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International audience; This paper presents a new observer design approach for a class of discrete-time nonlinear systems described by a polytopic quasi-LPV (qLPV) models. The contribution consists in developing an observer for qLPV systems where the parameters depend on the unmeasured states of the system. The approach consists in combining the algebraic techniques with polytopic qLPV observers. Firstly, with the assumption that the nonlinear system is algebraic, or partially algebraic, observable, the unmeasured states involved in the parameters are estimated, exactly, in finite time which provides an exact estimation of the parameters. Secondly, the qLPV observer is designed by using the estimated parameters and the its finite time estimation property. Asymptotic convergence of the state estimation error is then obtained by Lyapunov analysis and LMI constraints are established, ensuring such a property and provide a way to design the gains of the observer. In addition, the transient phase is analyzed and an optimization problem under LMI constraints is provided to minimize the over-shoot of the state estimation error in the transient phase. An example is provided to illustrate the performances of the proposed approach and comparisons.

International audience; This work addresses the model reference tracking control problem. It aims to highlight the encountered difficulties and the proposed solutions to achieve the tracking objective. Based on a literature overview of linear and nonlinear reference tracking, the achievements and the limitations of the existing strategies are highlighted. This motivates the present work to propose clear control algorithms for perfect and approximate tracking controls of nonlinear systems described by Takagi-Sugeno models. First, perfect nonlinear tracking control is addressed and necessary structural conditions are stated. If these conditions do not hold, approximate tracking control is proposed and the choice of the reference model to be tracked as well as the choice of the criterion to be minimized are discussed with respect to the desired objectives. The case of constrained control input is also considered in order to anticipate and counteract the effect of the control saturation.

International audience; The paper addresses a systematic procedure to deal with the state and parameter uncertainty estimation for nonlinear time-varying systems. This is realized by designinga robust observer for dynamic nonlinear systems using a Takagy-Sugeno (T-S) multi-model approach with unknown premise variables and nonlinear outputs.This approach allows to apply the tools of the linear automatic to dynamic nonlinear systems by using the Linear Matrix Inequalities (LMI) optimization.The observer estimates the model uncertainties, the states and minimizes the effect of external disturbances on the estimation error. The model uncertainties areincluded in the model in a polynomial way which allows to consider the model uncertainty estimation as a fault detection problem. The residual sensitivity to faultswhile maintaining robustness according to a noise signal is handled by Hinf/H− approach. The performance of the proposed method is illustrated by using the three-tank system.

International audience; For the improvement of the performance of technical processes, faults and abnormal system operation must be detected and identified. For that purpose different approaches for fault detection have been developed and, here, a model-based approach is used. A diagnosis strategy based on fuzzy residual analysis is presented in this paper. The proposed approach uses the analytical redundancy to detect and isolate faults on sensors. After a presentation of its principle, the method is applied to an urban water supply network. Thanks to the use of fuzzy concept, the suggested diagnosis procedure enables to take into account all the available data and knowledge. Moreover, its efficiency has been proved by using experimental data. Therefore, a supervision software has been developed on the basis of this fuzzy based fault isolation method.

The paper deals of the forecasting of daily maximum ground-ozone level in an urban area. As the phenomenon of ozone production is nonlinear, a nonlinear modelling based on the multiple model approach has been pursued. It consists of representing a system as a combination of locally valid affine models. The identification tasks of such a model include the determination of the number and the structure of the local models, the definition of the operating regimes associated to the local models and the parameter estimation. The application of the proposed procedure to ozone level forecasting is reported: results on learning and validation data show the performances of the model. The test of the model in real situation is presented.

International audience; The problem of obtaining reliable estimates of the state of a process is a fundamental objective in process supervision, these estimates being used to understand the process behaviour. Measurements are collected in order to know, at each time, the behaviour of the process and give a way to verify if its functioning is those that has been defined and given by the user. For that purpose, a wide variety of techniques has been developed to perform what is currently known as data reconciliation: the underlying idea is to check if the measurements fulfil the model of the process and, if it is not the case, to analyse what are the noises affecting the measurements and finally to correct the measurements. Unfortunately, the measurements may be unknowingly corrupted by gross errors which effects are added to those of the noise. As a result, the data reconciliation procedure can give rise to absurd results and the estimated variables are corrupted by this bias. Several schemes have been suggested to cope with the corruption of normal assumption of the errors by detecting a priori or a posteriori gross errors. Among them, an approach consists to take into account the non ideality of the measurement error distribution using an objective function constructed on contaminated error distribution. This approach has been developed for data reconciliation and has been tested on several applications. In this paper, we restrict our analysis to processes described by linear and bilinear mass balance equations. However, despite this limitation, this kind of models are of current use because they allow to describe total mass and partial mass balances. In the following, we adopt and develop the using of contaminated data distribution for the data reconciliation problem. Section 2 is devoted to shortly recall the background of data reconciliation problem. In Section 3, the proposed robust data reconciliation method is developed. It is thereafter illustrated through an academic example in Section 4.

