Stabilization and Reconstruction of Sampled-Data Boolean Control Networks Under Noisy Sampling Interval

In this article, we consider stabilization and reconstruction of sampled-data Boolean control networks (BCNs) under noisy sampling interval. A sampled-data BCN under noisy sampling interval is first converted into a probabilistic Boolean network (PBN). We then obtain some necessary and sufficient conditions for global stochastic stability of the considered sampled-data BCN under two types of noisy sampling intervals. However, in analyzing the stochastic stability of large-scale sampled-data BCNs under noisy sampling interval, using the abovementioned necessary and sufficient conditions, leads to huge computational cost. Therefore, for a large-scale sampled-data BCN, we have to transform it into a size-reduced probabilistic logical network. Then, by studying the stochastic stability of the probabilistic logical network, some sufficient conditions for global stochastic stability of the large-scale sampled-data BCN are obtained. Moreover, based on the given steady-state probabilities of the transformed PBN, the reconstruction problem of sampled-data BCNs under noisy sampling interval can be well-solved as a linear programming problem. Notably, the reconstruction method we presented here is also applicable to large-scale sampled-data BCNs.