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Optimal Supervisory Control of Probabilistic Discrete Event Systems

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2 Author(s)
Pantelic, V. ; Dept. of Comput. & Software, McMaster Univ., Hamilton, ON, Canada ; Lawford, M.

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 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.

Published in:

Automatic Control, IEEE Transactions on  (Volume:57 ,  Issue: 5 )

Date of Publication:

May 2012

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