Pinning controllability of dynamical networks based on synchronized motion performance

The right selection of the type and the number of driver nodes, play an important role in improving the controllability and the performance of the dynamical networks. In this paper the controllability and the performance of a network has been studied when a new approach for selecting the driver nodes, based on the three main node centrality criteria, has been proposed. For each criterion, the percentage of the least number of driver nodes to achieve the desired performance has been calculated for several network model structures. The results for pure random networks show that for the ‘’betweenness centrality criterion’’ the number of driver nodes is minimal. Similar results hold for Small World networks subject to the fact that for dense, the number of driver nodes increases. It is shown that the ‘’closseness centrality criterion’’ is the proper choice for the State Free networks especially when the network is dense. Another important result is that in Small World networks, increasing the nearest neighborhood coefficient, decrease the number of driver nodes for a desired performance. Similar results hold for Scale Free networks where increasing the heterogeneity coefficient improves the network pinning controllability.