The aim of the presented work is the control of Timed Event Graph to meet tight temporal constraints. The problem of temporal constraints is formulated in terms of control of linear Max-Plus models. First, the synthesis of a control law that ensures the satisfaction of a single constraint for a single input system is presented. Then, the single input multi-constraints problem is tackled and finally, the method is extended to the multi-inputs, multi-constraints problem. The proposed method is illustrated on the example of a simple production process.

We extend the notions of conditioned and controlled invariant spaces to linear dynamical systems over the max-plus or tropical semiring. We establish a duality theorem relating both notions, which we use to construct dynamic observers. These are useful in situations in which some of the system coefficients may vary within certain intervals. The results are illustrated by an application to a manufacturing system.