Tropical Abstractions of Max-Plus-Linear Systems

TL;DR

This paper introduces a method for creating finite abstractions of Max-Plus-Linear systems using tropical algebra, enabling finite-state models for discrete-event systems with improved computational techniques.

Contribution

It presents a novel tropical algebra-based approach to abstract MPL systems into finite-state transition systems, with algorithms and performance analysis.

Findings

Algorithms based on tropical algebra are effective for finite abstraction.

Performance benchmarks show advantages over existing methods.

Finite abstractions facilitate analysis of MPL systems.

Abstract

This paper describes the development of finite abstractions of Max-Plus-Linear (MPL) systems using tropical operations. The idea of tropical abstraction is inspired by the fact that an MPL system is a discrete-event model updating its state with operations in the tropical algebra. The abstract model is a finite-state transition system: we show that the abstract states can be generated by operations on the tropical algebra, and that the generation of transitions can be established by tropical multiplications of matrices. The complexity of the algorithms based on tropical algebra is discussed and their performance is tested on a numerical benchmark against an existing alternative abstraction approach.