Ensemble set controllability of Boolean control networks

In this paper, we investigate the ensemble controllability and reachability for a family of Boolean control networks (BCNs). First, BCNs are converted to discrete-time linear dynamics by the semi-tensor product. Then the ensemble controllability of BCNs is studied via a free control sequence and input Boolean network, respectively. Some necessary and sufficient conditions are obtained to judge the ensemble controllability. The existence of the input Boolean network for the ensemble controllability is also discussed. When there are unknown inputs in BCNs, necessary and sufficient conditions for the controllability are presented as well. Finally, examples are analyzed to show the effectiveness of the proposed results.