NET TRANSFORMATION AND THEORY OF REGIONS FOR OPTIMAL SUPERVISORY CONTROL OF PETRI NETS
Asma Ghaffari, Nidhal Rezg and Xiaolan Xie
INRIA and LGIPM, ISGMP-ILE DU SAULCY 57045 METZ CEDEX, FRANCE

In a previous work, we applied the theory of regions to design optimal Petri net controller by adding so-called control places to the plant Petri net model with uncontrolable transitions and forbidden states. Unfortunately, such a simple control-place-based solution does not always exist. In the present paper, we propose a new approach for designing optimal controller for bounded Petri nets using control places. The key idea consists in transforming the plant Petri net model, for which a control-place-based solution was not found, into a safe Petri net. Then, exploiting the result stating that forbidden state problems of safe Petri nets always have control-place-based solutions, the control problem of the transformed model is optimally solved using our previous result. An aggregated reachability graph of the transformed net having the same number of markings as the original model is defined for designing control places using the theory of regions. Further, there is no need to generate again all states of the transformed net. The aggregated reachability graph can be derived from the reachability graph of the original model. As a result, optimal controller design of the transformed net has the same complexity as the optimal controller design of the original bounded Petri net.
Keywords: Discrete event systems, Petri nets, Supervisory control, Manufacturing systems, Optimal control
Session slot T-Mo-A07: Petri Nets Modelling, Analysis and Synthesis of Manufact/Area code 3c : Discrete Event Dynamic Systems

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