Finding all controllers for disturbance decoupling of Boolean control networks

We investigate a type of disturbance decoupling problem (DDP) of Boolean control networks. Using semi-tensor product of matrices, the dynamics of Boolean control network is expressed in its algebraic form. All the necessary arguments of the functions of outputs are called output-friendly coordinates. In order to estimate the solvability of DDP, we give a necessary and sufficient condition of the output-friendly coordinates being always in a known invariant subspace. Then it is computationally feasible to construct all the valid feedback control matrices. The logical function of each controller can be recovered from the obtained feedback control matrix. We further discuss the constraints of the selection of the invariant subspace. Examples are provided to show the effectiveness of the proposed method.