Set Stabilization in Distribution of Probabilistic Boolean Control Networks

In this paper, we propose the concept of set stabilization in distribution of a probabilistic Boolean control network (PBCN), which determines whether the probability distribution converges to the distribution of the destination state subset under a certain control sequence. Then an algorithm is proposed to calculate the largest control invariant subset (LCIS) of a PBCN contained in a given set. We prove that for a PBCN, set stabilizability in distribution and set stabilizability in distribution by state feedback are equivalent. Based on this, a necessary and sufficient condition for set stabilizability in distribution is derived, and a control design method is proposed. Finally, examples are provided to illustrate the effectiveness of the proposed method.