Controllability and stabilization of Boolean control networks with state and input constraints

This paper investigates the controllability and stabilization of Boolean control networks (BCNs) with state and input constraints by using the semi-tensor product method, and presents a number of new results. First, a kind of constrained incidence matrix is proposed for BCNs with state and input constraints. Second, based on the constrained incidence matrix, several necessary and sufficient conditions are obtained for the controllability of the system. Third, the constrained BCN is converted to an equivalent unconstrained one, based on which some necessary and sufficient conditions are presented for the stabilization of the constrained BCN with open-loop and closed-loop controls, respectively. Finally, a practical example of the apoptosis network is studied by using the new results obtained in this paper. The study of illustrative examples shows that the new results presented in this paper are very effective in the analysis and control of BCNs with state and input constraints.