State feedback stabilization for probabilistic Boolean networks

A probabilistic Boolean network (PBN) is a discrete-time system composed of a family of Boolean networks (BNs) between which the PBN switches in a stochastic fashion. Studying control-related problems in PBNs may provide new insights into the intrinsic control in biological systems and enable us to develop strategies for manipulating complex biological systems using exogenous inputs. This paper investigates the problem of state feedback stabilization for PBNs. Based on the algebraic representation of logic functions, a necessary and sufficient condition is derived for the existence of a globally stabilizing state feedback controller, and a control design method is proposed when the presented condition holds. It is shown that the controller designed via the proposed procedure can simultaneously stabilize a collection of PBNs that are composed of the same constituent BNs.