Bilinear Dynamical Networks Under Malicious Attack: An Efficient Edge Protection Method
Bilinear Dynamical Networks Under Malicious Attack: An Efficient Edge Protection Method
复制标题
恶意攻击下的双线性动态网络：一种高效的边缘保护方法
DOI：
10.23919/acc50511.2021.9482847
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发表时间：
2021
期刊：
影响因子：
--
通讯作者：
E.D. Sontag
中科院分区：
文献类型：
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作者：
A. C. B. D. Oliveira;Milad Siami;E.D. Sontag
在大规模网络中，代理和链路往往容易受到攻击。在本文中，我们关注连续时间双线性网络，其中加性扰动模型对代理/状态的攻击或不确定性（节点扰动），乘性扰动模型对代理/状态之间的耦合的攻击或不确定性（链路扰动）。然后，我们根据网络的底层有向图以及外生不确定性和攻击的结构来研究网络鲁棒性概念。具体来说，我们使用网络的 $\mathcal{H}_{2}$-范数定义鲁棒性度量，并根据双线性系统的可达性格拉米安计算它。主要结果是，在某些条件下，该措施对于所有可能的受攻击链接的集合是超模块化的。超模性质有助于优化问题的有效解决。最后我们用几个例子来说明不同的结构如何使系统或多或少容易受到链接的恶意攻击。
In large-scale networks, agents and links are often vulnerable to attacks. In this paper, we focus on continuous-time bilinear networks, where additive disturbances model attacks or uncertainties on agents/states (node disturbances), and multiplicative disturbances model attacks or uncertainties on couplings between agents/states (link disturbances). We then investigate network robustness notion in terms of the underlying digraph of a network, and the structure of exogenous uncertainties and attacks. Specifically, we define the robustness measure using the $\mathcal{H}_{2}$-norm of the network and calculate it in terms of the reachability Gramian of the bilinear system. The main result is that under certain conditions, the measure is supermodular over the set of all possible attacked links. The supermodularity property facilitates the efficient solution of the optimization problem. We conclude with a few examples illustrating how different structures can make the system more or less vulnerable to malicious attacks on links.