The outputs robustness of Boolean control networks via pinning control

The outputs robustness is a property where the outputs of a system are insensitive to disturbances, and the property plays an important role in biological systems or engineering design. This paper presents an approach to analyze the outputs robustness with respect to disturbances (w.r.t. disturbances) for Boolean control networks (BCNs). Based on the wiring digraph of a BCN rather than the state transition digraph, an algorithm is proposed to construct a corresponding permutation digraph and permutation system. Then, we prove that if there exists a pinning controller such that the outputs of a permutation system are robust w.r.t. disturbances, then there must also exist another pinning controller such that the outputs of the corresponding original systems achieve robustness. Furthermore, pinning controllers are designed based on the neighbors of the pinned-nodes rather than all of the nodes. Finally, the proposed method is well demonstrated by a reduced signal transduction network.