Title :

Towards an effective study of the algebraic parameter estimation problem

Author(s) :

Quadrat, Alban [Auteur]
Non-Asymptotic estimation for online systems [NON-A]

Conference title :

IFAC 2017 Workshop Congress

City :

Toulouse

Country :

France

Start date of the conference :

2017-07-10

English keyword(s) :

orthogonal polynomials
annihilators
symbolic computation
algebraic systems theory
Parameter estimation problem
expansion into a basis
ring of differential operators

HAL domain(s) :

Mathématiques [math]/Optimisation et contrôle [math.OC]
Mathématiques [math]/Anneaux et algèbres [math.RA]
Mathématiques [math]/Algèbres d'opérateurs [math.OA]
Informatique [cs]/Calcul formel [cs.SC]

English abstract : [en]

The paper aims at developing the first steps toward a symbolic computation approach to the algebraic parameter estimation problem defined by Fliess and Sira-Ramirez and their coauthors. In this paper, within the algebraic ...
Show more >The paper aims at developing the first steps toward a symbolic computation approach to the algebraic parameter estimation problem defined by Fliess and Sira-Ramirez and their coauthors. In this paper, within the algebraic analysis approach, we first give a general formulation of the algebraic parameter estimation for signals which are defined by ordinary differential equations with polynomial coefficients such as the standard orthogonal polynomials (Chebyshev, Jacobi, Legendre, Laguerre, Hermite, ... polynomials). Based on a result on holonomic functions, we show that the algebraic parameter estimation problem for a truncated expansion of a function into an orthogonal basis of L_2 defined by orthogonal polynomials can be studied similarly. Then, using symbolic computation methods such as Gröbner basis techniques for (noncommutative) polynomial rings, we first show how to compute ordinary differential operators which annihilate a given polynomial and which contain only certain parameters in their coefficients. Then, we explain how to compute the intersection of the annihilator ideals of two polynomials and characterize the ordinary differential operators which annihilate a first polynomial but not a second one. These results, which are at the core of the algebraic parameter estimation, are implemented in the Non-A package built upon the OreModules software.Show less >

Language :

Anglais

Peer reviewed article :

Oui

Audience :

Internationale

Popular science :

Non

Collections :

• Centre de Recherche en Informatique, Signal et Automatique de Lille (CRIStAL) - UMR 9189

Source :

Harvested from HAL