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On the Trade-off Between Controllability and Robustness in Networks of Diffusively Coupled Agents

机译：扩散耦合Agent网络的可控性与鲁棒性之间的权衡

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In this paper, we study the relationship between two crucial properties in linear dynamical networks of diffusively coupled agents, that is controllability and robustness to noise and structural changes in the network. In particular, for any given network size and diameter, we identify networks that are maximally robust and then analyze their strong structural controllability. We do so by determining the minimum number of leaders to make such networks completely controllable with arbitrary coupling weights between agents. Similarly, we design networks with the same given parameters that are completely controllable independent of coupling weights through a minimum number of leaders, and then also analyze their robustness. We utilize the notion of Kirchhoff index to measure network robustness to noise and structural changes. Our controllability analysis is based on novel graph-theoretic methods that offer insights on the important connection between network robustness and strong structural controllability in such networks.
机译：在本文中，我们研究了扩散耦合剂线性动力学网络中两个关键特性之间的关系，即对噪声和网络结构变化的可控制性和鲁棒性。特别是，对于任何给定的网络大小和直径，我们都将确定最大鲁棒性的网络，然后分析其强大的结构可控性。我们通过确定最小数量的领导者来做到这一点，以使这些网络在代理之间的任意耦合权重下完全可控。类似地，我们设计具有相同给定参数的网络，这些参数完全可以通过最少数量的引导程序独立于耦合权重进行控制，然后还分析了它们的鲁棒性。我们利用基尔霍夫指数的概念来衡量网络对噪声和结构变化的鲁棒性。我们的可控性分析基于新颖的图论方法，可提供有关网络鲁棒性与此类网络中强大的结构可控性之间的重要联系的见解。

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