Pinning controllability of autonomous Boolean control networks

Autonomous Boolean networks (ABNs), which are developed to model the Boolean networks (BNs) with regulatory delays, are well known for their advantages of characterizing the intrinsic evolution rules of biological systems such as the gene regulatory networks. As a special type of ABNs with binary inputs, the autonomous Boolean control networks (ABCNs) are introduced for designing and analyzing the therapeutic intervention strategies where the binary inputs represent whether a certain medicine is dominated or not. An important problem in the therapeutic intervention is to design a control sequence steering an ABCN from an undesirable location (implying a diseased state) to a desirable one (corresponding to a healthy state). Motivated by such background, this paper aims to investigate the reachability and controllability of ABCNs with pinning controllers. Several necessary and sufficient criteria are provided by resorting to the semi-tensor product techniques of matrices. Moreover, an effective pinning control algorithm is presented for steering an ABCN from any given states to the desired state in the shortest time period. Numerical examples are also presented to demonstrate the results obtained.