A K-Controllable Matching Algorithm for Network Systems

The traditional maximum matching method could be used to choose the driver nodes of a directed network so that entire network is controllable. However controllability is not sufficient for the large-scale network in engineering applications, where the state of the entire network is expected to be driven to the desired value in a given period of time. In this paper, the concept of K-Controllability is utilized to describe the controllability performance based on the traditional controllability theory. A K-Controllable Matching Algorithm (KCMA) is proposed to determine the driver nodes with optimized control chains, so that the upper bound of the controllability index K is as small as possible. The KCMA algorithm is verified by combining the specific network model with the actual network, which shows that the performance of the KCMA algorithm is better than that of the traditional matching algorithm.