Didier Maquin

Blind source separation, wavelet denoising and discriminant analysis for EEG artefacts and noise cancelling

Abstract This paper proposes an automatic method for artefact removal and noise elimination from scalp electroencephalogram recordings (EEG). The method is based on blind source separation (BSS) and supervised classification and proposes a combination of classical and news features and classes to improve artefact elimination (ocular, high frequency muscle and ECG artefacts). The role of a supplementary step of wavelet denoising (WD) is explored and the interactions between BSS, denoising and classification are analyzed. The results are validated on simulated signals by quantitative evaluation criteria and on real EEG by medical expertise. The proposed methodology successfully rejected a good percentage of artefacts and noise, while preserving almost all the cerebral activity. The “denoised artefact-free” EEG presents a very good improvement compared with recorded raw EEG: 96% of the EEGs are easier to interpret.

State and unknown input estimation for discrete time multiple model

This paper deals with the state estimation of nonlinear discrete systems described by a multiple model with unknown inputs. The main goal concerns the simultaneous estimation of the systems state and the unknown inputs. This goal is achieved through the design of a multiple observer based on the elimination of the unknown inputs. It is shown that the observer gains are solutions of a set of linear matrix inequalities. After that, an unknown input estimation method is proposed. An academic example and an application dealing with message decoding illustrate the effectiveness of the proposed multiple observer.

Simultaneous state and unknown inputs estimation with PI and PMI observers for Takagi Sugeno model with unmeasurable premise variables

In this paper, a proportional integral (PI) and a proportional multiple integral observer (PMI) are proposed in order to estimate the state and the unknown inputs of nonlinear systems described by a Takagi-Sugeno model with unmeasurable premise variables. This work is an extension to nonlinear systems of the PI and PMI observers developed for linear systems. The state estimation error is written as a perturbed system. First, the convergence conditions of the state estimation errors between the system and each observer are given in LMI (Linear Matrix Inequality) formulation. Secondly, a comparison between the two observers is made through an academic example.

Design of sliding mode unknown input observer for uncertain Takagi-Sugeno model

This paper addresses the analysis and design of a sliding mode observer on the basis of a Takagi-Sugeno (T-S) model subject both to unknown inputs and uncertainties. The main contribution of the paper is the development of a robust observer with respect to the uncertainties as well as the synthesis of sufficient stability conditions of this observer. The stabilization of the observer is performed by the search of suitable Lyapunov matrices. It is shown how to determine the gains of the local observers, these gains being solutions of a set of linear matrix inequalities (LMI). The validity of the proposed methodology is illustrated by an academic example.

State estimation of uncertain multiple model with unknown inputs

This paper is dedicated to the synthesis of a sliding mode multiple observer. The considered systems are represented by an uncertain (nonlinear) multiple model with unknown inputs. Stability conditions of such observers are expressed in terms of linear matrix inequalities (LMI). An example of simulation is given to illustrate the proposed method.

Sliding mode multiple observer for fault detection and isolation

This paper deals with the design of a sliding mode multiple observer (an observer based on a multiple model) allowing to estimate the state vector of a nonlinear dynamical system. This latter is influenced by unknown inputs which act on it through a known transmission matrix. The state estimation and consequently the output estimation can therefore be classically used for detecting and isolating faults.

State estimation for non-linear systems using a decoupled multiple model

The multiple model approach is an elegant and a powerful tool for modelling real-world complex processes. In this modelling framework, a judicious combination of a set of submodels makes it possible to describe the behaviour of a non-linear system. Two different structures of multiple models can be distinguished according to whether the submodels share a common state vector (Takagi-Sugeno multiple model) or not (decoupled multiple model). This latter structure is an interesting alternative to the popular Takagi-Sugeno multiple model because different dimensions of submodels can be considered. The decoupled multiple model is nowadays increasingly used to perform the identification and the control of non-linear systems. However, to our knowledge, the state estimation problem of non-linear systems represented by this structure is not thoroughly investigated. The present paper deals with this worthwhile problem.

Fault detection and isolation using sliding mode observer for uncertain Takagi-Sugeno fuzzy model

This paper addresses fault detection and isolation (FDI) problem using a sliding mode fuzzy observer on the basis of a uncertain Takagi-Sugeno (T-S) fuzzy model. First, a robust fuzzy observer with respect to the uncertainties is designed. The convergence of the fuzzy observer is performed by the search of suitable Lyapunov matrices. It is shown how to synthesis observers using a set of linear matrix inequalities (LMI) conditions. Once the fuzzy observer is designed, FDI problem for nonlinear systems described by T-S fuzzy systems using the fuzzy observer is presented. A bank of fuzzy observer is then designed in order to investigate fault diagnosis problems. The validity of the proposed methodology is illustrated on a dynamic vehicle model.

Design of observers for Takagi-Sugeno systems with immeasurable premise variables : an L2 approach

A new observer design method is proposed for Takagi-Sugeno systems with immeasurable premise variables. Since the state estimation error can be written as a perturbed system, then the proposed method is based on the L2 techniques to minimize the effect of the perturbations on the state estimation error. The convergence conditions of the observer are established by using the second method of Lyapunov and a quadratic function. These conditions are expressed in terms of Linear Matrix Inequalities (LMI). Finally, the performances of the proposed observer are improved by eigenvalues clustering in LMI region.

Parameter estimation of switching piecewise linear system

During the last years, a number of methodological papers on models with discrete parameter shifts have revived interest in the so-called regime switching models. Piecewise linear models are attractive when modelling a wide range of nonlinear system and determining simultaneously i) the data partition ii) the time instant of change iii) the parameter values of the different local models. This is a difficult problem for which no solution exists in the general case and we show here some aspects and particular results concerning the problem of off line learning of switching time series. We propose a method for identifying the parameters of the local models when choosing an adapted weighting function, this function allowing to select the data for which each local model is active. Indeed the proposed method is able to solve simultaneously the data allocation and the parameter estimation. The feasibility and the performance of the procedure is demonstrated using several academic examples.