Controllability of Boolean Networks via Mixed Controls

Controllability is one of the most important properties of a Boolean control network (BCN). Essentially there are two kinds of controls: 1) networked inputs and 2) free logical inputs. This letter considers controllability of BCNs under mixed controls. The technique proposed is to convert a BCN with two kinds of controls into a set controllability problem. Using results obtained for set controllability, a necessary and sufficient condition for controllability of BCNs with mixed inputs is obtained. Some examples are presented to depict the theoretical results.

I. Introduction

In 1969 Kauffman proposed Boolean networks (BNs) to describe gene regularity networks [1]. Since then BNs have become a powerful tool in analysing logical networks. Then, to manipulate logical networks, Boolean control networks (BCNs) emerged. Several special kinds of BCNs have been investigated [2], [3].