Some Tractable Supervisory Control Problems for Discrete-Event Systems Modeled by Büchi Automata

Discrete-event systems (DES) are modeled by Büchi automata together with a means of on-line control. In this setting we extend the concept of a controllable language introduced by Ramadge and Wonham to infinite strings and derive conditions for the existence of a supervisor (controller) to implement a prescribed closed-loop behavior. Our main interest is in a class of DES called product systems. These are DES composed of a finite set of asynchronous components. A control problem for such a system typically requires the synthesis of an on-line controller so as to achieve some prescribed coordinated behavior of the component subsystems. One of the principal difficulties in this task is that the size of the state space increases exponentially with the number of components. We show that despite this fact several interesting control synthesis problems for such systems are computationally feasible and we develop algorithms for their solution.