Sensor fault detection and isolation method is proposed in this paper. The method is only based on the knowledge of the input and output data. Any parameter estimation nor system order determination are necessary. The proposed technique uses matrix projection in subspace framework. The sensitivity of the method to sensor faults is shown. The method is applied for sensor fault detection and isolation in a grinding circuit.

Generally, faults are easily detected in linear systems. There exist a large number of proven methods for linear systems resolution. On the other hand, methods in non-linear cases are much more difficult to find and apply only to a limited number of situations. In a great majority of cases, the system is transposable to a piecewise linear structure and the fault detection can be done using linear system methods. The approach under study uses Finite Memory Observers (FMO) to detect sensor faults and actuator faults.

National audience; Dans cet article, nous proposons une nouvelle approche formelle pour l'évaluation des bornes de l'état d'un système incertain. La méthode qui en résulte utilise une représentation par intervalles, et repose sur la construction d'un système dynamique augmenté, où le nouveau vecteur d'état est composé des bornes inférieure et supérieure de l'état du système incertain. Il est important de noter que nous considérons des incertitudes structurées, où seules les bornes de chaque coefcient des matrices du système sont supposées connues.

State reconstruction approach is very useful for the detennination of the number of components retained in the PCA (Principal component analysis) model and for fault isolation (Dunia, 1996). An extension of this approach based on a NLPCA (Non Linear PCA) model is described in this paper. The NLPCA model is obtained using two RBF (Radial basis Function) networks where the nonlinear transformations of the input variables (that characterize the nonlinear principal component analysis) are modeled as a linear sum of radially symmetric kernel functions. A simulation example is given to show the performances of the proposed approach.

Published in Journal of Physics: Conference Series, 570:072004, 2014.; International audience; Technological advances in the process industries during the past decade haveresulted in increasingly complicated processes, systems and products. Therefore, recentresearches consider the challenges in their design and management for successful operation.While principal component analysis (PCA) technique is widely used for diagnosis, its structurecannot describe nonlinear related variables. Thus, an extension to the case of nonlinear systemsis presented in a feature space for process monitoring. Working in a high-dimensional featurespace, it is necessary to get back to the original space. Hence, an iterative pre-image techniqueis derived to provide a solution for fault diagnosis. The relevance of the proposed technique isillustrated on artificial and real dataset.

International audience; This chapter aims to detect oscillatory failures affecting a flight control surface (FCS) –specifically an aileron– of an aircraft. It presents the principle of supervision and the design of a soft sensor for the oscillatory failure case detection. The chosen principle for diagnosis is based on testing the adequacy of available measures in a control system (CS) servo-loop toward its model. Two kinds of failures must be detected, which are identified as “liquid failure” and “solid failure” as a disturbing signal is superimposed on or replaces the control signal. The chapter tackles the problem of fault detection and isolation (FDI) by the test of standard deviation. This problem is treated by a correlation test between several residuals. The quantitative analysis of residues (rb(t), rs(t) and rl(t)) confirms visual study and shows how the recognition is automatically processed from a numerical point of view.

International audience; The proposed work addresses the model reference tracking control problem. It aims to highlight the encoutered difficulties and the proposed solutions to achieve the tracking objective for nonlinear systems described by Takagi-Sugeno (T-S) models. Different control strategies are exposed. Exact state tracking is proposed and structural conditions for it are given. Approximate state tracking is also studied. The choice of the reference model to be tracked is discussed, as well as the criterion to be minimized to achieve given tracking objectives.

International audience; The proposed paper addresses the Finite Memory Observer (FMO) design applied to polytopic models. After a brief introduction on FTO for linear systems, the nonlinear models represented in a Takagi-Sugeno (T-S) or Polytopic form are then considered. The considered observer design will be applied to investigate the fault diagnosis for nonlinear discrete-time systems subject to unknown input where joint system states and unknown inputs estimation is proposed.

