An algebraic method for multi-dimensional derivative estimation

Samer Riachy; Yara Bachalany; Mamadou Mboup; Jean-Pierre Richard

inria-00275461, version 1

An algebraic method for multi-dimensional derivative estimation

Samer Riachy ()^c^, 1, 2, Yara Bachalany ()^a^, 1, Mamadou Mboup ()^b^, 2, 3, 4, Jean-Pierre Richard^c^, 1, 2

MED'08, 16th IEEE Mediterranean Conference on Control and Automation (2008)

Résumé : This communication revisits the algebra-based results for derivative estimation presented by Fliess and coauthors in 2005. It is proposed, here, to consider multidimensional functions, namely scalar or vector fields of several variables. Such fields are locally represented by a vector Taylor series expansion, and a computation technique is presented so to put successive partial derivatives (for instance, the gradient, the Hessian matrix...) as functions of iterated integrals of the measured quantities.

a – Université des Sciences et Technologies de Lille - Lille I
b – Université René Descartes - Paris V
c – Ecole Centrale de Lille
1 : Laboratoire d'Automatique, Génie Informatique et Signal (LAGIS)
CNRS : UMR8146 – Université Lille I - Sciences et technologies – Ecole Centrale de Lille
2 : ALIEN (INRIA Saclay - Ile de France/Inria Lille - Nord Europe)
INRIA – Polytechnique - X – Ecole Centrale de Lille – CNRS : UMR8146
3 : Centre de Recherche en Informatique de Paris 5 (CRIP5)
Université Paris V - Paris Descartes
4 : UFR de Mathématiques et Informatique [Paris V]
Université Paris V - Paris Descartes

inria-00275461, version 1
http://hal.inria.fr/inria-00275461
oai:hal.inria.fr:inria-00275461
Contributeur : Jean-Pierre Richard <>
Soumis le : Mercredi 23 Avril 2008, 23:18:14
Dernière modification le : Mercredi 19 Septembre 2012, 22:00:45

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