Supervisory control of Petri nets using routing functions: Starvation avoidance issues

In this paper, we present a new point of view on supervisory control of Petri nets by using routing functions instead of the traditional control places. We first show the relation between the two notions. In the second part of the paper, we illustrate the use of routing functions by showing how to compute a renting function in order to avoid starvation in general Petri nets. This control uses a continuous version of the net and a description of the evolution of the net under the form of linear algebraic equations, As for the computational part, we use algebraic polynomial geometry in the continuous case and Diophantine equations for the discrete version of the Petri net under study.