Optimal state-flipped control and learning for synchronization of probabilistic Boolean networks

This paper studies the synchronization with probability $1$ in Probabilistic Boolean Networks (PBNs) by combining optimal state-flipped control and Q-learning. Within the framework of the Semi-Tensor Product (STP), the synchronization problem is transformed into a set stabilization problem, and the verification criteria are proposed to achieve synchronization. To improve computational efficiency, a reachable set criterion based on state-flipping is introduced, leading to the development of an algorithm for identifying optimal flipping sequences. For large-scale PBNs, a two-step Q-learning-based optimization strategy is proposed: the first step generates the Q-table, and the second step enumerates all optimal state-flipping sequences that reach the synchronization set, thus reducing the computational complexity of the synchronization problem for large-scale PBNs. Finally, numerical simulations demonstrate the effectiveness and practicality of the proposed methods.