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Authors: Mourad Ahmane and Laurent Truffet

Affiliation: Institut de Recherche en Communications et Cybernétique de Nantes, IRCCyN, UMR-CNRS 6597, École Centrale Nantes; École des Mines de Nantes, France

Keyword(s): Max-plus algebra, geometric approach, set invariance, residuation.

Related Ontology Subjects/Areas/Topics: Discrete Event Systems ; Informatics in Control, Automation and Robotics ; Signal Processing, Sensors, Systems Modeling and Control

Abstract: Haar’s Lemma (1918) provides the algebraic characterization of the inclusion of polyhedral sets. This Lemma has been involved many times in automatic control of linear dynamical systems when the constraint domains (state and/or control) are polyhedrons. More recently, this Lemma has been used to characterize stochastic comparison w.r.t linear orderings of Markov chains with different state spaces. Stochastic comparison is involved in the simplification of complex stochastic systems in order to control the approximation error made. In this paper we study the positive invariance of a max-plus ellipsoid by a max-plus linear dynamical system. We remark that positive invariance of max-plus ellipsoid is a particular case of polyhedron inclusion and we use Haar’s Lemma to derive sufficient condition for the positive invariance. As an application we propose a method to compute a static state feedback control.

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Paper citation in several formats:
Ahmane, M. and Truffet, L. (2006). SUFFICIENT CONDITION OF MAX-PLUS ELLIPSOIDAL INVARIANT SET AND COMPUTATION OF FEEDBACK CONTROL OF DISCRETE EVENT SYSTEMS. In Proceedings of the Third International Conference on Informatics in Control, Automation and Robotics - Volume 2: ICINCO; ISBN 978-972-8865-61-0; ISSN 2184-2809, SciTePress, pages 99-106. DOI: 10.5220/0001219600990106

@conference{icinco06,
author={Mourad Ahmane. and Laurent Truffet.},
title={SUFFICIENT CONDITION OF MAX-PLUS ELLIPSOIDAL INVARIANT SET AND COMPUTATION OF FEEDBACK CONTROL OF DISCRETE EVENT SYSTEMS},
booktitle={Proceedings of the Third International Conference on Informatics in Control, Automation and Robotics - Volume 2: ICINCO},
year={2006},
pages={99-106},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0001219600990106},
isbn={978-972-8865-61-0},
issn={2184-2809},
}

TY - CONF

JO - Proceedings of the Third International Conference on Informatics in Control, Automation and Robotics - Volume 2: ICINCO
TI - SUFFICIENT CONDITION OF MAX-PLUS ELLIPSOIDAL INVARIANT SET AND COMPUTATION OF FEEDBACK CONTROL OF DISCRETE EVENT SYSTEMS
SN - 978-972-8865-61-0
IS - 2184-2809
AU - Ahmane, M.
AU - Truffet, L.
PY - 2006
SP - 99
EP - 106
DO - 10.5220/0001219600990106
PB - SciTePress

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