Net Transformation and Theory of Regions for Optimal Supervisory Control of Petri Nets

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 controlplace-based solution does not always exist. In the present paper, we propose a new approach for designing optimal controller for ordinary 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-placebased solutions, the control problem of the transformed mo del is optimally solved using our previous result. Besides, by assigning a priority to transitions of the transformed model, the complexity is considerably reduced.