Criteria stochastic filtering of max-plus discrete event systems with bounded random variables
Guilherme Espindola-Winck, Laurent Hardouin, Mehdi Lhommeau, Rafael Santos Mendes · IFAC-PapersOnLine · 2022
A wide range of Discrete Event Systems (DES) such as manufacturing systems, telecommunications networks, transportation networks, and parallel computing, etc., can be modelled as max-plus systems in which maximization and addition are the main operations. In this paper, we use a nonlinear approach to deal with the error-estimation of nondeterministic max-plus systems with bounded random variables. This estimation is carried out following the ideas of the stochastic filtering theory for classical time-driven dynamic systems. The probability densities for the entries of the system matrices are assumed to be known, and a prediction-correction filtering scheme is used to compute the estimated state. The filtering algorithm is based on the minimization of a criterion, which is capable to evaluate the estimation-error, and to deal with the trade-off between prediction and measurement.