Partial Pinning Control for the Synchronization of Fractional-Order Directed Complex Networks

摘要

This paper mainly studies the synchronization problem of fractional-order directed complex networks through partial pinning control. Unlike other papers, the network studied in this paper is neither strongly connected nor contains directed spanning trees. By utilizing the directed acyclic graph condensation and Layering theory, the network is decomposed into several strong connected components and then divided into layers. It proved that all or part of nodes in the network can achieve synchronization with the pinner’s trajectory, only when the root strong connected components in the upstream of these nodes are pinned and satisfy some sufficient conditions. In addition, according to the ControlRank algorithm, an optimized strategy is designed to solve the problem of the optimal selection of the pinning nodes to ensure the specific nodes of the network can achieve synchronization eventually. Meanwhile the amount of control energy cost will also be given in this paper. Finally, two simulation examples are given to verify the reliability and feasibility of the optimized algorithm.