In this work, strategies to devise an optimal feedback control of probabilistic Boolean control networks (PBCNs) are discussed. Reinforcement learning (RL) based control is explored in order to minimize model design efforts and regulate PBCNs with high complexities. A Q-learning random forest (QLRF) algorithm is proposed; by making use of the algorithm, state feedback controllers are designed to stabilize the PBCNs at a given equilibrium point. Further, by adopting QLRF stabilized closed-loop PBCNs, a Lyapunov function is defined, and a method to construct the same is presented. By utilizing such Lyapunov functions, a novel self-triggered control (STC) strategy is proposed, whereby the controller is recomputed according to a triggering schedule, resulting in an optimal control strategy while retaining the closed-loop PBCN stability. Finally, the results are verified using computer simulations.
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