Research On Structural Controllability For Network Based On K Steps

More and more large-scale and complex network systems are arisen in contemporary society with extensive application and development of computer technology, in order to enable large-scale network system to operate effectively, before applying the controllers, structural controllability of network system is discussed by analysis of the structure of network. Especially along with expansion of the scale of network system, much more attention has been paid to the information transmission among nodes in network and the resulted control problem. Therefore, the index of structural controllability is introduced in this thesis to characterize the performance indices when network system can be controlled within finite time.The network system is described by two kinds of description methods in this thesis, which are the directed graph and the structural matrix. Based on the study of structural controllability, the concept of the index of structural controllability is proposed in this thesis and discussed from two angles respectively. From the perspective of the structural matrix, the range of the index of structural controllability is analyzed in this thesis and control chains formed by nodes controlled by each controller control are discussed on the basis of the arrangement of the structural matrix.Furthermore, an algorithm is proposed to obtain the index and related control chains, which provides scientific basis for the corresponding research on the design of controllers and the effective division of subgroup in large-scale network from the perspective of graph theory. Finally,on the basis of previous researches, the relationship between the selection of controllers and the structural controllability within k step is discussed, and deepens the understanding of the complex network system.