International audience; This paper proposes a new representation of discrete bilinear model by developing its coefficients associated to the input, to the output and to the crossed product on three independent Laguerre orthonormal bases. Compared to classical bilinear model, the resulting model entitled bilinear-Laguerre model ensures a significant parameter number reduction as well as simple recursive representation. However, this reduction is still subject to an optimal choice of the Laguerre poles defining the three Laguerre bases. Therefore, we propose an analytical solution to optimize the Laguerre poles which depend on Fourier coefficients defining the bilinear-Laguerre model, and that are identified using the regularized square error. The identification procedures of the Laguerre poles and Fourier coefficients are combined and carried out on a sliding window to provide an online identification algorithm of the bilinear-Laguerre model. The bilinear-Laguerre model as well as the proposed algorithm are illustrated and tested on a numerical simulation and validated on the Continuous Stirred Tank Reactor System (CSTR).

International audience; The paper addresses a systematic procedure to deal with the state, unknown input and parameter uncertainty estimation for nonlinear time-varying systems. This is realized by designing a robust observer for dynamic nonlinear systems using a Takagi-Sugeno (T-S) multi-model (MM) approach with nonlinear outputs. The method applies the technique of descriptor systems by considering unknown inputs and parameter uncertainty as auxiliary state variables. This approach allows to apply the tools of the linear automatic to dynamic nonlinear systems by using the Linear Matrix Inequalities (LMI) optimization. The observer estimates the previous mentioned variables and minimizes the effect of external disturbances on the estimation error. The model uncertainties are included in the model in a polynomial way which allows to consider the model uncertainty estimation as a fault detection problem. The residual sensitivity to faults while maintaining robustness according to a noise signal is handled by Hinf/H- approach.

For process control improvement, coherency of information supplied by sensors must first be ensured. Because of the presence of random and possibly gross errors, the model equations of the process are not generally satisfied. The problem of data reconciliation in order to satisfy the model constraints is considered in this article. The simultaneous presence of errors in process input and output measurements poses serious problem in the rectification of data. The proposed procedure to solve this problem involves the use of a special filter to estimate both the parameters, the states and the inputs of a process; smoothing of both estimations of the input and the output is increased by adding in the filter a variance term. Application is proposed for rainfall data validation in order to improve urban sewer network control.

The aim of this paper is to establish analytical equations for the problem of finding optimum real poles of the generalized orthonormal basis (GOB) for the class of discrete time systems which unit sample response is of the form h ( k ) = ∑ i = 1 P A i b i k , where Ai and -1

International audience; This paper deals with the estimation of linear time invariant (LTI) systems using Laguerrien models. The Laguerre functions used in this paper are presented in their general form, i.e. using two exponential factors. The main contribution of this paper is the development of an algorithm which performs the decomposition of a signal into Laguerre series for negative as well as positive time domains. These two decompositions are then aggregated to form a unique bilateral expansion. The method is then used to decompose input and output signals defined for positive as well as negative time (the case of non zero initial conditions of the state process is considered) into their bilateral Laguerre expansions in order to compute the parameters of the transfer function of the system that needs to be identified.

A diagnosis strategy based on fuzzy reasoning is presented in this paper. The first stage of the suggested approach consists in generating residuals revealing of the process functioning state. Two methods of residuals generation for linear-dynamic systems, based on the exploitation of analytical redundancy, are proposed. Then, a procedure of fault isolation using these residuals and based on fuzzy concepts is explained and implemented. To illustrate and show the validity of this approach, it's applied to experimental signals collected on a urban water supply network.

A general procedure, based on the knowledge of the input and the output signals, is proposed to approximate the prescribed linear time-invariant (LTI) systems by means of optimal Laguerre models. The main contribution of this paper is to apply the Newton Raphson's iterative technique to compute the so-called optimal Laguerre pole in a continuous time case (or optimal time scale factor in a discrete-time case) and especially to show that the gradient and the Hessian can be expressed analytically. Moreover, the excitations used are not limited to the ones that ensure the orthogonality of the outputs of Laguerre filters (i.e., Dirac delta or white noise) as is usually done in existing methods, however persistently exciting input signal(s) are used. The proposed procedure, will be directly formulated for SISO systems, SISO systems being a special case with the number of inputs equal to one. The proposed algorithm has direct applications in system identification, model reduction, and noisy modeling.

In this paper we propose an observer for a class of non-linear systems. We consider the stability of the observer where the non-linearities are bounded. This paper gives also the link between the bound of the modelling errors and the dynamic of the observer.

