Duality between invariant spaces for max-plus linear discrete event systems

TL;DR

This paper extends the concepts of invariant spaces to max-plus linear systems, establishing a duality theorem and constructing dynamic observers, with applications in manufacturing systems.

Contribution

It introduces a duality theorem linking conditioned and controlled invariant spaces in max-plus systems and develops dynamic observers for systems with interval-varying coefficients.

Findings

Established a duality theorem for invariant spaces in max-plus systems

Constructed dynamic observers for systems with uncertain coefficients

Demonstrated the approach with a manufacturing system example

Abstract

We extend the notions of conditioned and controlled invariant spaces to linear dynamical systems over the max-plus or tropical semiring. We establish a duality theorem relating both notions, which we use to construct dynamic observers. These are useful in situations in which some of the system coefficients may vary within certain intervals. The results are illustrated by an application to a manufacturing system.