Compact supervisors for general constraint enforcement in Petri net models with uncontrollable transitions

Petri net (PN) models of production processes are subject to a number of heterogeneous constraints, both static (e.g., limitation and sharing of resources, job limitation) and behavioral (e.g., liveness, reversibility). All of these constraints can be indirectly formulated as generalized mutual exclusion constraints (GMECs), which are conveniently implemented as monitor places suitably connected to the transitions of the open-loop PN plant model. The design procedure is typically sequential, dealing separately with each control objective, possibly resulting in a redundant supervisor. The process is further complicated in the presence of uncontrollable transitions. An integrated modeling approach is here proposed to solve the redundancy problem by accounting for all the specifications in a single design step that optimizes the number of required GMECs and the permissivity of the resulting supervisor. The supervisor can be then implemented as a monitor-based supervisor or, in some cases, as a logical predicate.