Max-plus linear inverse problems: 2-norm regression and system identification of max-plus linear dynamical systems with Gaussian noise

Research output: Contribution to journalArticle

Abstract

In this paper we present new theory and algorithms for 2-norm regression over the max-plus semiring. As an application we also show how max-plus 2-norm regression can be used in system identification of max-plus linear dynamical systems with Gaussian noise. We also introduce and provide methods for solving a max-plus linear inverse problem with regularization, which can be used when the original problem is not well posed.

LanguageEnglish
Pages1-31
Number of pages31
JournalLinear Algebra and its Applications
Volume579
Early online date29 May 2019
DOIs
StatusE-pub ahead of print - 29 May 2019

Keywords

  • Inverse problem
  • Max-plus algebra
  • System identification
  • Tropical algebra

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Numerical Analysis
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics

Cite this

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title = "Max-plus linear inverse problems: 2-norm regression and system identification of max-plus linear dynamical systems with Gaussian noise",
abstract = "In this paper we present new theory and algorithms for 2-norm regression over the max-plus semiring. As an application we also show how max-plus 2-norm regression can be used in system identification of max-plus linear dynamical systems with Gaussian noise. We also introduce and provide methods for solving a max-plus linear inverse problem with regularization, which can be used when the original problem is not well posed.",
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