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

James Hook

doi:10.1016/j.laa.2019.05.024

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

James Hook

Department of Mathematical Sciences

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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.

Original language	English
Pages (from-to)	1-31
Number of pages	31
Journal	Linear Algebra and its Applications
Volume	579
Early online date	29 May 2019
DOIs	https://doi.org/10.1016/j.laa.2019.05.024
Publication status	Published - 15 Oct 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

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10.1016/j.laa.2019.05.024

Max_plus_2_Reg_JLHAccepted author manuscript, 499 KBLicence: CC BY-NC-ND

Cite this

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AB - 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.

KW - Inverse problem

KW - Max-plus algebra

KW - System identification

KW - Tropical algebra

UR - https://www.scopus.com/pages/publications/85066280034

U2 - 10.1016/j.laa.2019.05.024

DO - 10.1016/j.laa.2019.05.024

M3 - Article

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JO - Linear Algebra and its Applications

JF - Linear Algebra and its Applications

ER -

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

Abstract

Keywords

ASJC Scopus subject areas

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