Titre :

Characterization of " low-pass filtering " for some nonlinear ODE's

Auteur(s) :

Riachy, Samer [Auteur]
Laboratoire QUARTZ [QUARTZ ]
Non-Asymptotic estimation for online systems [NON-A]

Titre de la manifestation scientifique :

IFAC WC 2017

Ville :

Toulouse

Pays :

France

Date de début de la manifestation scientifique :

2017-07-10

Mot(s)-clé(s) en anglais :

Big magnitude noise
Characterization of " low-pass filtering " for nonlinear systems
transport equation

Discipline(s) HAL :

Mathématiques [math]/Optimisation et contrôle [math.OC]

Résumé en anglais : [en]

The characterization of low-pass linear filters is nowadays a simple question relying on eigenvalue criteria, Bode diagram, Nyquist or Nichols plots. For nonlinear systems, the problem is more tricky. The present work ...
Lire la suite >The characterization of low-pass linear filters is nowadays a simple question relying on eigenvalue criteria, Bode diagram, Nyquist or Nichols plots. For nonlinear systems, the problem is more tricky. The present work tempts to develop a methodology for the characterization of " low-pass filtering " for nonlinear systems. Inspired by the DiPerna-Lions theory and relying on the theory of characteristics, the proposed method associates to the nonlinear ODE a linear transport PDE. A characterization of " low-pass filtering " is then deduced from developments on the PDE. Smooth ODE's of the form \dot{x} = F (x) are considered where the vector field F (x) is perturbed by an additive, rapidly oscillating, noise m which may have a big magnitude F (x + m). An intuitive observation is proved in this first contribution: if F has bounded derivatives, then the sensitivity of x to m decreases as the bound gets smaller or as m fluctuates faster.Lire moins >

Langue :

Anglais

Comité de lecture :

Oui

Audience :

Internationale

Vulgarisation :

Non

Collections :

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

Source :

Harvested from HAL