Abstrações de supervisores localmente modulares para aplicação na solução de problemas de planejamento

Abstract

An approach to solving a scheduling problem in manufacturing systems is the integration of optimization methods with Supervisory Control Theory. This theory allows to restrict the search space to include solutions that respect the safety and nonblockingness of the system. If, instead of this behavior, an abstraction of the behavior of the system under control is used, it is possible to further reduce the optimization search space. This work extends a previous result, by the use of abstractions on supervisors obtained by the local modular synthesis, rather than the monolithic supervisor. The abstractions consist in the natural projection, which has the observer property, of the local modular supervisors to the set of controllable events. The main result guarantees that any string obtained from the abstractions will execute in the phisical system, in the presence of the uncontrollable events. As the monolithic synthesis suffers from the problem of computational explosion, the extension makes feasible the use of abstractions even when it is not possible to deal with the monolithic problem. Besides, experimental data show that the abstraction reduces the search space by a factor of 10, at least, when comparing to the original supervisor.