Set Controllability of Boolean Control Networks Under Stochastic Function Perturbation

In this paper, we investigate the effect on set controllability and observability of Boolean control networks (BCNs) under stochastic function perturbation. To begin with, the logical functions of BCNs under stochastic function perturbation are converted into an algebraic expression by using semi-tensor product (STP) of matrices. Next, several effective criteria are given to guarantee controllability and set controllability of system under stochastic function perturbation. A sufficient condition for judging observability is obtained by set controllability. In the end, the validity of the obtained theoretical results is examined through a biological example.