State Estimation of Max-Plus Linear Discrete Event Systems

The work developed in this paper contributes to the study of state reconstruction method for Max-Plus linear discrete event systems. In many systems, directly measurable states often do not provide all the information needed to fully describe the system’s behavior. This limitation raises the challenge of state reconstruction, which can be addressed through the use of a state estimator. Among the various observers employed in classical systems, the Luenberger observer is considered as one of the most widely used due to its simplicity and effectiveness. In this paper, we propose adapting and applying the Luenberger observer to Max-Plus linear discrete event systems. We provide necessary and sufficient conditions for the existence of this observer. Illustrative example is given in order to illustrate the capacity of the proposed method.