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International audience; In this paper, a decoupled multiple model approach is used in order to cope with the state estimation of uncertain nonlinear systems. The proposed decoupled multiple model provides flexibility in the modelling stage because the dimension of the submodels can be different and this constitutes the main difference with respect to the classically used multiple model scheme. The state estimation is performed using a Proportional Integral Observer (PIO) which is well known for its robustness properties with respect to uncertainties and perturbations. The Lyapunov second method is employed in order to provide sufficient existence conditions of the observer, in LMI terms, and to compute the optimal gains of the PIO. The effectiveness of the proposed methodology is illustrated by a simulation example.

When a metallic surface is tested by the eddy-current technique, defects produce events on the electrical signal coming from the sensor whose particular signature is a function of different factors such as the shape, size and position of any defects. Thanks to the introduction of modern digital signal processing methods, the quality of detection of events in the signal may be appreciably improved. The reliability of the decision mechanism, entrusted with reducing non-detection and limiting false alarms, is then increased and allows consideration of automatic testing. The work presented here was done jointly by the Institut de Recherches de la Siderurgie Francaise (IRSID) of the Usinor-Sacilor group and the aboratoire d' Automatique et de Recherche Appliquee (LARA) of the Centre de Recherche en Automatique de Nancy (CRAN).

Hermès special issue on Hybrid Systems; International audience; Cet article concerne le diagnostic des systèmes dynamiques hybrides par approches continues. Il rassemble quelques résultats et conclusions obtenus au travers de l'Action spécifique 193, intitulée « Diagnostic des systèmes dynamiques hybrides », soutenue par le département STIC du CNRS et rattachée au GDR MACS et au RTP 20. Les contributions principales concernent d'une part, l'estimation du mode de fonctionnement et l'identification des lois de commutation. D'autre part, les contributions concernent l'amélioration de la discernabilité des défauts par une évaluation de l'amplitude de ces derniers et par la combinaison de décisions statiques et dynamiques. Les approches proposées sont illustrées sur un support commun constitué d'un système à deux réservoirs.

International audience; This paper deals with the state estimation of nonlinear systems. Our approach is based on the representation of a nonlinear system with the help of a decoupled multiple model. This kind of multiple model constitutes an alternative to the classic Takagi-Sugeno multiple model. Indeed, in opposition to this last, in the decoupled multiple model the dimension (i.e. the number of states) of the submodels may be different. In order to cope with the state estimation problem a Proportional-Integral observer (PIO) is designed. Indeed, in contrast to the classic Proportional observer the PIO is known by its robustness properties. Sufficient conditions for ensuring the estimation error convergence are given in LMI form.

International audience; Switching systems are a particular class of hybrid systems. They are described by several operating regimes, called modes, each of them being active under certain particular conditions. When the switching mechanism is perfectly known, it is easy to handle such systems because the knowledge of the active regime at any moment is available. On the other hand, in the case where there is no information about the switching mechanism, the situation is more complicated. In this configuration, it is difficult to carry out a fault diagnosis scheme or to synthesize a control law. This paper addresses the issue of the determination of the active mode at any moment, using only the system's input/output data. Conditions that guarantee the uniqueness of the determined active mode are also given.

International audience; This paper deals with the problem of data validation of an instrumentation system applied in the aerospace area. The fault diagnosis method used for the validation is based on the principle of the parity space approach. Residuals are generated thanks to the analytical redundancy relations given by the model and the important number of sensors. Indeed, we propose a procedure, which permits us to compute systematically all the redundancy equations for the residual generation phase. The additional concept, called residuals structuration, is necessary to isolate the detected faults. Finally, the data validation task consists in isolating the failing data and in sending only the valid information to a control system. An application to an aerospace system illustrates the proposed algorithm.

International audience; This paper addresses the analysis and design of a sliding mode observer on the basis of a Takagi-Sugeno (TS) 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.

