Controllability and stabilization of Boolean control networks by the auxiliary function of flipping

In this article, a hybrid method combining flip matrix approach and an open (or closed) loop control is proposed to study global controllability and stabilization of Boolean control networks (BCNs). First, the necessary and sufficient condition for global controllability of BCNs, by flipping some members of a perturbation set and under free control sequences, is proposed. After that, using a search algorithm, the minimal perturbation sets for global controllability (MS-GCs) of the BCN are obtained. Next, we propose a necessary and sufficient criterion for global stabilization of BCNs by flipping some members of a perturbation set and under a state feedback control. Similarly, an algorithm is given to search for the minimal perturbation sets for global stabilization (MS-GSs) of the BCN. Moreover, the time-optimal MS-GSs of the BCN are also obtained by an algorithm. Some examples are given to illustrate the effectiveness of the results.