Optimal Petri net supervisor synthesis for forbidden state problems using marking mask.

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.