Stabilization of Probabilistic Boolean Networks via State-Flipped Control and Reinforcement Learning

In this paper, the state-flipped control technique is explored to investigate the stabilization of probabilistic Boolean networks (PBNs). Changing the values of many nodes from 0 to 1 (or from 1 to 0) is called the state-flipped control. The concepts of fixed point, reachable sets, and finite-time global stabilization of PBNs under state-flipped control are proposed. Several necessary and sufficient conditions for global stabilization are also derived based on the reachable sets of a given state. Furthermore, a model-free reinforcement learning (RL) algorithm, namely $Q$-learning ($Q$L), is presented to design a flip sequence for any state that steers the state to a given destination state, thereby achieving finite-time global stabilization via state-flipped control. In addition, the process of finding the minimum flip set is proposed under the semi-tensor product and $Q$L methods. Finally, the viability of the results in the paper is shown by considering a 12-gene hepatocellular cancer cell tumor network.