In this paper, an extended model of induction machines bearing short-circuits on a single stator phase is proposed. It is shown that a model based on five differential equations whose state vector contains only stator variables expressed in the stator Park base is more relevant to represent such failures. Moreover a simpler model, valid for small short-circuits, is obtained by linearization. It is further extended in order to take into account resistor disturbances. Finally, a structural analysis is developed to point out; that the stator currents are sufficient to generate residuals for discriminating failures under abnonnal operation.

This paper addresses the state and sensor fault estimation for nonlinear systems represented by Takagi-Sugeno (T-S) models. The considered faults are time-varying and with multiplicative effect on the sensor output signals. The proposed estimation procedure is based firstly on the sector nonlinearity approach using the convex polytopic transformation where the original system is equivalently rewritten as a Takagi-Sugeno system with unmeasurable premise variables and, secondly on the design of an observer allowing the fault estimation by solving an LMI optimization problem. An application of the proposed approach to a simplified model of an activated sludge reactor model is proposed.

International audience; System often has several operating modes that are controlled by the operator to follow a desired change or not in the case of fault occurrence or change due to the environment of the system. The challenge is to be able to know the current operating mode in order to apply the appropriate controls. The aim of this work is to recognize the active mode at any time, and to estimate the switching time between modes. The proposed method is able to detect mode changes without the knowledge of the model parameters characterising each mode. An application in continuous casting illustrates the ability to detect a variation of a friction coefficient.

International audience; A systematic approach to joint state and time-varying param eter estimation for nonlin- ear systems is proposed in this paper. Applying the sector no nlinearity transformation to both the system nonlinearities and the time-varying para meters, the original system is equivalently rewritten as a Takagi-Sugeno system with un measurable premise vari- ables. A joint state and parameter observer whose parameter s are designed by solving an LMI optimization problem is then proposed. The target app lication is a realistic model of an activated sludge wastewater treatment plant, be ing an uncertain nonlinear system affected by a time-varying parameter.

International audience; This study considers the problem of fault-tolerant control (FTC) by trajectory tracking for uncertain non-linear system described by Takagi-Sugeno models. The considered faults are constant, exponential or polynomial. The provided results are easily formulated in terms of linear matrix inequalities by employing the descriptor redundancy property. This latter introduces 'virtual' dynamics both in the active FTC control law scheme and in the output error allowing to decouple the gains of the active FTC controller, the observer gain matrices and the system ones. Numerical examples are given to illustrate the efficiency of the proposed approach.

International audience; This work concerns the model reference tracking control problem for nonlinear systems represented by Takagi-Sugeno (T-S) models, with a guaranteed L2 performance to attenuate the tracking error for bounded reference inputs. The objective is to make the system states follow as closely as possible the model reference states. The control scheme is based on a parallel distributed compensation controller fed by a state observer for Takagi-Sugeno systems with unmeasurable premise variables. The observer/controller synthesis is formulated in terms of linear matrix inequalities. Systems with noise output measurments are also envisaged with the use of filter. Simulation example are given to illustrate the design procedures and tracking performance of the proposed approach.

International audience; This paper adresses the stabilization of nonlinear systems described by Takagi-Sugeno models affected by input actuator saturation. A parallel distributed compensation design is used for the state feedback controller. Stabilization conditions in the sense of the Lyapunov method are derived and expressed as a linear matrix inequality problem. The obtained gains depend on the actuator saturation limits. A cart-pendulum example is presented to illustrate the effectiveness of the proposed approach.

International audience; This paper deals with nonlinear systems control with input saturation and parametric uncertainties. The considered nonlinear systems are represented by Takagi-Sugeno models. The proposed controller is a parallel distributed compensation state feedback. Stabilization conditions are derived with the Lyapunov method and expressed as an optimization problem under linear matrix inequality (LMI) constraints. The obtained controller gains depend on the saturation limits. The descriptor approach for modelling is also applied to reduce the number of LMI. An academic example is presented with a comparison between the proposed approach and a conventional controller.

International audience; We propose a new type of Proportional Integral (PI) state observer for a class of nonlinear systems in continuous time which ensures an asymptotic stable convergence of the state estimates. Approximations of non-linearity are not necessary to obtain such results, but the functions must be, at least locally, of the Lipschitz type. The obtained state variables are exact and robust against noise. Naslin's damping criterion permits synthesizing gains in an algebraically simple and efficient way. Both the speed and damping of the observer response are controlled in this way. Model simulations based on a Sprott strange attractor are discussed as an example.

