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首页> 外文期刊>SIAM Journal on Control and Optimization >CHARACTERIZATIONS AND CRITERIA FOR SYNCHRONIZATION OF HETEROGENEOUS NETWORKS TO LINEAR SUBSPACES
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CHARACTERIZATIONS AND CRITERIA FOR SYNCHRONIZATION OF HETEROGENEOUS NETWORKS TO LINEAR SUBSPACES

机译：异构网络与线性子空间同步的特征和标准

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In this paper, we investigate synchronization issues in heterogeneous complex networks. We start with a necessary condition for the existence of synchronous trajectories by analyzing the vector fields of isolated nodes. Then, by geometrical methods of differential equations, a closed invariant set is introduced to characterize the synchronous trajectories. Especially, the omega-limit sets of all the synchronous trajectories are contained in this closed invariant set. Afterward, assuming that the vector fields of all the isolated nodes are identical in a linear subspace, an equivalent network is found such that the equivalent network can be composed of two simpler networks with lower dimensions. Based on this composition, global synchronization criteria for the equivalent network are developed by combining the corresponding Lyapunov-like functions of quadratic form (and even beyond quadratic form) for these two simpler networks. Furthermore, we alternatively use different functions for different nodes to construct Lyapunov functions, arriving at an extended criterion which can be applicable for more networks. Finally, three examples are given to illustrate the validity and advantages of our theoretical results.
机译：在本文中，我们调查异构复合网络中的同步问题。通过分析孤立节点的矢量字段，从一个必要条件开始存在同步轨迹。然后，通过微分方程的几何方法，引入闭合不变集以表征同步轨迹。特别是，所有同步轨迹的欧米茄限制集包含在此封闭的不变集中。之后，假设所有隔离节点的矢量字段在线性子空间中相同，发现等效网络，使得等效网络可以由具有较低维度的两个更简单的网络组成。基于该组合物，通过将相应的Lyapunov样功能组合对这两个更简单的网络的二次形式（甚至超越二次形式）的相应Lyapunov样功能组合来开发等同网络的全局同步标准。此外，我们还使用不同节点的不同功能来构建Lyapunov函数，到达扩展标准，这可以适用于更多网络。最后，给出了三个例子来说明我们理论结果的有效性和优势。

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