Stabilisation of probabilistic Boolean control networks: a self-triggered method using deep reinforcement learning

In this paper, we present a novel feedback control method for probabilistic Boolean control networks (PBCNs) leveraging the ideas from reinforcement learning (RL). Specifically, we employ a model-free RL technique, namely double deep-Q network (DDQN), to tackle the self-triggering control (STC) problem, resulting in optimal state feedback controllers that effectively stabilise PBCNs at designated equilibrium points. Furthermore, we introduce a novel STC algorithm, referred to as the ‘Smart Self-Triggering Control’ (SSTC) algorithm. SSTC enables the controller to make intelligent decisions, optimising either the number of step counts to reach an equilibrium or minimising the system-controller communications. Our approach is model-free, offering scalability and providing an efficient solution for controlling large-scale PBCNs. To validate our findings, we apply our method to various PBCN models of gene regulatory networks (GRNs).