Methods and applications of max-plus algebras

Abstract

Exotic algebras such as the max-plus semiring, or the tropical semirings, have been invented many times in various fields: discrete event system theory, communication networks as well as timing analysis of digital circuits. Despite this apparent profusion, there is a set of common basic results and problems, which seems to be useful in most applications. In recent research the relevancy of discrete event systems (DES) steadily increases, In order to handle DES the introduction of a DES-system theory is useful. This article outlines the DES-system theory and shows an algorithm for an efficient calculation of the optimal control in dioids.