State feedback based output tracking control of probabilistic Boolean networks

This paper studies the state feedback based output tracking control of probabilistic Boolean control networks (PBCNs) by using the semi-tensor product of matrices. A series of reachable sets (with probability 1) is defined inductively for PBCNs, and some useful properties are obtained for the reachable sets. Based on the properties of the reachable sets, a necessary and sufficient condition is presented for the state feedback based output tracking control of PBCNs. Meanwhile, a constructive procedure is proposed to design state feedback laws for PBCNs to track a constant reference signal. The study of two illustrative examples shows that the obtained new results are very effective.