Cluster Synchronization of Boolean Networks under State-Flipped Control with Reinforcement Learning

In this brief, cluster synchronization of Boolean Networks (BNs) under state-flipped control is considered. We show how the cluster synchronization problem can be transformed into a set stabilization problem, based on which we give a theorem to judge whether the cluster synchronization of BNs can be achieved under a given flip set. Moreover, when the network structure is unknown, the $Q$ -learning $(QL)$ algorithm, a model-free reinforcement learning algorithm, is developed to search control sequences to achieve cluster synchronization. Some numerical examples are used to verify the validity of the theoretical results at the end.