Gradient-based controllers for timed 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 control design for timed continuous Petri nets that are described as piecewise affine systems. In this context, the marking vector is considered as the state space vector, weighted marking of place subsets are defined as the model outputs and the model inputs correspond to multiplicative control actions that slow down the firing rate of some controllable transitions. Structural and functional sensitivity of the outputs with respect to the inputs are discussed in terms of Petri nets. Then, gradient-based controllers (GBC) are developed in order to adapt the control actions of the controllable transitions according to desired trajectories of the outputs.

Mots clés: machine learning; Petri nets; hybrid systems; discrete event systems

Domaines: Automatique / Robotique

Dimitri Lefebvre, Edouard Leclercq, Fabrice Druaux, Philippe Thomas. Gradient-based controllers for timed continuous Petri nets. International Journal of Systems Science, 2015, 46 (9), pp.1661-1678. ⟨10.1080/00207721.2013.827264⟩. ⟨hal-00853970⟩