International audience; Multiple model approach is a powerful tool for modelling nonlinear systems. Two structures of multiple models can be distinguished. The first structure is characterised by decoupled submodels, i.e. with no common state (decoupled multiple model), in opposition to the second one where the submodels share the same state (Takagi-Sugeno multiple model). A wide number of research works investigate the state estimation of nonlinear systems represented by a classic Takagi-Sugeno multiple model. On the other hand, to our knowledge, the state estimation of the decoupled multiple model has not been investigated extensively. This paper deals with the state estimation of nonlinear systems represented by a decoupled multiple model. Conditions for ensuring the convergence of the estimation error are formulated in terms of a set of Linear Matrix Inequalities (LMIs) employing the Lyapunov direct method.

International audience; This paper addresses the analysis and design of a Sliding Mode Fuzzy Observer (SMFO) on the basis of a Takagi-Sugeno (T-S) fuzzy model. The main contribution of the paper is the development of a robust fuzzy observer with respect to the uncertainties as well as the synthesis of sufficient stability conditions of this observer. The stabilisation of the fuzzy 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 (LMIs). The validity of the proposed methodology is illustrated by an estimation of the yaw rate of automatic steering of vehicles.

Parameter estimation mainly consists in characterising a parameter set consistent with measurements, the model and the equation error description. The problem to be solved is that of finding the set of admissible parameter values corresponding to an admissible error. The uncertainties must be treated by a global analysis of the problem: both the equation error and the parameter set are considered unknown. Then, a solution is given as a domain of time-variant parameters and a bounded set of the error. This procedure consists in explaining the measurements performed at all time by optimising a precision criterion based on the polytope theory.

International audience; Multiple-model approach is an interesting alternative and a powerful tool for modelling complex processes. This paper deals with the off-line identification of non-linear systems employing the multiple-model approach. We use an uncoupled state multiple-model in opposition to the classically used coupled state multiplemodel (Takagi-Sugeno). The use of this new mutiple-model structure reveals a new undesirable phenomenon, called unhooking, that deteriorates the quality of the obtained approximation. An original solution is proposed to avoid this phenomenon.

International audience; In the paper an approach to real-time identification of pulse energy conversion system (PECS) parameters is developed. The approach is based on the preliminary bifurcation analysis and geometrical interpretation of the fractal properties revealed in PECS dynamics. The approach has in aim to establishing of a functional dependence between both phase variable values measured and parameter values sought.

In this paper a sensor fault detection and isolation procedure based on principal component analysis (PCA) is proposed to monitor an air quality monitoring network. The PCA model of the network is optimal with respect to a reconstruction error criterion. The sensor fault detection is carried out in various residual subspaces using a new detection index. For our application, this index improves the performance compared to classical detection index SPE. The reconstruction approach allows, on one hand, to isolate the faulty sensors and, on the other hand, to estimate the fault amplitudes.

International audience; In this note, we propose a simple and efficient crypto-system based on a chaotic time delay model. It consists of two steps: the first one assures the transmitter/receiver synchronization while the second step focuses on the encryption/decryption procedure. The synchronization is performed through a non linear state observer design, driven by the transmitted signal. Both full order and reduced order state estimation techniques are established. One of the main results is that sufficient conditions for asymptotic convergence, to assure the synchronization, are derived in terms of Linear Matrix Inequalities (i.e. convex problem) easily and numerically tractable. Efficiency of the proposed approach is shown through the transmission of two encrypted messages : a sound wave and a digital picture. Finally, some security issues are discussed at the end of this note.

A procedure for generating analytical redundancy equations for process fault detection and isolation is described. This procedure uses a direct approach by considering the relations betwen the inputs and the outputs of the process. Systems with known or partially known inputs are considered. A numerical example is presented. >

International audience; This paper deals with the stability analysis of interval Takagi-Sugeno model. Based on a quadratic Lyapunov function, new asymptotic stability conditions for continuous case are presented without any assumption on the norm of matrices uncertainties. This result is obtained directly according to the bounds (minimal and maximum) of the intervals of each element of matrices representing the system. These stability conditions, extended to the design of controller, are formulated in terms of linear matrix inequalities (LMI). Example is given to illustrate the proposed method.

