Controllability of higher order Boolean control networks

Using the semi-tensor product method, this paper investigates the controllability of a μth order Boolean control network. After a brief introduction on semi-tensor product of matrices to μth order Boolean control networks, the controllability issue is studied. First, a systematic procedure to reconstruct the logical dynamic of a μth order Boolean control network from its network transition matrix is presented for design purpose. Then, the controllability via two types of controls is considered. Necessary and sufficient conditions are provided for each case. The application of input-state incidence matrix to the controllability of μth order Boolean control networks is studied. Finally, as an application, examples are given to illustrate the effectiveness of the obtained results.