An approach for enforcing a class of GMECs on time Petri nets with uncontrollable transitions

Abstract Real-time control is of great significance for practical plants such as intelligent manufacturing systems and transportation systems, and timing information should be integrated in their discrete models. The existing specifications expressed by generalized mutual exclusion constraints (GMECs) do not consider timing specifications in the control design of these models, which would be restrictive for the control specifications of a timed system. In the framework of time Petri net (TPN) models, this paper introduces a class of GMECs, called time GMECs (TGMECs), in which each GMEC is associated with a restricted time interval. By restricting the firing intervals of controllable transitions, an efficient method based on control functions is proposed to implement TGMECs on a TPN system in presence of uncontrollable transitions. The core of the reported method is to employ the transitions-related timing constraints in a partial modified state class graph (PMSCG) to solve mathematical programming problems. Such a PMSCG is a graph recently introduced to enhance the supervisor permissiveness for a TPN system with GMECs. In particular, the terminal condition for the construction of a PMSCG is modified. By taking advantage of the PMSCG, an online control procedure is presented to implement the supervision for TGMECs in a maximally permissive way.