Introduction to max-plus algebra

This tutorial will focus on the basics of max-plus algebra along with relevant topics. Max-plus algebra is a discrete algebraic system in which the max and plus operations are defined as addition and multiplication in conventional algebra. Using this system, the behavior of a class of discrete event systems can be represented by simple linear equations, by which modeling, analysis, and control of the systems can be realized. We will start with a simple project scheduling problem to understand the basic usage of max-plus algebra. The focus will then be oriented to its detailed definition and observe relevant properties in terms of graph theory, net theory, and so on. In the latter part, we will move on to modeling and formulation methods in control theory viewpoint. Several application examples as schedule solvers will be introduced, followed by several recent advances achieved by the presenter.