International audience; This paper deals with the robust fuzzy observer design problem for a class of uncertain nonlinear system represented by Takagi-Sugeno model. 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.

International audience; Interval analyses are well known in the mathematics literature but have found few applications in control engineering. Based on the interval concept, we present here a methodology for data reconciliation and mass balance equilibration which is a very classical problem in mineral and chemical engineering. Indeed, this problem is solved with the view of inequality constraints which allows us to represent measurements by interval without particular knowledge and hypothesis about the density probability function of the measurement errors. As a main result, the paper gives a set of solutions for the reconciled data under an interval form and not only one solution as is the case with classical approaches.

National audience; Nous proposons une méthode basée sur l'analyse en composantes principales pour la détection et la localisation de défauts de capteurs d'un réseau de surveillance de la qualité de l'air. Le modèle ACP du réseau de mesures est optimal au sens d'un critère basé sur l'erreur de reconstruction des différentes variables. La détection des défauts de capteurs est réalisée dans différents sous-espaces résiduels à l'aide d'un nouvel indicateur de détection. Enfin, la reconstruction des variables permet, d'une part, en la combinant avec l'indicateur de détection, de localiser les capteurs défaillants et, d'autre part, d'estimer l'amplitude des défauts.

International audience; On-line optimisation provides a means for maintaining a process around its optimum operating plant. An important component of optimisation relies in data reconciliation which is used for obtaining consistent data. On a mathematical point of view, the formulation is generally based on the assumption that the measurement errors have normally pdf with zero mean. Unfortunately, in the presence of gross errors, all of the adjustments are greatly affected by such biases and would not be considered as reliable indicators of the state of the process. This paper proposes a data reconciliation strategy that deals with the presence of such gross errors. Application to size flowrates and concentration data in mineral processing is provided.

This paper proposes a method to discuss the stability analysis of multiple models. The proposed stability analysis is based on the use of scalar Lyapunov functions and the properties of M-matrices. An example is included to illustrate the proposed method.

International audience; In this paper, a new formulation of the problem of mass and energy balance equilibration in the case of unknown-but-bounded errors is proposed. The bounds of the errors are specified over both a measurement noise and the balance equations. Both bounds are mainly motivated by experimental considerations of the measurement precision; with a more general interpretation, they can be considered as parameters that the user has to adjust to make the reconciliation possible. The method is particularly suitable for linear models but has been extended to nonlinear ones as well. Simulations provide results that compare favorably with those of classical reconciliation methods involving maximum likelihood estimation based on statistical knowledge of the measurement errors.

International audience; The paper describes an identification technique of switching system. The considered system is represented as a weighted sum of local models. To estimate the switching times, a change detection technique is applied. It provides the weights associated to the local models. The Markov parameters of these models are identified by a subspace method. This calculation can yield similar local models which are merged. The procedure of parameter identification an models merging is repeated until convergence. The performance of the approach is investigated on a simulation example.

Analysing the behaviour of physical systems often leads to realise that a natural representation consists in building mixed continuous / discrete models. Multimodels or hybrid models are adapted representations for complex physical systems by introducing transitions (smooth or not) between local behaviours. This paper presents some technical points dealing with the determination of the time transition from one local model to another one. More generally, our purpose is to estimate, at each time, the state of the associated process.