International audience; This paper presents a new recursive optimal filter structure for joint input and state estimation of linear time- varying discrete systems in the presence of unknown inputs. The method is concerned with the direct feedthrough matrix which has an arbitrary rank. The resulting filter is optimal in the sense of the unbiased minimum-variance (UMV) criteria. The paper extends the existing results, in particular the ones of Hsieh in 2009. A numerical example is given in order to make a comparison between the proposed filter and the Hsieh filter developed by [7].

International audience; This paper proposes a new representation of discrete bilinear model by developing its coefficients associated to the input, to the output and to the crossed product on three independent Laguerre orthonormal bases. Compared to classical bilinear model, the resulting model entitled bilinear-Laguerre model ensures a significant parameter number reduction as well as simple recursive representation. However, such reduction still constrained by an optimal choice of Laguerre pole characterizing each basis. To do so, we develop a pole optimization algorithm which constitutes an extension of that proposed by Tanguy et al. [22]. The bilinear-Laguerre model as well as the proposed pole optimization algorithm are illustrated and tested on a numerical simulations and validated on the Continuous Stirred Tank Reactor (CSTR) System.

International audience; In this paper, a new method for determining the Principal Component Analysis (PCA) model structure for system diagnosis is proposed. This method, based on the variables reconstruction principle, determines the PCA model optimizing detection and isolation of single or multiple faults affecting redundant or non redundant variables of a system. This new method has been validated by a simulation example.

This article proposes a new representation of the ARX models on independent and orthonormal Laguerre bases by filtering the process input and output using Laguerre orthonormal functions. The resulting model, entitled ARX–Laguerre model, ensures the parameter number reduction with a recursive and easy representation. However, this reduction is still subject to an optimal choice of the Laguerre poles defining both Laguerre bases. Therefore, we propose an analytical solution to optimise the Laguerre poles which depend on Fourier coefficients defining the ARX–Laguerre model, and that are identified using the regularised square error. The identification procedures of the Laguerre poles and Fourier coefficients are combined and carried out on a sliding window to provide an online identification algorithm of the ARX–Laguerre model. The proposed algorithm is tested on numerical simulation and validated on a benchmark system manufactured by Feedback known as Process Trainer PT326.

International audience; The contribution of this paper is to propose a systematic approach to the observer design for linear time-varying systems. It is based on the exact rewriting of the original time-varying system into a polytopic linear model (PLM). This transformation uses the sector nonlinearity approach based on the convex polytopic transformation. Then a joint state and parameter observer can be designed for the PLM and the estimation errors convergence are proved.

Chapter 6; International audience

International audience; In this paper, the problem of observer design for nonlinear Lipschitz systems is treated. An emphasis is put on maximizing the admissible Lipschitz constant for which the observer design is possible. This problem is tackled using a Takagi-Sugeno modeling approach. The idea is to re-write the state estimation error dynamics as an autonomous Takagi- Sugeno system, using the Mean Value Theorem and the sector nonlinearity transformation. The stability of the state estimation error is studied with the Lyapunov theory by using a non- quadratic Lyapunov function and by computing its variation between m consecutive samples. The interest of these manip- ulations is to obtain LMI conditions admitting solutions for large values of the Lipschitz constant. Finally, two examples are provided in order to hilight the performances of the proposed approach.

International audience; The paper studies the problem of simultaneously estimating the state and the fault of linear stochastic discrete-time varying systems with unknown inputs. The fault and the unknown inputs affect both the state and the output. However, if the dynamical evolution models of the fault and the unknown inputs are available the filtering problem will be solved by the Optimal Three-Stage Kalman Filter (OThSKF). The OThSKF is obtained after decoupling the covariance matrices of the Augmented state Kalman Filter (ASKF) using a Three-Stage U-V transformation. Nevertheless, if the fault and the unknown inputs models are not perfectly known the Robust Three-Stage Kalman Filter (RThSKF) will be applied to give an unbiased minimum-variance estimation. Finally, a numerical example is given in order to illustrate the proposed filters.

