MINIMIZING THE CARDINALITY OF AN EVENTS SET FOR SUPERVISORS OF DISCRETE-EVENT DYNAMICAL-SYSTEMS

In this paper we study sufficient observation and work spaces for supe rvisors of a class of discrete-event dynamical systems (DEDS), We use finite state automata to model a DEDS. The finite automata generates a formal language defined over the set of events in the DEDS. A supervi sor is a feedback system that observes a generated trace of events and dynamically disables (or enables) a subset of controllable events suc h that the closed-loop system behaves as desired, We model the desired behavior of the DEDS by a sublanguage defined over the set of events. A sufficient observation space is a collection of events whose observ ation by a supervisor is enough to realize a given desired behavior, A sufficient work space is a sufficient observation space such that the control action of the supervisor is limited to only the controllable elements of the work space. In many cases, there exists a sufficient w ork (or observation) space that is smaller tha'n the set of all events , In this work, we construct algorithms to evaluate a sufficient work (or observation) space. The reduction of work (or observation) spaces results in reducing the number of event detectors, communication, and command channels between the supervisor end the plant.