initial values. To realize the fixed-time cluster synchronization, a simple distributed protocol by pinning control technique is designed, whose validity is rigorously proved, and some sufficient criteria for fixed-time cluster synchronization are also obtained. Especially, when the cluster number is one, the cluster synchronization becomes the complete synchronization problem; when the intrinsic dynamics for each node is missed, the fixed-time cluster synchronization becomes the fixed-time cluster (or complete) consensus problem; when the network has only one node, the coupling term between nodes will disappear, and the synchronization problem becomes the simplest master-slave case, which also includes the stability problem for nonlinear systems like neural networks. All these cases are also discussed. Finally, numerical simulations are presented to demonstrate the correctness of obtained theoretical results.
Synchronization of linearly coupled reaction-diffusion neural networks with hybrid coupling and time-varying delays via aperiodically intermittent pinning control
Tongji University（同济大学）；The Key Laboratory of Embedded System and Service Computing, Ministry of Education（教育部嵌入式系统与服务计算重点实验室）；Shandong University（山东大学）
