Compact Supervisory Control of Discrete Event Systems by Petri Nets With Data Inhibitor Arcs

This work proposes a novel structure in Petri nets, namely data inhibitor arcs, and their application to the optimal supervisory control of Petri nets. A data inhibitor arc is an arc from a place to a transition labeled with a set of integers. A transition is disabled by a data inhibitor arc if the number of tokens in the place is in the set of integers labeled on it. Its formal definitions and properties are given. Then, we propose a method to design an optimal Petri net supervisor with data inhibitor arcs to prevent a system from reaching illegal markings with respect to control specifications. Two techniques are developed to reduce the supervisor structure by compressing the number of control places. Finally, a number of examples are used to illustrate the proposed approaches and experimental results show that they can obtain optimal Petri net supervisors for the net models that cannot be optimally controlled by pure net supervisors. A significant result is that the proposed approach can always lead to an optimal supervisor with only one control place for bounded Petri nets on the premise that such a supervisor exists.