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Tradeoff Between Controllability and Robustness in Diffusively Coupled Networks
IEEE Transactions on Control of Network Systems ( IF 4.2 ) Pub Date : 2020-07-24 , DOI: 10.1109/tcns.2020.3011814
Waseem Abbas , Mudassir Shabbir , A. Yasin Yazicioglu , Aqsa Akber

In this article, we demonstrate a conflicting relationship between two crucial properties— controllability and robustness —in linear dynamical networks of diffusively coupled agents. In particular, for any given number of nodes $N$ and diameter $D$ , we identify networks that are maximally robust using the notion of Kirchhoff's index and then analyze their strong structural controllability. For this, we compute the minimum number of leaders, which are the nodes directly receiving external control inputs, needed to make such networks controllable under all feasible coupling weights between agents. Then, for any $N$ and $D$ , we obtain a sharp upper bound on the minimum number of leaders needed to design strong structurally controllable networks with $N$ nodes and $D$ diameter. We also discuss that the bound is best possible for arbitrary $N$ and $D$ . Moreover, we construct a family of graphs for any $N$ and $D$ such that the graphs have maximal edge sets (maximal robustness) while being strong structurally controllable with the number of leaders in the proposed sharp bound. We then analyze the robustness of this graph family. The results suggest that optimizing robustness increases the number of leaders needed for strong structural controllability. Our analysis is based on graph-theoretic methods and can be applied to exploit network structure to co-optimize robustness and controllability in networks.

中文翻译:

扩散耦合网络中可控制性与鲁棒性之间的权衡

在本文中,我们演示了两个关键属性之间的冲突关系- 可控性健壮性 -在扩散耦合代理的线性动力学网络中。特别是对于任何给定数量的节点$ N $ 和直径 $ D $ ,我们使用基尔霍夫指数的概念确定了最大鲁棒性的网络,然后分析了其强大的结构可控性。为此,我们计算了最小数量的领导者,即直接接收外部控制输入的节点,使该网络在代理之间的所有可行耦合权下都是可控的。然后,对于任何$ N $$ D $ ,我们获得了设计强大的结构可控网络所需的最少领导者数量的清晰上限 $ N $ 节点和 $ D $直径。我们还讨论了对任意值的最佳边界$ N $$ D $ 。此外,我们为任何$ N $$ D $从而使图具有最大的边集(最大的鲁棒性),同时在结构上可以通过建议的尖锐边界中的前导数进行控制。然后,我们分析该图族的鲁棒性。结果表明,优化鲁棒性会增加强大的结构可控性所需的引线数量。我们的分析基于图论方法,可用于开发网络结构以共同优化网络的鲁棒性和可控性。
更新日期:2020-07-24
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