Edge Removal and Q-Learning for Stabilizability of Boolean Networks

This article develops a new edge removal mechanism for the global stabilizability of Boolean networks (BNs). In order to achieve the edge removal control, several control variables are properly placed into the dynamics of BNs based on the fundamental logical operators. On the basis of the new edge removal mechanism, several necessary and sufficient conditions are obtained for the global stabilizability and set stabilizability of BNs. Furthermore, a kind of stable edge removal control is proposed and achieved via the $Q$ -learning algorithm to optimize the edge removal mechanism. As an application, the edge removal control is used to verify whether or not the mammalian cortical area development model can be made stabilizable to the expected stable states.