Identification of labeled Time Petri nets

In a previous paper we presented an approach to identify a Time Petri net system, given a set of observed timed sequences. The set of transitions, which coincides with the set of events, is assumed to be known, while the net structure, the initial marking and the firing duration of transitions are computed in one stage solving a mixed-integer linear programming problem derived from a set of logical predicates. In this paper we extend this approach by allowing that two transitions may share the same event label. Then, the identified model is a labeled Time Petri net system. The identification problem can still be solved via a mixed-integer linear programming problem but the constraint set previously determined is modified.