Méthode formelle de commande sous contraintes de temps dans les dioïdes

Abstract

We consider a class of controlled timed event graphs subject to strict temporal constraints. Such a graph is deterministic, in the sense that its behavior only depends on the initial marking and on the control that is applied. This behavior can be modelled by a system of difference equations that are linear in the Min-Plus algebra. The temporal constraint is represented by an inequation that is also linear in the Min-Plus algebra. Then, a method for the synthesis of a control law ensuring the respect of the constraint is described. We give explicit formulas characterizing a control law, which, if two conditions are satisfied, ensures the validity of the temporal constraints. It is a causal state feedback, involving delays. The method is illustrated on a real example of a production system.