Localization of DES Supervisory Control with Respect to Each Controllable Event

Supervisory control synthesis in discrete-event systems may encounter increasing the state cardinality. Increase in the number of states causes the computational complexity in supervisor synthesis and makes the implementation of the supervisor in industrial systems difficult. Localization of a supervisor is a method to reduce the number of states in the monolithic supervisor w.r.t. each component of the plant. Also, the synchronization of local controllers with the plant is control equivalent to the monolithic supervisor. In this paper, localization of a monolithic supervisor w.r.t. each controllable event is proposed, in order to facilitate implementation of local controllers. Two methods are proposed based on generalizing existing methods. The first method localizes a supervisor based on self-looping some states by disabled events which cannot be disabled by the corresponding local controller. The second one executes the supervisor localization based on removing transitions in the plant model that are disabled in some states of the monolithic supervisor, and are not supposed to be disabled by the corresponding local controller. In both methods, the supervisor is reduced w.r.t. the (reduced) plant model. The proposed methods are more flexible and may lead to less number of states, comparing to the results of existing method. It is proved that the two methods yield same results.