Chapitre 7; International audience

International audience; This paper proposes a new approach of observer design for nonlinear systems described by a Takagi-Sugeno model. Its main contribution concerns models with premise variables depending on the system states which are completely or partially unknown. This case is more difficult than when the premise variables are known or measured. Indeed, in that case, weighting functions of the observer depend on state estimates and the state estimation error is then governed by a Lipschitz nonlinear system. Here, two mains results are established. Firstly, relaxed stability conditions guaranteeing asymptotic stability of the observer by using a polyquadratic Lyapunov function are provided. This aims to reduce the conservativeness compared to the existing works and enhance the maximal admissible Lipschitz constant for which the linear matrix inequality (LMI) conditions are feasible. Secondly, the Input-to-State Stability concept combined to a polyquadratic Lyapunov function are used for guaranteeing a bounded state estimation error which relaxes the conservativeness related to the Lipschitz constant. The robustness aspect is dealt with respect to some bounded modeling uncertainties and additive bounded perturbations. The stability conditions are expressed in terms of LMI.

International audience; The paper proposes the observer synthesis for uncertain nonlinear systems affected by unknown inputs described by the multi-model formulation with unmeasurable decision variables. A proportional multi-integral observer is considered in order to estimate the state and the unknown inputs and minimize the influence of the model uncertainties. The stability analysis and the observer synthesis are expressed through linear matrix inequalities based on the Lyapunov method. The performances of the proposed observer synthesis method are highlighted through the application to a waste-water treatment plant model, which is an uncertain nonlinear system affected by unknown inputs.

International audience; Dans cette communication, une nouvelle méthode de détermination de la structure d'un modèle ACP pour des fins de diagnostic de système est proposée. Cette méthode, basée sur le principe de reconstruction de variables, détermine les modèles ACP optimisant la détection et la localisation de défauts simples ou multiples affectant les différentes variables d'un système. Cette nouvelle méthode a été validée sur un exemple de simulation.

International audience; This article proposes an analytical method for decomposing a dynamic nonlinear system into a multiple model form in order to reduce its complexity and to study more easily identification, stability analysis and controller design problems. The majority of existing methods are order reduction based techniques, which come with an information loss of the initial system, whereas the method proposed here avoids this particular loss. The multiple model constitutes an efficient tool to represent nonlinear systems. These are decomposed into several linear time invariant systems (LTI) which are weighted and aggregated that allows to benefit from important analysis tools. This method is applied to a simplified activated sludge reactor model.

International audience; This paper deals with the problem of sensor fault tolerant control for Takagi-Sugeno nonlinear systems. Firstly, a residual generator is designed in order to detect and isolate sensor faults. Secondly, a nonlinear observer based controller, adopting the so-called parallel distributed compensation (PDC) structure is designed. The PDC controller is based on a weighted blending of the estimated states provided by different observers. Each observer is constructed to estimate the system state from the inputs and only one output. The blending of the estimates depends on the residual magnitudes in order to minimize the use of faulty estimates in the control law. The stability of the global closed-loop system is studied by Lyapunov theory and the gains of the fault tolerant controller are obtained by solving Linear Matrix Inequalities (LMI). Numerical examples are provided.

A new identification method, recursive and sequential through multiple; model (RSMM) is presented and evaluated using computer simulation. RSMM is especially suited for identification of multi-input-multi-output (MIMO) systems with jumping or rapidely changing parameters. The method consists of multiple recursive least-square algorithms running in parallel each with a weighting factor and sequential estimation of the internal variables appearing in the description of the MIMO model.

In this paper, we propose two methods to detect and to localize instrument or actuator failures in linear dynamic systems. These methods are based on analytical redundancy and uses a simultaneous states and inputs estimation. Using the concept of standardized least square residuals, residuals can be generated in a number of ways and the design of fault detection and fault isolation scheme can be presented. The performances of the proposed methods are illustrated on a real process: an inverted pendulum.

In the case of a non-stationary system whose the structure is described by jumping parameters, the residuals found from the difference between measured outputs and inputs model are affected by the variation of those parameters. Therefore, it becomes difficult to distinguish a sensor fault from an actuator fault or a perturbation due to parameters jumping. To bypass this difficulty, an adaptive algorithm has been developed and allows us to scan the fluctuation of model parameters. This algorithm can also give robust residuals for parameters jumping.

International audience; In the context of model-based failure detection and diagnosis, there is a residual generation which can be obtained through a generalized parity space concept. This paper presents a new algorithm involving the generation of redundancy or parity equations for dynamic linear time-invariant systems. The proposed scheme involves the successive elimination of state sub-vectors and their replacement by output values as well as the processing of an output done one at a time to avoid matrix inversion. Some examples point out the numerical efficiency of the proposed procedure.