Set Stabilization of Probabilistic Boolean Control Networks via Self-Triggered Control

This paper addresses the set stabilization problem of probabilistic Boolean control networks (PBCNs) via a self-triggered control strategy. Firstly, the algebraic representation of the considered PBCNs is established by employing the semi-tensor product (STP) of matrices. Secondly, Lyapunov functions (LFs) are introduced for the set stabilization analysis, and a constructive algorithm for deriving such LFs is provided. On this basis, a necessary and sufficient condition in terms of the LF is obtained to determine whether a PBCN can achieve stabilization to a prescribed target set with probability one. Furthermore, a design method for self-triggered controls (STCs) is developed. Finally, the Escherichia coli lactose operon is presented as an example to validate the theoretical results of this paper.