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 <inline-formula> <tex-math notation="LaTeX">$Q$ </tex-math></inline-formula>-learning <inline-formula> <tex-math notation="LaTeX">$(QL)$ </tex-math></inline-formula> 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.