An Improvement of Optimal Control Strategy for a Fixed Number of Control Nodes

Structural controllability has become a problem of paramount importance in complex networked systems. For a fixed number of control nodes, though the optimal control configuration(OCC) of directed networks can make its controllability index maximum, the controllability index of this strategy has inaccuracy when the network contains the unreachable cyclic subnetworks. In this paper, we propose an improved optimal control strategy based on unreachable paths deletion for a fixed number of control nodes. We classify multiple subnetworks selected by the OCC strategy and distinguish the direction of connecting edges between subnetworks. Then, the unreachable paths search algorithm is used to screen and eliminate the unreachable path sets, which can ensure the accuracy of the controllability index. The comparison results show that the controllability index of the improved strategy is strictly smaller than that of the original one. Moreover, we demonstrate the effectiveness of this improved strategy is influenced by the number of control nodes, uniformity, and density of the ER network and SF network.