Event-driven optimal control of continuous Petri nets

Optimally controlling a hybrid system is a challenging problem for which mainly continuous-time and discrete-time methods have been suggested. In this paper, the problem of optimal control is addressed in the framework of continuous Petri nets, a kind of hybrid systems whose state evolution is piecewise linear. The proposed approach consists of transforming the continuous Petri net into an equivalent hybrid system whose evolution is described by means of discrete-event steps. In particular, each step coincides with the occurrence of an event in the continuous Petri net. Thus, the number of steps required to know the behavior of the Petri net is minimum, while the accuracy is completely preserved. It is shown how to design a mixed integer linear programming problem in order to compute the optimal control solution of different performance criteria.