Reinforcement Learning Approach to Feedback Stabilization Problem of Probabilistic Boolean Control Networks

In this letter, we study the control of probabilistic Boolean control networks (PBCNs) by leveraging a model-free reinforcement learning (RL) technique. In particular, we propose a Q-learning (QL) based approach to address the feedback stabilization problem of PBCNs, and we design optimal state feedback controllers such that the PBCN is stabilized at a given equilibrium point. The optimal controllers are designed for both finite-time stability and asymptotic stability of PBCNs. In order to verify the convergence of the proposed QL algorithm, the obtained optimal policy is compared with the optimal solutions of model-based techniques, namely value iteration (VI) and semi-tensor product (STP) methods. Finally, some PBCN models of gene regulatory networks (GRNs) are considered to verify the obtained results.