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This article addresses the forbidden state problem in discrete-event systems (DESs) modeled with Petri nets. Given a control specification, we first decide the sets of forbidden and admissible markings. Then, the minimal mask set of first-met forbidden markings (FFMs) and the minimal root set of admissible markings are computed by marking mask that is implemented using a class of special places in a plant, called competitive places. Marking mask can effectively filtrate the markings to be processed such that the two obtained sets are in general much smaller than the sets of originally specified forbidden and admissible markings, respectively. Monitors computed by place invariants are used to forbid the forbidden markings. It is shown that a maximally permissive (optimal) supervisor can be computed if it exists. Integer linear programming is used to optimize the structure of a supervisor. The minimal mask set of FFMs and root set of admissible markings efficiently reduce the computational overhead because of much fewer constraints and variables in the formulated programming problem. The developed methodology is illustrated by parameterized examples. [ABSTRACT FROM AUTHOR]

Petri nets are a widely used tool to model, analyze and control discrete event systems that arise from automated production, intelligent transportation, and workflow management. For a class of Petri nets with uncontrollable transitions, this paper proposes a bottom-up algorithm to transform a given generalized mutual exclusion constraint into an optimal admissible one. Based on the transformation, a design method is proposed to synthesize an optimal supervisor. Compared with the existing methods that require the computation of exponential complexity, the proposed one can obtain an optimal supervisor with polynomial complexity. [ABSTRACT FROM AUTHOR]