Event-triggered control for output regulation of probabilistic Boolean control networks under dimension reduction method

This paper studies the output regulation problem (ORP) of probabilistic Boolean control networks (PBCNs) via dimension reduction method, which aims to detect whether the output trajectories of a PBCN can track the time-varying output signals generated by an external Boolean network. Firstly, a dimension reduction auxiliary system is constructed, whose dimension is much smaller than the augmented system in the previous methods. By analyzing the set stabilization of the auxiliary system and the original PBCN, a necessary and sufficient condition to detect the solvability of the ORP is presented. Secondly, a type of event-triggered controls is designed, which are composed of the set stabilizers of the original PBCN and the constructed dimension reduction system. Finally, an example is provided to illustrate the feasibility of the proposed method.