Control of Temporal Constraints Based on Dioid Algebra for Timed Event Graphs

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. As it is wellknown, this behavior can be modelled by a system of difference equations that are linear in the Min-Plus algebra (R ∪ {+∞}, min, plus). 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. Two sufficient conditions are given, in terms of initial tokens and delays along the graph. We give explicit formulas characterizing a control law, which, if the conditions are satisfied, ensures the validity of the temporal constraints. This control law is also defined as a linear system over the Min-Plus algebra. It is a causal state feedback, involving delays. The method is illustrated on a production system.