Minimum-cost control of directed complex networks - Ding, Jie (2018)
Complex networks emerge in diverse areas, ranging from social to biological, economic and technological systems. Among these applications, controlling the complex networks is one of the most important problem, which can guarantee reliable and efficient operations of the network. Specifically, according to control theory, a dynamic network system is controllable if it can be driven from any initial state to any desired final state with appropriate external inputs. Existing works mainly focus on the problem of finding the minimum number of nodes connected with external input signals under different conditions such that the resulting network system is controllable. However, as we know when the Gramian matrix tend to be singular, the control cost of the network will be prohibitively large, resulting in the network is theoretically controllable but practically uncontrollable. Therefore, controlling the network with minimum cost has been an important problem to be solved.