Heuristic Search of Supervisors by Approximated Distinguishers*

The use of distinguishers was introduced for Supervisory Control Theory (SCT) in order to simplify the task of modeling specifications, while guaranteeing the synthesis of maximally permissive supervisors. Besides, by approximating the language of a distinguisher, a supervisor can be obtained with computational savings in the synthesis, although there is no guarantee that this is the maximally permissive solution. The main purpose of this work is to propose a procedure to obtain the least restrictive achievable supervisor, in the context of approximations in the SCT with distinguishers. The procedure consists of a heuristic search for the supervisor with the highest language measure in the space formed by supervisors obtained using approximated distinguishers. A search procedure based in Genetic Algorithms was implemented and a case study illustrates the results of the method.