Control Of Stochastic Discrete Event Systems: Existence

In earlier papers [3, 2, 1] we introduced the formalism of probabilistic languages for modeling the stochastic qualitative behavior of discrete event systems (DESs). In this paper we present a framework for their supervisory control, where control is exercised by dynamically disabling certain controllable events. The control objective is to design a supervisor such that the controlled system never executes any illegal traces (their occurrence probability is zero), and legal traces occur with minimum prespecified occurrence probabilities. We provide a condition for the existence of a supervisor. We also present an algorithm to test this existence condition when the probabilistic languages are regular (so that they admit probabilistic automata representation with finitely many states)