Controllability of Boolean control networks with respect to part of the variables

In this paper, we analyze the controllability problems of Boolean control networks (BCNs) with respect to a given part of variables by referring to the semi-tensor product (STP) of matrices. First, the concept of partial controllability for a BCN is given. Second, based on the properties of STP, a simple algebraic representation for the evolution of the given part of variables is derived, and thereby providing the reachable sets precisely. Finally, some necessary and sufficient conditions are obtained for the partial controllability of BCNs. In addition, the upper bound of time to check the criterions is given. One numerical example is worked out to illustrate the obtained results.