论文标题
多量级和定向复杂网络的规定时间同步
Prescribed-Time Synchronization of Multiweighted and Directed Complex Networks
论文作者
论文摘要
在本说明中，我们通过固定控制研究了多重和定向复杂网络（MWDCN）的规定时间（PT）同步。与有限的时间和固定时间同步不同，可以根据需要预留同步的时间，这与初始值和参数无关，例如耦合强度。首先，我们通过不当的整体，医院规则和泰勒扩张理论揭示了PT稳定性的本质。以前为PT稳定性建立的许多控制器都可以包括在我们的新模型中。然后，我们将此新结果应用于MWDCNS作为应用程序。仔细讨论在规定时间的同步误差，因此可以达到PT同步。网络拓扑可以定向和断开连接，这意味着外耦合矩阵（OCM）可以不对称并且不连接。节点之间的关系允许合作或竞争性，因此OCM和内部耦合矩阵（ICM）的元素可以是正面的或负面的。我们使用重新排列的变量的订单技术将ICM和OCM结合在一起以获取总矩阵，这可以在多重和单加权网络之间建立桥梁。最后，提出模拟以说明我们理论的有效性。
In this note, we study the prescribed-time (PT) synchronization of multiweighted and directed complex networks (MWDCNs) via pinning control. Unlike finite-time and fixed-time synchronization, the time for synchronization can be preset as needed, which is independent of initial values and parameters like coupling strength. First and foremost, we reveal the essence of PT stability by improper integral, L'Hospital rule and Taylor expansion theory. Many controllers established previously for PT stability can be included in our new model. Then, we apply this new result on MWDCNs as an application. The synchronization error at the prescribed time is discussed carefully, so, PT synchronization can be reached. The network topology can be directed and disconnected, which means that the outer coupling matrices (OCMs) can be asymmetric and not connected. The relationships between nodes are allowed to be cooperative or competitive, so elements in OCMs and inner coupling matrices (ICMs) can be positive or negative. We use the rearranging variables' order technique to combine ICMs and OCMs together to get the sum matrices, which can make a bridge between multiweighted and single-weighted networks. Finally, simulations are presented to illustrate the effectiveness of our theory.
