Block-based minimum input design for the structural controllability of complex networks

Abstract

Traditional control system design to complex networks is generally implemented by integrated structural analysis aiming at a global network. However, such a global method may be inefficient, in particular, when a massive network with a huge number of nodes and associations is considered. In this paper, motivated by the idea of “dividing and dealing”, we propose a block-based approach to the issue of minimum input design for structural controllability (MIDSC) of complex networks that potentially incurs in higher efficiency. Specifically, we consider a large-scale networked system that consists of several local blocks. The main challenge for control configuration design of this class of systems is how to find the minimum inputs of global network according to the local block information while maintaining system’s structural controllability. To this end, two block-based graphical algorithms are developed to meet the conditions required for achieving structural controllability, and meanwhile determine an optimal solution for addressing the MIDSC problem. The complexity of the proposed method is analyzed, which is also compared with existing algorithms designed mainly based on monolithic model. In particular, we show that, under some mild conditions on blocking structure, the complexity of the proposed algorithm is strictly lower than that of existing algorithms to the MIDSC problem.