A multiobjective formulation for Just-in-Time control of constrained Max-Plus Linear Systems in infinite horizon

Some Timed Discrete Event Systems (TDES) can be modeled by Timed Event Graph (TEG) and consequently described by Max-Plus algebra as state space equation. This paper present a multiobjective dynamic optimization problem with constraints in order to perform the Just-in-Time control in infinite horizon. These constraints are applied on the inputs trasitions firing dynamic and on the state transitions firing dynamic by a semimodule equation and by a model reference to the system. To find the optimal (greatest) solution to the input dates, we use the Residuation Theory and the Theory of Semimodules. With the methodology presented in this work, it is possible to determine the maximum firing date to each state transitions and each input transition. Two numeric examples are presented to demonstrate the control applicability.