Use of a metric in supervisory control of probabilistic discrete event systems

This work represents a natural extension of our work on optimal probabilistic supervisory control of probabilistic discrete event systems (PDESs). In that work, a pseudometric on the initial states of two probabilistic automata that represent probabilistic systems is used to measure the distance between two systems. The pseudometric is given a fixed point characterization. This paper gives a logical characterization of the same pseudometric that justifies the intuition that two systems are close if they satisfy similar properties. A trace characterization of the pseudometric is then derived from the logical characterization. Further, the solution of the problem of approximation of a given probabilistic automaton with another automaton is suggested such that the new model is as close as possible to the original one in the pseudometric. The significance of the approximation is then discussed.