Local asymptotic set stabilization of probabilistic Boolean control networks via state feedback control

Abstract

This paper investigates the local asymptotic set stabilization of probabilistic Boolean control networks via state feedback control. In order to identify the largest control convergence region, we introduce state/control input constraints and develop a refining procedure. The process iteratively removes non-stabilizable states and ineffective control inputs from the constraint sets, ultimately guaranteeing that the system is stabilizable within the reduced state constraint set. Furthermore, it is proven that the reduced state constraint set is exactly equal to the largest control convergence region of the system. A state feedback controller is synthesized through the proposed method to asymptotically stabilize the system over the largest control convergence region. Finally, the methodology is applied to two simplified biological models to demonstrate its effectiveness.