Reinforcement Learning of Optimal Supervisor Based on Language Measure

Recently, Wang and Ray introduced a signed real measure for formal languages, called a language measure, to evaluate performance of strings generated by discrete event systems. They proposed a synthesis method of an optimal supervisor based on the language measure. If exact description of a discrete event system and the specification is not available, a learning-based approach is useful. In this paper, first, we clarify the relationship between the Bellman equation and a performance index of the languages generated by the controlled discrete event systems. Next, using the relationship, we propose a learning method of the optimal supervisor based on reinforcement learning where costs of disabling of events and the evaluation of reaching states are taken into consideration. Finally, by computer simulation, we illustrate an efficiency of the proposed method.