Set Stabilization and Robust Set Stabilization of Periodically Time-Varying Boolean Control Networks

This paper investigates set stabilization and robust set stabilization of periodically time-varying Boolean control networks (PTVBCNs) by combining state-flipping mechanism and state feedback control. Firstly, two algorithms are proposed to check whether systems with or without disturbance inputs can be stabilized to the set under the hybrid control. Next, the state feedback matrices are designed by a constructive method such that systems can be stabilized to the given set for two cases. In addition, some algorithms are proposed to find the corresponding flip sequence with minimum cardinality that drives any initial state to the given set in two cases. Finally, some examples are given to illustrate the good performance of the obtained results.
Note to Practitioners
—In this paper, we address the problems of set stabilization and robust set stabilization of periodically time-varying Boolean control networks using the semi-tensor product. This provides essential theoretical support for the interventional treatment of gene regulatory networks, aiming to transfer all states in the network to a healthy state, which is significant for gene therapy. In gene regulatory networks, we need to consider whether the system’s evolution can transfer all states to a healthy state and how to apply external effects to states that cannot achieve a healthy condition through the system’s evolution alone. Choosing when and how to exert external influence can achieve our goals, which is the significance of our research. This paper provides effective methods to solve the above problems.