Max-algebraic hybrid automata: Modelling and equivalences

TL;DR

This paper introduces max-algebraic hybrid automata, a new modeling framework that unifies and extends existing max-plus linear systems and automata, facilitating analysis and control of discrete-event systems.

Contribution

It formalizes max-algebraic hybrid automata, bridging automata theory and switching max-plus linear systems, and extends hybrid automata concepts to max-plus algebra.

Findings

Unifies max-plus automata and hybrid systems

Formalizes the relationship between automata and switching systems

Provides a foundation for analysis and control in max-plus algebra

Abstract

This article introduces the novel framework of max-algebraic hybrid automata as a hybrid modelling language in the max-plus algebra. We show that the modelling framework unifies and extends the switching max-plus linear systems framework and is analogous to the discrete hybrid automata framework in conventional algebra. In addition, we show that the framework serves as a bridge between automata-theoretic models in max-plus algebra and switching max-plus linear systems. In doing so, we formalise the relationship between max-plus automata and switching max-plus linear systems in a behavioural sense. This also serves as another step towards importing tools for analysis and optimal control from conventional time-driven hybrid systems to discrete-event systems in max-plus algebra.