Towards Optimal Supervisory Control of Probabilistic Discrete Event Systems

This paper considers optimal supervisory control of probabilistic discrete event systems (PDESs). PDESs are modeled as generators of probabilistic languages. The probabilistic supervisors employed enable/disable events with certain probabilities. We consider the case when there exists no probabilistic supervisor to match the behaviour of a plant to a probabilistic requirements specification. First, we define a notion of distance between two probabilistic generators. Then, given a plant and a desired probabilistic behaviour, we present an algorithm that minimizes the distance between the desired behaviour and the behaviour of the controlled plant achievable under probabilistic control.