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.