论文标题
双线性动力网络中的边缘选择
Edge Selection in Bilinear Dynamical Networks
论文作者
论文摘要
我们为连续的双线性动力网络的设计和鲁棒性分析开发了一些基本原理，在该网络中，攻击者可以操纵某些代理/节点之间的互连/边缘的强度。我们制定了边缘保护优化的问题，即选择有限数量的无攻击边缘并最大程度地减少了对双线性动力网络的攻击的影响。尤其是，$ \ Mathcal {h} _2 _2 $ - 双线性系统的norm norm众所周知，众所周知，可以捕获与其线性相似的攻击，以捕获具有有价值的ISSERTENS sigents senders sendings sendings sendings，以捕获其最大程度的启动。确切的优化问题是边缘数量的组合，蛮力方法的可扩展性差。但是，我们表明$ \ Mathcal {H} _2 $ -NORM作为成本函数是超模型的，因此允许有效的最佳解决方案的贪婪近似值。我们通过数值模拟说明和比较了理论发现的有效性。
We develop some basic principles for the design and robustness analysis of a continuous-time bilinear dynamical network, where an attacker can manipulate the strength of the interconnections/edges between some of the agents/nodes. We formulate the edge protection optimization problem of picking a limited number of attack-free edges and minimizing the impact of the attack over the bilinear dynamical network.In particular, the $\mathcal{H}_2$-norm of bilinear systems is known to capture robustness and performance properties analogous to its linear counterpart and provides valuable insights for identifying which edges are most sensitive to attacks. The exact optimization problem is combinatorial in the number of edges, and brute-force approaches show poor scalability. However, we show that the $\mathcal{H}_2$-norm as a cost function is supermodular and, therefore, allows for efficient greedy approximations of the optimal solution. We illustrate and compare the effectiveness of our theoretical findings via numerical simulations.
