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 [6] 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.
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