# Optimal Supervisory Control of Probabilistic Discrete Event Systems

### by Vera Pantelic, Mark Lawford

**Abstract:**

Probabilistic discrete event systems (PDES) are modeled as generators of probabilistic languages and the supervisors 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 behaviour 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 behaviour of the plant under control is ``as close as possible'' to the desired behaviour. 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 behaviour of the plant is presented.

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### BibTeX Entry

@ARTICLE{PantelicLawford12,
title={Optimal Supervisory Control of Probabilistic Discrete Event Systems},
author={Vera Pantelic and Mark Lawford},
journal={Automatic Control, IEEE Transactions on},
year={2012},
month={May},
volume={56},
number={5},
pages={1110-1124},
keywords={ control system synthesis, discrete event systems, stochastic control, discrete-event systems, probabilisitic supervisory control},
}

Mark Lawford
Last modified: Thurs Nov 24 11:02:36 EDT 2011