# Computation of Probabilistic Supervisory Controllers for Model Matching

### by S. Postma and M. Lawford

**Abstract:**
Probabilistic discrete event systems (PDES)
generalize discrete event systems (DES) by attaching an occurence
probability to each event so that the underlying DES becomes a generator
of a probabilistic language. In this paper PDES supervisors generalize DES supervisors by attaching a probability to the enablement of each controllable events that is updated
after each event observation. When an event is disabled, its probability is
redistributed via the probability distrubution conditioned on the remaining possible event outcomes.
The control problem considered is to find, if possible,
a probabilistic supervisory
controller such that the probabilistic language generated by the
closed loop system matches a given probabilistic specification language. In
\cite{LawWon:93} necessary and sufficient conditions for the existence
of a probabilistic supervisor were stated with partial proof. This paper completes the proof
of the conditions and provides an algorithm that can be used to compute a solution to the model matching problem when it exists.

### Download

Allerton2004.pdf (pdf 161k)

### BibTeX Entry

@InProceedings{PostmaLawford:04,
author = {Steven Postma and Mark Lawford},
title = {Computation of Probabilistic Supervisory Controllers for Model Matching},
booktitle = {Proceedings of the 42nd Annual
Allerton Conference on Communication, Control, and Computing},
year = {2004}
}

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Mark Lawford
Last modified: Thu Aug 9 12:43:05 EDT 2001