Admissible initial conditions and control of timed event graphs

Processes modelized by timed event graphs like automated production lines, can be represented by a linear system over the dioid (min, plus). We define and characterize the set of admissible initial conditions which give rise to nondecreasing solutions. These solutions coincide with the possible evolution of the associated event graph. These initial conditions are used to determine whether or not a given output trajectory can be achieved by the graph. The optimal input which leads to the best approximation of the output is computed.