Control of stochastic discrete event systems: synthesis

We (1996) have presented a framework for their supervisory control, where control is exercised by dynamically disabling certain controllable events thereby nulling the occurrence probabilities of disabled events, and increasing the occurrence probabilities of enabled events proportionately. The control objective is to design a supervisor such that the controlled system never executes any illegal traces, and legal traces occur with minimum prespecified occurrence probabilities. In other words, the probabilistic language of the controlled system lies within a prespecified range, where the upper bound is a “non-probabilistic language” representing a legality constraint. We provide a condition for the existence of a supervisor, and also present an algorithm to test this condition when the probabilistic languages are regular. In this paper we give a technique to compute online a maximally permissive supervisor achieving the specified lower and upper bound constraints