This study investigates the asynchronous controllability of non-homogeneous Markov switch generalized asynchronous Boolean control networks (NMHGABCNs) and random switching signals in these networks, aiming to follow a non-homogeneous Markov process. The controllability of the proposed networks is achieved using the discrepancy between the Markov chain mode and the control mode. Assisted by the semi-tensor product (STP), the algebraic forms of the NMHGABCNs are obtained, and the sufficient and necessary criteria for their asynchronous controllability are derived. The effectiveness of controllability is demonstrated through two examples, which validate the theoretical results.

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.