论文标题
研究边缘修改对网络控制系统的影响
Investigating the effect of edge modifications on networked control systems
论文作者
论文摘要
本文研究了复杂网络控制系统中边缘的添加/去除的影响，以改善其可控性，系统性能或对外部干扰的鲁棒性。我们获得的传输功能公式允许用$ \ hinf $和$ \ htwo $ norms量化边缘修改的影响。对于具有正边缘重量的稳定网络，我们表明可以针对每个可能的单个边缘修改以及相关的稳定余量来精确计算$ \ hinf $ norm。对于$ \ htwo $ norm，我们获得了下限。由于该界限链接到Gramian可控性的痕迹，因此可以使用它来减少控制所需的能量。相反，当动力学是拉普拉斯类型时，规范就会无限。但是，相关的位移系统是稳定的，对于它们而言，可以量化边缘修改的效果。特别是，在这种情况下，我们在$ \ hinf $ norm上提供了上限，并计算任意边缘添加的$ \ htwo $ norm的确切值。
This paper investigates the impact of addition/removal of edges in a complex networked control system, for the purposes of improving its controllability, system performances or robustness to external disturbances. The transfer function formulation we obtain allows to quantify the impact of an edge modification with the $\hinf$ and $\htwo$ norms. For stable networks with positive edge weights, we show that the $\hinf$ norm can be computed exactly for each possible single edge modification, as well as the associated stability margin. For the $\htwo$ norm we instead obtain a lower bound. Since this bound is linked to the trace of the controllability Gramian, it can be used for instance to reduce the energy needed for control. When instead the dynamics is of Laplacian type, then the norms become unbounded. However, the associated displacement systems are stable and for them the effect of edge modifications can be quantified. In particular, in this case we provide an upper bound on the $ \hinf$ norm and compute the exact value of the $ \htwo $ norm for arbitrary edge additions.
