Supervisor abstraction to deal with planning problems in manufacturing systems

Abstract

Finite-state automata and Supervisory Control Theory have been used to model and solve job-shop scheduling and planning problems. However, even if it seems to be easier to work with DFA and SCT, this solution will suffer with “the curse of dimensionality”, which can cause state explosion when the system becomes bigger and more complex. This paper presents a set of sufficient conditions that allow to work with abstractions of the supervisor, instead of the supervisor itself, as the search universe to solve a planning problem. Such abstraction is the natural projection of the supervisor into the set of controllable events and it should satisfy the observer property. This abstraction is smaller then the original automaton, which reduces the search universe for the optimization algorithms. Also, we present a set of conditions for the model of the system and specifications that will results on the satisfaction of the observer property.