  This paper investigates the stabilization of probabilistic Boolean networks
(PBNs) via a novel pinning control strategy based on network structure. In a
PBN, the evolution equation of each gene switches among a collection of
candidate Boolean functions with probability distributions that govern the
activation frequency of each Boolean function. Owing to the stochasticity, the
uniform state feedback controller, independent of switching signal, might be
out of work, and in this case, the non-uniform state feedback controller is
required. Subsequently, a criterion is derived to determine whether uniform
controllers is applicable to achieve stabilization. It is worth pointing out
that the pinning control designed in this paper is based on the network
structure, which only requires local in-neighbors' information, rather than
global information (state transition matrix). Moreover, this pinning control
strategy reduces the computational complexity from $O(2^{2n})$ to
$O(n2^\alpha)$, and thus it has the ability to handle some large-scale
networks, especially the networks with sparse connections. Finally, the
mammalian cell-cycle encountering a mutated phenotype is modelled by a PBN to
demonstrate the obtained results.
