The equivalence issue of two kinds of controllers in Boolean control networks

In this paper, the equivalence issue between state feedback controller and free sequence controller in Boolean control network (BCN) is investigated. Based on the algebraic representation of Boolean networks, we prove that a Boolean control network can be stabilized to a cycle or a fixed point via free sequence controller if and only if there is a state feedback controller which can derive the Boolean control network to the cycle or the fixed point. Then, two algorithms are provided to find the state feedback controller. After that, we prove that a BCN can be globally controllable by free sequence controller, while the BCN is not necessarily globally controllable by state feedback controller. At last, an example is given to illustrate the results.