The set of realizations of a max-plus linear sequence is semi-polyhedral

被引：1

作者：

Blondel, Vincent ^{[2
]}

Gaubert, Stephane ^{[3
,4
]}

Portier, Natacha ^{[1
,5
]}

机构：

[1] Univ Lyon, LIP, Ecole Normale Super Lyon, CNRS,UCBL,INRIA,ENS Lyon,UMR 5668, F-69364 Lyon 07, France

[2] Catholic Univ Louvain, Dept Ingn Math, Large Graphs & Networks, B-1348 Louvain, Belgium

[3] Ecole Polytech, CMAP, F-91128 Palaiseau, France

[4] Ecole Polytech, INRIA, F-91128 Palaiseau, France

[5] Univ Toronto, Dept Comp Sci, Toronto, ON M5S 1A1, Canada

来源：

JOURNAL OF COMPUTER AND SYSTEM SCIENCES | 2011年 / 77卷 / 04期

关键词：

Max-plus algebra; Minimal realization; Discrete event systems; Semi-polyhedral set; Formal series; Semiring; DISCRETE-EVENT SYSTEMS; PERFORMANCE EVALUATION; DYNAMIC-SYSTEMS; GEOMETRY;

D O I：

10.1016/j.jcss.2010.08.010

中图分类号：

TP3 [计算技术、计算机技术];

学科分类号：

0812 ;

摘要：

We show that the set of realizations of a given dimension of a max-plus linear sequence is a finite union of polyhedral sets, which can be computed from any realization of the sequence. This yields an (expensive) algorithm to solve the max-plus minimal realization problem. These results are derived from general facts on rational expressions over idempotent commutative semirings: we show more generally that the set of values of the coefficients of a commutative rational expression in one letter that yield a given max-plus linear sequence is a finite union of polyhedral sets. (C) 2010 Elsevier Inc. All rights reserved.

引用

页码：820 / 833

页数：14

共 50 条

[21] Soluble approximation of linear systems in max-plus algebra
Cechlárová, K
Cuninghame-Green, RA
KYBERNETIKA, 2003, 39 (02) : 137 - 141
[22] Solutions of max-plus linear equations and large deviations
Akian, Marianne
Gaubert, Stephane
Kolokoltsov, Vassili
2005 44th IEEE Conference on Decision and Control & European Control Conference, Vols 1-8, 2005, : 7787 - 7792
[23] On the Control of Max-plus Linear System in Dioid of Interval
Zhang Yanan
Zhang Zilong
Tao Yuegang
2014 33RD CHINESE CONTROL CONFERENCE (CCC), 2014, : 4148 - 4152
[24] SYSTEMS OF FUZZY NUMBER MAX-PLUS LINEAR EQUATIONS
Rudhito, M.
Wahyuni, Sri
Suparwanto, Ari
Susilo, Frans
JOURNAL OF THE INDONESIAN MATHEMATICAL SOCIETY, 2011, 17 (01) : 17 - 28
[25] MAX-PLUS LINEAR SYSTEMS AT BUS LINE SYNCHRONIZATION
Pesko, Stefan
Turek, Richard
PROCEEDINGS OF THE INTERNATIONAL CONFERENCE QUANTITATIVE METHODS IN ECONOMICS (MULTIPLE CRITERIA DECISION MAKING XVI), 2012, : 180 - 185
[26] Soluble approximation of linear systems in max-plus algebra
Cechlárová, K
Cuninghame-Green, RA
SYSTEM STRUCTURE AND CONTROL 2001, VOLS 1 AND 2, 2001, : 809 - 811
[27] New transience bounds for max-plus linear systems
Charron-Bost, Bernadette
Fugger, Matthias
Nowak, Thomas
DISCRETE APPLIED MATHEMATICS, 2017, 219 : 83 - 99
[28] Reachability and observability of linear systems over max-plus
Gazarik, MJ
Kamen, EW
KYBERNETIKA, 1999, 35 (01) : 2 - 12
[29] Comparing Disjunctive and Concise Approaches for Set-Guaranteed Estimation in Max-Plus Linear Systems
Espindola-Winck, Guilherme
Hardouin, Laurent
Lhommeau, Mehdi
IFAC PAPERSONLINE, 2024, 58 (01): : 36 - 41
[30] Reinforcement Learning for Stochastic Max-Plus Linear Systems
Subramanian, Vignesh
Farhadi, Farzaneh
Soudjani, Sadegh
2023 62ND IEEE CONFERENCE ON DECISION AND CONTROL, CDC, 2023, : 5631 - 5638

← 1 2 3 4 5 →