National audience; Lorsque des mesures sont effectuées sur un système, il est utile de s'assurer de leur cohérence. Pour cela, il est nécessaire de disposer de redondances permettant de comparer différentes estimées d'une même grandeur. Généralement, deux modes de redondance, l'un matériel, l'autre analytique, sont utilisés. Dans les deux cas, la redondance est traduite par des modèles (du système de mesure, ou des relations liant les grandeurs à mesurer) ; ces modèles ont cependant une précision limitée et une façon de prendre en compte ce fait est de décrire les imperfections et les imprécisions par des paramètres incertains mais bornés. Cette présentation montre comment décrire des modèles à paramètres incertains et bornés, comment les utiliser pour la validation de données et, en particulier, comment estimer l'état d'un système décrit par un modèle statique linéaire. Pour simplifier l'exposé, le cas de systèmes de mesure linéaires statiques à incertitudes additives et multiplicatives est considéré et quelques idées d'extension sont évoquées.

International audience; In this communication one presents an algorithm for the robust identification (in respect to abnormal values) of the parameters of a MIMO system with strong interconnections between inputs and outputs. This recursive algorithm is based on the model of Huber that consists of a decomposition of the noise measurement in two random sequences; the first yields for the zero mean noise of measure and second for the presence of abnormal values in the output signal. An example of simulation is proposed to illustrate the performances of this technique by regard to other existent techniques

International audience; This paper deals with the stability analysis of Takagi-Sugeno models (T-S). Based on piecewise quadratic Lyapunov functions and the use of the so-called S-procedure, new asymptotic stability conditions for both continuous and discrete T-S models are presented. The stability conditions are formulated in linear matrix inequalities (LMIs). Examples are given to illustrate the advantage of the proposed method.

International audience; To solve the fault detection and isolation problem, many techniques are based on state estimation. The divergence phenomenon of the state estimation error due to the accumulation of model uncertainties leads to the design of finite memory observer for both discrete and continuous time representations. Such observers are therefore more efficient for fault detection. This paper presents an extension of the finite memory observer so that both the input and the state of the system are estimated on a fixed number of measurements. The relevance is that the estimation can be performed even if the data are not given with the same sampling period. In addition, actuator and sensor fault detection and isolation can be performed within bank of observers driven by different subsets of input and output measurements. Further, a new residual can be defined so that the residual robustness to model uncertainties might be improved as it has already been shown and applied by Nuninger et al. (1997) within finite memory state estimation.

International audience; This paper discusses conditions on stability and stabilization of continuous T-S fuzzy systems. Stability analysis is derived via a non-quadratic Lyapunov function technique and LMIs (linear matrix inequalities) formulation to obtain an efficient solution. The non-quadratic Lyapunov function is built by inference of quadratic Lyapunov function of each local model. We show that the stability condition of the open-loop T-S systems is assured under certain restrictions on the rate of change of state variables. Following a similar approach, the stabilization of closed-loop continuous T-S fuzzy systems using the well-known PDC (parallel distributed compensation) technique is investigated. The design methodology is illustrated by numerical examples.

International audience; In this paper, the separation principle for discrete nonlinear systems in multiple model representation is investigated. The separation principle deals with a property which allows the multiple observer and the multiple controller to be designed separately. Using the quadratic Lyapunov technique and LMIs (Linear Matrix Inequalities) formulation, sufficient conditions for the global exponential stability of discrete multiple controllers are derived which are dual to those for the global exponential convergence of discrete multiple observers. A numerical example is given to illustrate the method.

International audience; The paper aims to optimise the structure of a multiple model described by output error local models. Two complementary techniques are proposed for this purpose. The first one deals with the simplification of the local model structure using a pruning approach. The second concerns the optimisation of the number of sub-models and consists in merging neighbouring models that can describe the same behaviour of the system. Their performances are illustrated on simulation examples.

The paper aims to describe the problem of modelling non-linear dynamic systems using a multiple model representation, also known in fuzzy set literature as Takagi-Sugeno model. The basic principle of this approach is to represent the system as an interpolation of locally valid models. Proposed identification algorithms concern the parameter estimation and the structure determination (local model orders, number of local models). Three applications of this approach to environmental system management are reported: modelling of a wastewater treatment plant, ozone concentration prediction is an urban area and finally modelling of rainfall-runoff relationship for sensor fault diagnosis in urban sewage network.

