Optimizing Network Controllability with Minimum Cost
Xiao Wang, Linying Xiang · Complexity · 2021
In this paper, the issue of optimally modifying the structure of a directed network to guarantee its structural controllability is investigated. Given a directed network, in order to obtain a structurally controllable system, a framework for finding the minimum number of directed edges that need to be added to the network is proposed. After we get these edge‐addition configurations, we further calculate the network cost of each optimization scheme and choose the one with the minimum cost. Our main contribution is twofold: first, we provide an algorithm able to find all optimal network modifications in polynomial time; second, we provide a way to calculate the cost of optimizing the network based on the node betweenness. Numerical simulations are given to illustrate the theoretical results.