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首页> 外文期刊>IEEE Transactions on Systems, Man, and Cybernetics >Optimizing Pinning Control of Complex Dynamical Networks Based on Spectral Properties of Grounded Laplacian Matrices
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Optimizing Pinning Control of Complex Dynamical Networks Based on Spectral Properties of Grounded Laplacian Matrices

机译：基于接地拉普拉斯矩阵的光谱特性优化复杂动力网络的钉扎控制

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摘要

Pinning control of a complex network aims at forcing the states of all nodes to track an external signal by controlling a small number of nodes in the network. In this paper, an algebraic graph-theoretic condition is introduced to optimize pinning control. When individual node dynamics and coupling strength of the network are given, the effectiveness of pinning scheme can be measured by the smallest eigenvalue of the grounded Laplacian matrix obtained by deleting the rows and columns corresponding to the pinned nodes from the Laplacian matrix of the network. The larger this smallest eigenvalue, the more effective the pinning scheme. Spectral properties of the smallest eigenvalue are analyzed using the network topology information, including the spectrum of the network Laplacian matrix, the minimal degree of uncontrolled nodes, the number of edges between the controlled node set and the uncontrolled node set, etc. The identified properties are shown effective for optimizing the pinning control strategy, as demonstrated by illustrative examples. Finally, for both scale-free and small-world networks, in order to maximize their corresponding smallest eigenvalues, it is better to pin the nodes with large degrees when the percentage of pinned nodes is relatively small, while it is better to pin nodes with small degrees when the percentage is relatively large. This surprising phenomenon can be explained by one of the theorems established.
机译：复杂网络的固定控制旨在强制所有节点的状态来通过控制网络中的少量节点来跟踪外部信号。在本文中，引入了代数图理论条件以优化钉扎控制。当给出网络的各个节点动力学和耦合强度时，通过删除来自网络的拉普拉斯矩阵的循环节点的行和列来通过接地的拉普拉斯矩阵的最小特征值来测量钉扎方案的有效性。这种最小的特征值越大，钉扎方案越有效。使用网络拓扑信息进行分析最小特征值的光谱特性，包括网络拉普拉斯矩阵的频谱，最小的不受控制节点，受控节点集之间的边数和不受控制的节点集等。所识别的属性如通过说明性示例所证明的，所示的优化钉扎控制策略有效。最后，对于无规模和小世界网络，为了最大化它们对应的最小特征值，当钉扎的节点的百分比相对较小时，最好将具有大程度的节点引脚，同时销钉节点更好当百分比相对较大时，小程度。这种令人惊讶的现象可以通过建立的定理之一解释。

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