International audience; In this paper, we present a systematic framework for the design of gain scheduled observer based controllers for affine linear parameter-varying (LPV) systems. Our approach is based on parameter-dependent Lyapunov functions. We give sufficient conditions for the synthesis of the observer gain and of the state feedback controller gain separately and we show that the closed-loop system obtained with the observer based controller is stable. The main contribution of this paper is the fact that the state feedback gain synthesis is formulated as a more easily tractable condition and this is achieved by the application of the multiconvexity concept and the introduction of a slack variable

International audience; Fault detection in linear static models with uncertain parameters is studied in this paper. Using a parity space technique, a method based on the bounding approach is proposed. Several types of structured faults may affect a physical system and in this context, two cases are distinguished: - the structured fault is a prior identified as a region in the parameter space, by considering the physical knowledge on the studied system. The corresponding procedure is called supervised. - the second case corresponds to a fault which has an unknown structure. The corresponding procedure is called unsupervised fault. In this article, a strategy consists first in characterizing various fault structures and then in establishing a fault detection and identification (FDI) procedure by using interval analysis.

This paper examines the problem of modelling a non-linear dynamic system by a Takagi–Sugeno model. Although this type of model is well adapted to the representation of a system with non-linear behaviour, its use does however raise real problems in the identification of its structure and parameters, mainly because of the enormous combinatorial increase in model complexity as a function of the number of inputs, and the coupling between the premises and consequence parts. We propose a simplified model structure and an algorithm for the identification of this structure and its parameters. The method is illustrated with reference to data from a wastewater treatment plant of the Greater Nancy Urban Authority. Copyright © 2001 John Wiley & Sons, Ltd.

International audience; In this paper, the design of a parameter-dependent state observer that allows to estimate the state of an affine linear parameter-varying (LPV) system is investigated. The observer has the property of being parameter-dependent since the corresponding state space matrices are scheduled using an interpolation method. Moreover, the stability of the estimation error is based on the existence of an affine parameter-dependent Lyapunov function. The main contribution of this paper is that the problem of the observer design and the existence of such a Lyapunov function is interpreted as a flexible LMI feasibility condition. Some illustrative examples are presented at the end of this paper.

International audience; Investigates a state observation design problem for discrete time linear parameter varying (LPV) systems. The main contribution of the paper consists in providing an interpolation scheme to build the LPV observer. We show that an appropriate choice of the interpolation functions allows us to use available quadratic stability conditions to design an LPV observer

International audience; In this paper, the design of a scheduled observer which allows to estimate the state of an affine LPV system is investigated. The state and the gain matrices of the observer are scheduled by using an interpolation method which is linear according to each parameter but which is nonlinear according to the parameter vector. The stability of the estimation error is based on the existence of an affine parameter-dependent Lyapunov function. The problem of the observer design and the existence of a such Lyapunov function is interpreted as an LMI feasibility problem with a rank constraint. An example is presented.

International audience; The identification of a TS model with output error local models is considered. The premise part of the TS model is assumed to be described by a lattice partition. The main problem involved is the determination of the premise variables, the associated number of modalities and the structure of the local models. The premise optimisation is solved by a forward approach and the structure of the local models are further refined using a pruning technique. The application of the overall procedure on a simulation example is reported.

International audience; The paper deals with the simplification of the rule base of the Takagi-Sugeno model. The proposed technique assumes an initial lattice partition of the premise space. The complexity of the rule base is optimised through two sequential operations: elimination of the less important rules followed by the merging of neighbouring rules that can describe the same behaviour of the system. The identified structure is further refined by adjusting the parameters of the membership functions. The procedure is illustrated on a simulation example

International audience; Fault detection and process monitoring using principal component analysis (PCA) has been studied intensively and largely applied to industrial processes. This paper proposes an approach to sensor fault detection and isolation via principal component analysis and its application to sensor failure detection of an air quality monitoring network in Lorraine, France. The method suggested by Dunia et al. (1996) is sensitive to model errors. For this reason, a test on the last principal components is proposed for the detection and the localisation of sensor failure.

