Towards optimal supervisory control of probabilistic discrete event systems

Abstract—Probabilistic discrete event systems (PDES) are modeled as generators of probabilistic languages and the supervi-sors employed are a probabilistic generalization of deterministic supervisors used in standard supervisory control theory. In the case when there exists no probabilistic supervisor such that the behavior of a plant under control exactly matches the probabilistic language given as the requirements specification, we want to find a probabilistic control such that the behavior of the plant under control is “as close as possible ” to the desired behavior. First, as a measure of this proximity, a pseudometric on states of generators is defined. Two algorithms for the calculation of the distance between states in this pseudometric are described. Then, an algorithm to synthesize a probabilistic supervisor that minimizes the distance between generators representing the achievable and required behavior of the plant is presented. Index Terms—Discrete event systems, optimal control, stochastic systems, supervisory control. I