Asymptotical Stabilization for Probabilistic Boolean Control Networks under Operators and Inputs Constraints

In this paper, asymptotical stabilization of probabilistic Boolean control networks (PBCNs) with a switching signal being an independent identically distributed process has been systematically studied. Here, the binary operators connecting logical functions of state nodes and pinning controllers are constrained to certain sets. By establishing matrix representation of operators and input constraints, several criteria for asymptotical stabilization have been established. The proposed asymptotical stabilization extends the results of Boolean networks (BNs) under static pinning control, which is more practical in real-word control design systems. Finally, simulations are given to verify the effectiveness of the obtained theoretical results.