Reinforcement learning-based composite suboptimal control for Markov jump singularly perturbed systems with unknown dynamics

In this article, a model-free parallel reinforcement learning method is proposed to solve the suboptimal control problem for the Markov jump singularly perturbed systems. First, since fast and slow dynamics coexist in Markov jump singularly perturbed systems, it may lead to ill-conditioned numerical problems during the controller design process. Therefore, the original system can be decomposed into independent subsystems at different time-scales by employing the reduced order method. Besides, a model-based parallel algorithm is designed to obtain the optimal controllers of the fast and slow subsystems respectively. Moreover, within the framework of reinforcement learning, the composite controller of the Markov jump singularly perturbed systems can be obtained without system dynamics. Finally, a numerical example is introduced to prove the effectiveness of proposed algorithms.