Abstraction of the Supervisory Control Solution to Deal With Planning Problems in Manufacturing Systems

In industry, the performance has to be optimized to allow its competitiveness. The goal then is to use the resources at their maximal capacity, reduce the production time, and be flexible to adapt to the customers requests. The closed-loop behavior of a system under the supervisory control theory (SCT) guarantees nonblockingness and safety requirements and, thus, it can be used as the search universe for a planning problem. SCT suffers with the "curse of dimensionality" when systems become bigger and more complex. This article presents a set of sufficient conditions that allow to work with abstractions of the closed-loop behavior (supremal controllable sublanguage), instead of the closed-loop behavior 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 satisfying the observer property. This process leads to a reduction of the search space.