Double reinforcement learning for cluster synchronization of Boolean control networks under denial of service attacks

This paper investigates the asymptotic cluster synchronization of Boolean control networks (BCNs) under denial-of-service (DoS) attacks, where each state node in the network experiences random data loss following a Bernoulli distribution. First, the algebraic representation of BCNs under DoS attacks is established using the semi-tensor product (STP) of matrices. Using matrix-based methods, some necessary and sufficient algebraic conditions for BCNs to achieve asymptotic cluster synchronization under DoS attacks are derived. For both model-based and model-free cases, appropriate state feedback controllers guaranteeing asymptotic cluster synchronization of BCNs are obtained through set-iteration and double-deep Q-network (DDQN) methods, respectively. Besides, a double reinforcement learning algorithm is designed to identify suitable state feedback controllers. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed approach.