Minimal pinning control for set stability of Boolean networks

In this paper, set stability of Boolean networks (BNs) is studied based on semi-tensor product of matrices. First, an index-vector is introduced to verify whether a BN can be set stable from an initial set to a destination set. Then, an algorithm is proposed to obtain the minimal set of pinning nodes to achieve set stability, if a BN is not set stable. Moreover, in order to reduce the computational complexity, a hybrid pinning control technique is proposed, where the designed controllers are not entirely dependent on all the nodes of the networks. Further, the issue of synchronization is discussed by using the proposed hybrid pinning control methods. Finally, simulations are presented to illustrate the effectiveness of the obtained results in this paper.