In this paper, using semi-tensor product and the vector form of Boolean logical variables, the Boolean control network (BCN) is expressed as a bilinear discrete time system about state and control variables. Based on the algebraic form, the reachability and controllability of BCNs are discussed. Also, the necessary and sufficient conditions for reachability and controllability are given. At last, the control sequence that steers one state to another is constructed. The reachability and controllability discussed here are under certain constraint, where the trajectory of states are avoiding some undesirable states set. The definitions discussed in this paper have practical meaning.
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