Output Tracking Control of Probabilistic Boolean Control Networks

Probabilistic Boolean control network (PBCN) is a discrete-time dynamical system comprised of a collection of Boolean control networks (BCNs) and switching among them in a stochastic manner. In this paper, the output tracking control of PBCNs is investigated via state feedback and output feedback control. By resorting to the algebraic state-space representation of BCNs, necessary and sufficient conditions for the solvability of the output tracking control problem are presented. A constructive procedure is given to obtain all possible state feedback and output feedback controllers such that the output of PBCNs tracks a constant reference signal. Finally, a PBCN model of a simple manufacturing system is considered to illustrate the effectiveness of the proposed results.