Control of stochastic discrete event systems modeled by probabilistic languages

In earlier papers [7], [6], and [5], we introduced the formalism of probabi listic languages for modeling the stochastic qualitative behavior of discre te event systems (DESs), In this paper, we study their supervisory control where the control is exercised by dynamically disabling certain controllabl e events thereby nulling the occurrence probabilities of disabled events, a nd increasing the occurrence probabilities of enabled events proportionatel y. This is a special case of "probabilistic supervision" introduced in [15] , The control objective is to design a supervisor such that the controlled system never executes any illegal traces (their occurrence probability is z ero), and legal traces occur with minimum prespecified occurrence probabili ties,In other words, the probabilistic language of the controlled system li es within a prespecified range, where the upper bound is a "nonprobabilisti c language" representing a legality constraint, We provide a condition for the existence of a supervisor. We also present an algorithm to test this ex istence condition when the probabilistic languages are regular (so that the y admit probabilistic automata representation with finitely many states), N ext, we give a technique to compute a maximally permissive supervisor onlin e.