This letter aims at modeling and real-time control of a flexible manufacturing system (FMS) that is operated by multi-skilled mobile robots. By introducing the idea of a unique ideal clean configuration and the effective disruption event, the concepts of Opportunity Window (OW) and Permanent Production Loss (PPL) are extended to the FMS. The control considered in this letter is a robot assignment problem where individual robots are dynamically assigned to each workstation in real time to improve performance. The problem is formulated as a Markov Decision Process (MDP) and solved using the Double Deep Q-Network (DDQN) reinforcement learning algorithm. PPL is used as the reward setting for training and a space discretization is used between each workstation to capture real time movement of the robots on the plant floor. The effectiveness of the control strategy is then demonstrated by comparing the results to several heuristic control schemes.