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Tropical Abstractions of Max-Plus Linear Systems

TitleTropical Abstractions of Max-Plus Linear Systems
Publication TypeConference Paper
Year of Publication2018
AuthorsMufid MSyifa'ul, Adzkiya D, Abate A
Conference NameFormal Modeling and Analysis of Timed Systems
PublisherSpringer International Publishing
Conference LocationCham
ISBN Number978-3-030-00151-3
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.

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