State Estimation for Probabilistic Boolean Networks via Outputs Observation

Dimensionality Reduction Method for the Output Regulation of Boolean Control Networks

This article proposes a dimensionality reduction approach to study the output regulation problem (ORP) of Boolean control networks (BCNs), which has much lower computational complexity than previous results. First, an auxiliary system which is much smaller in scale than the augmented system in previous approach is constructed. By analyzing the set stabilization of the auxiliary system as well as the original BCN, a necessary and sufficient condition to detect the solvability of the ORP is presented. Second, a method to design the state feedback controls for the ORP is proposed. Finally, two biological examples are given to demonstrate the effectiveness and advantage of the obtained new results.

Long-Run Behavior Estimation of Temporal Boolean Networks With Multiple Data Losses

This brief devotes to investigating the long-run behavior estimation of temporal Boolean networks (TBNs) with multiple data losses, especially the asymptotical stability. The information transmission is modeled by Bernoulli variables, based on which an augmented system is constructed to facilitate the analysis. A theorem guarantees that the asymptotical stability of the original system can be converted to that of the augmented system. Subsequently, one necessary and sufficient condition is obtained for asymptotical stability. Furthermore, an auxiliary system is derived to study the synchronization issue of the ideal TBNs with normal data transmission and TBNs with multiple data losses, as well as an effective criterion for verifying synchronization. Finally, numerical examples are given to illustrate the validity of the theoretical results.

Resolution of Fuzzy Relational Inequalities with Boolean Semi-Tensor Product Composition

Resolution of fuzzy relational inequalities (FRIs) plays a significant role in decision-making, image compression and fuzzy control. This paper studies the resolution of a kind of FRIs with Boolean semi-tensor product composition. First, by resorting to the column stacking technique, the equivalent form of FRIs with Boolean semi-tensor product composition is obtained, which is a system of FRIs (SFRIs) with max–min composition. Second, based on the semi-tensor product method, all the solutions to FRIs with Boolean semi-tensor product composition are obtained by finding all possible parameter set solutions. Finally, a general procedure is developed for the resolution of FRIs with Boolean semi-tensor product composition. Two illustrative examples are worked out to show the effectiveness of the obtained new results.