Algorithms for determining networks´ feasible control schemes

Research on controlling complex networks is of theoretical and engineering importance. Recently various results on controllability of complex networks based on network science methods are reported. In this paper, starting from the methods in control theory, we develop several analytical algorithms to solve the structural controllability problems for networks. For a network with given topology, by analyzing the corresponding structural matrix, we discuss how to get the set of feasible control schemes which guarantee structural controllability with minimal driver nodes. Two algorithms for determining the set of feasible control schemes are proposed, and the applicability and limitations of these algorithms to practical complex networks are also discussed.