Towards Supervisory Control of Generally-Distributed Discrete-Event Systems

Abstract

We develop a process-theoretic approach for generally-dis-tributed discrete-event systems with unrestricted nondeterminism that is geared towards supervisory control. Supervisory control theory deals with synthesis of models of supervisory controllers that ensure safe and nonblocking behavior of the supervised system. The models are synthesized based on a model of the uncontrolled system and a formalization of the control requirements. Even though there exist extensions of supervisory control theory for timed and Markovian discrete-event systems, there are hardly any investigations of supervisory control of discrete-event systems with generally-distributed delays. General distributions provide for (convenient) modeling of important real-world phenomena that cannot be consistently modeled by means of real time or Markovian (exponentially-distributed) delays, like heavy-tail or uniformly distributed processes. Our theory relies on a behavioral preorder termed partial bisimulation, for which we provide a suitable extension. Based on the proposed theory we provide for an appropriate abstraction of the stochastic behavior, which enables us to employ standard supervisory controller synthesis tools. The synthesized supervisor can, thereafter, be coupled with the stochastic model of the unsupervised system and abstracted to a generalized semi-Markov process for the purpose of analysis and simulation.