30/11/2018

Closed-loop continuous-time model identification with noisy input-output

Stéphane VICTOR, Arnold DIUDICHI,Pierre MELCHIOR

 IMS- UMR 5218 — Université de Bordeaux

Abstract: In this paper, system identification is proposed for closed-loop systems in input/output noisy context. Although instrumental variable techniques exist in the literature, the proposed filtering in input/ouput noisy context is not optimal. Also, three algorithms are proposed, and the closed-loop simplified refined instrumental variable for continuous-time system gives optimal results: estimates are consistent and with minimum variance. The main contributions relies on the filtering of the instruments and signals considered.

 

LTI and LPV gray-box state-space model identification: to $H_\infty$-norm and beyond

Guillaume Mercère (Poitiers University, Poitiers, France), Daniel Vizer (University of Technology and Economics of Budapest, Budapest, Hungary), Olivier Prot (Limoges University, Limoges, France), Edouard Laroche (Strasbourg University, Strasbourg, France)

Abstract: Estimating consistent parameters of a structured gray-box state-space representation is still a difficult task in system identification even when LTI models are handled. While many solutions are now available in the literature to determine the order as well as the matrices of a black-box LTI state-space model, it is well-known that the estimated (fully-parameterized) state-space matrices are unique modulo a non-singular similarity transformation matrix. This property could have serious consequences if the system being identified is a real physical system. Indeed, if the true model contains physical parameters, then the identified system could no longer have the physical parameters in a form that can be extracted easily. By assuming that the system has been identified consistently in a fully-parameterized form, the question addressed in this presentation then is how to recover the physical parameters from this initially estimated black-box form. A specific attention is paid to solutions resorting to recent developments dedicated to the optimization of $H_\infty$-norm-based cost functions. These (new) developments are introduced for LTI state-space models, then extended to LPV state-space representations, with a specific attention to the local approach.

 

Nonlinear System Identification with Kernels: Applications of Derivatives in the RKHS.

Yusuf Bhujwalla.
CRAN - Université de Lorraine


Abstract: Many physical properties can be expressed in terms of functional derivatives - such as linearity, separability, oscillation and many more besides. This presentation looks at how derivative properties can be incorporated into the estimation of nonlinear models, and what such an approach might offer. The methods presented formulate constraints as regularization terms on a nonparametric kernel-based model. This offers both a manner of control which is distinct from that which can be obtained through the kernel, and control over properties which cannot otherwise be controlled through the kernel function. This presentation will show how such constraints can be formulated and give several simulation examples, to illustrate the scope of the methods. Keywords: nonlinear system identification, nonparametric methods, kernel methods, regularization, RKHS, derivatives in the RKHS.

 

Local stability analysis of microwave circuits

Adam Cooman, Fabien Seyfert, Martine Olivi, Sylvain Chevillard and Laurent Baratchart.
All authors are with INRIA, Sophia Antipolis
 

Frequency domain simulation methods have become very popular in modern simulators for RF and microwave electronic circuits. These methods, like Har- monic Balance or DC, constrain the frequency grid of the circuit solution. This constraint can lead the simulator to find unstable solutions of the electronic circuit’s differential equations. A stability analysis is therefore required once the solution has been found.

To test the stability of these steady-state solutions, the circuit is linearised around the solution and several non-parametric frequency response functions of the linearised circuit are determined. The stability analysis therefore boils down to determining whether a given non-parametric frequency response of a linear system is stable or not. Microwave circuits contain distributed elements (transmission lines), which causes the frequency responses to be non-rational.

Our approach to analyse the stability of a frequency response (∈ L2) is to split it into a stable and unstable part. The stable part is a function in the Hardy space H2 while the unstable part lies in its orthogonal complement H2 = L2 ⊖ H2 . The stable and unstable parts are obtained by projecting the frequency response onto the bases of H2 and H2 respectively. With this non-parametric approach, we can easily determine whether a given frequency response has poles in the right half-plane or not.

In this presentation, we will discuss the details and limitations of this func- tional approach. We will also explain how the unstable poles in the circuit can be estimated once the unstable part of the frequency response is obtained. 

 


Caractérisation de cellules électrochimiques à partir de modèles fractionnaires

Achraf Nasser Eddine, Benoît Huard, Jean-Denis Gabano, Thierry Poinot
Laboratoire d'Informatique et d'Automatique pour les Systèmes - Université de Poitiers


Une cellule électrochimique peut être représentée par un circuit électrique équivalent composé de 3 éléments : la résistance de l’électrolyte et de connectique, le transfert de charge et la diffusion. La modélisation des cellules électrochimiques est un moyen utilisé pour évaluer précisément les caractéristiques internes de celles-ci, permettant ainsi la détermination des états de charge et de santé. Deux types de mesures sont utilisés pour trouver le modèle d’impédance de cellules électrochimiques : la spectroscopie (dans le domaine fréquentiel) et la chronopotentiométrie (dans le domaine temporel). L’avantage principal de la spectroscopie réside dans la précision de sa modélisation, puisqu’elle représente séparément chaque partie de l’impédance interne de la cellule électrochimique. Par contre, l’inconvénient principal de cette modélisation fréquentielle est qu’elle nécessite un temps important pour représenter la partie de diffusion agissant en basse fréquence.
L’objectif de cette présentation est de déterminer une procédure d’identification, dans le domaine temporel, capable de retrouver le modèle de l’impédance interne des cellules électrochimiques préalablement identifié dans le domaine fréquentiel. Ce modèle est basé sur des systèmes fractionnaires et il est validé expérimentalement sur un système électrochimique de type Ferri/Ferro.