Gradient-based controllers for continuous Petri nets

Dimitri Lefebvre (1) , Edouard Leclercq (1) , Fabrice Druaux (1) , Philippe Thomas (2)

1 GREAH - Groupe de Recherche en Electrotechnique et Automatique du Havre
2 CRAN - Centre de Recherche en Automatique de Nancy

This paper is about the control design of hybrid dynamical systems modelled with Petri nets. For this purpose, continuous Petri nets with variable speeds are investigated and described as piecewise bilinear linear state space representations. In this context, the marking vector is considered as a state space vector, subsets of places are defined as the model outputs, and the transitions are divided into non controllable ones and controllable ones that correspond to the model inputs. Gradient-based controllers are proposed and discussed in order to adapt the maximal firing frequencies of the controllable transitions according to desired trajectories of the output markings.

Mots clés: Petri net; learning; gradient

Domaines: Automatique / Robotique

Dimitri Lefebvre, Edouard Leclercq, Fabrice Druaux, Philippe Thomas. Gradient-based controllers for continuous Petri nets. 2012. ⟨hal-00569926⟩