Linear and Integer Programmes in Supervisory Control of Petri Nets

Constructing supervisors for Petri nets of which the uncontrollable part is acyclic can be done by solving linear integer programme. In this paper, we construct a closed-form solution of the corresponding linear programme and provide in this way a lower bound of the supremal controllable subset of the legal set. Further, we show that in a lot of cases this technique can be used to construct a closed-form solution of the original linear integer programme. We recover existing results in supervisory control and show how to treat a class of acyclic nets containing both choice places and a synchronising transition.