SUFFICIENT CONDITION OF MAX-PLUS ELLIPSOIDAL INVARIANT SET AND COMPUTATION OF FEEDBACK CONTROL OF DISCRETE EVENT SYSTEMS

Mourad Ahmane, Laurent Truffet

2006

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.

Paper Citation

in Harvard Style

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 3: ICINCO, ISBN 978-972-8865-61-0, pages 99-106. DOI: 10.5220/0001219600990106

in Bibtex Style

@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 3: ICINCO,},
year={2006},
pages={99-106},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0001219600990106},
isbn={978-972-8865-61-0},
}

in EndNote Style

TY - CONF
JO - Proceedings of the Third International Conference on Informatics in Control, Automation and Robotics - Volume 3: 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
AU - Ahmane M.
AU - Truffet L.
PY - 2006
SP - 99
EP - 106
DO - 10.5220/0001219600990106