On reachability and controllability of switched Boolean control networks

This paper investigates the reachability and controllability of switched Boolean control networks (BCNs) by using the semi-tensor product method. First, a kind of switching-input-state transfer graph is defined, based on which and the algebraic expression of switched BCNs we thus propose a new kind of switching-input-state incidence matrix that contains the complete information of the switching-input-state transfer graph. Second, by the switching-input-state incidence matrix, several necessary and sufficient conditions are obtained for the reachability and controllability of switched BCNs. Finally, an algorithm is established to find a switching sequence and a control scheme to realize the reachability of switched BCNs in the shortest time. The study of an illustrative example shows that the new results obtained in this paper are very effective in investigating the reachability and controllability of switched BCNs.