Max-plus algebra and max-plus linear discrete event systems: An introduction

被引：17

作者：

De Schutter, Bart ^{[1
]}

van den Boom, Ton ^{[1
]}

机构：

[1] Delft Univ Technol, Delft Ctr Syst & Control, NL-2628 CD Delft, Netherlands

来源：

WODES' 08: PROCEEDINGS OF THE 9TH INTERNATIONAL WORKSHOP ON DISCRETE EVENT SYSTEMS | 2008年

关键词：

MODEL-PREDICTIVE CONTROL; PERFORMANCE EVALUATION; DYNAMIC-SYSTEMS; BEHAVIOR; GRAPHS;

D O I：

10.1109/WODES.2008.4605919

中图分类号：

TP3 [计算技术、计算机技术];

学科分类号：

0812 ;

摘要：

We provide an introduction to the max-plus algebra and explain how it can be used to model a specific class of discrete event systems with synchronization but no concurrency. Such systems are called max-plus linear discrete event systems because they can be described by a model that is "linear" in the max-plus algebra. We discuss some key properties of the max-plus algebra and indicate how these properties can be used to analyze the behavior of max-plus linear discrete event systems. We also briefly present some control approaches for max-plus linear discrete event systems, including model predictive control. Finally, we discuss some extensions of the max-plus algebra and of max-plus linear systems.

引用

页码：36 / 42

页数：7

共 50 条

[41] Stable Model Predictive Control for Constrained Max-Plus-Linear Systems
Ion Necoara
Bart De Schutter
Ton J. J. van den Boom
Hans Hellendoorn
Discrete Event Dynamic Systems, 2007, 17 : 329 - 354
[42] Stable model predictive control for constrained max-plus-linear systems
Necoara, Ion
De Schutter, Bart
van den Boom, Ton J. J.
Hellendoorn, Hans
DISCRETE EVENT DYNAMIC SYSTEMS-THEORY AND APPLICATIONS, 2007, 17 (03): : 329 - 354
[43] A model predictive control for max-plus-linear systems with interval parameters
Masuda, Shiro
2006 SICE-ICASE International Joint Conference, Vols 1-13, 2006, : 5458 - 5461
[44] An improved predictive control model for stochastic max-plus-linear systems
Qu, Jingguo
Zhang, Zilong
Zhang, Huiqi
CHAOS SOLITONS & FRACTALS, 2019, 128 : 210 - 218
[45] Modeling and control of switching max-plus-linear systems with random and deterministic switching
Ton J. J. van den Boom
Bart De Schutter
Discrete Event Dynamic Systems, 2012, 22 : 293 - 332
[46] Model predictive control for perturbed max-plus-linear systems: A stochastic approach
van den Boom, TJJ
De Schutter, B
PROCEEDINGS OF THE 40TH IEEE CONFERENCE ON DECISION AND CONTROL, VOLS 1-5, 2001, : 4535 - 4540
[47] Modeling and control of switching max-plus-linear systems with random and deterministic switching
van den Boom, Ton J. J.
De Schutter, Bart
DISCRETE EVENT DYNAMIC SYSTEMS-THEORY AND APPLICATIONS, 2012, 22 (03): : 293 - 332
[48] MPC for max-plus-linear systems: Closed-loop behavior and tuning
van den Boom, T
De Schutter, B
PROCEEDINGS OF THE 2001 AMERICAN CONTROL CONFERENCE, VOLS 1-6, 2001, : 325 - 330
[49] Modelling and temporal evaluation of networked control systems using timed automata with guards and (max, plus ) algebra
Tamssaouet, F.
Amari, S.
INTERNATIONAL JOURNAL OF SYSTEMS SCIENCE, 2018, 49 (10) : 2073 - 2088
[50] Stabilization of max-plus-linear systems using model predictive control: The unconstrained case
Necoara, Ion
van den Boom, Ton J. J.
De Schutter, Bart
Hellendoorn, Hans
AUTOMATICA, 2008, 44 (04) : 971 - 981

← 1 2 3 4 5 →