International audience; This paper deals with a fault detection method taking model uncertianties into account. Only sensor imperfections are considered; moreover every uncertain parameter is represented by a bounded variable. By this membership approach, a model represents a set of feasible behaviours; therefore, interval analysis is used to build consistency tests based on the parity space approach. A fault is detected when the residual vector is outside its domain of feasible values. Unfortunately, the dependencies between bounded variables make the previous domain too complex to be exactly evaluated. The proposed solution leads to an overestimation obtained by using a paving algorithm.

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International audience; Data reconciliation has proven to be an e€fective technique for providing frequent, accurate and consistent "best estimates" of plant operation data. However, in almost all the proposed techniques until today, the mathematical model of the process has been considered as exact. In point of fact, this hypothesis is uncommon and frequently the models used are uncertain. This paper proposes a new technique of data reconciliation which is able to exploit the knowledge about the uncertainties of the model with regard to which the reconciliation is done. It leads to the solution of a classical quadratic optimisation problem subject to constraints. The originality of the proposed technique is to use penalty functions for solving this problem and to weight each constraint with regard to their uncertainties.

International audience; We are concerned here with dynamical processes whose states and inputs are measured or partially measured. Due to the noise which corrupt the measurements, we want to simultaneously estimate the states and the inputs. For the case where all the measurements are available, the estimation may be considered as a filtering technique; otherwise, the problem is more complicated as we want also to obtain an estimation of the unmeasured variables. In the very particular but difficult situation where not any inputs is measured, the problem may be linked to those involving unknown input observers; in signal processing, when the system is time-invariant, this problem is often referred to as deconvolution. The proposed technique is applioed for measurements corrupted by noise which generally gives bad estimations of the unknown inputs. In order to obtain smooth estimations, additional constraints are proposed.

International audience; This paper presents PID tuning method. The proposed method is based on the performances represented by a permitted domain for time response of the controlled system. To reach these performances, the controller parameters have to satisfy inequality constraints which can be solved by linear matrix inequality (LMI) methods. A brief introduction reviews the principle of parameters adjustment of a controller due to the model method. An approximate method of adjustment with respect to inequality constraints is considered. An optimal version is then given

International audience; Static linear models characterized by bounded uncertainties on both the equation error and the parameters are studied. The additive equation error is assumed to belong to an interval while the parameters fluctuate inside a time-invariant bounded domain. An algorithm is proposed for evaluating different bounded domains. The algorithm can be extended to cope with the determination of the central value of the domain containing the parameters. Contrary to most of traditional estimators, the resulting estimator takes into account the distribution of the uncertainties of a model

International audience; This paper focuses on an original fault detection method, able to take into account parameter uncertainties described by bounded variables. Intervals offer an attractive alternative for uncertain modelling and allow a straightforward generation of adaptive thresholds. This method is based on the parity space approach. The original point treated herein concerns the choice of the parity matrix, according to uncertain matrices of state representations. After expressing external forms of parity relations, interval arithmetic is used to evaluate internal forms and to deduce residual enclosures delimiting normal operation field. Then, we stress on the problems caused by dependencies between interval variables.

When a transfer function is expanded on the basis of Laguerre filters, the question of how well does the expansion converge arises frequently. Beyond this problem, the convergence domain of the Laguerre series must be determined in the s-plane, as is usually done for the Laplace transform of time-domain functions. In the usual approach, this analysis is made in two complementary stages: first of all, the convergence conditions of Fourier (also called Laguerre or Laguerre-Fourier) coefficients is determined and then, based on the assumption that these coefficients are convergent, a worst-case-study is carried out to determine the convergence domain of the Laguerre series. A novel approach is proposed in this paper which drops away the coupling between the convergence of the Fourier coefficients and the convergence of the Laguerre series. Thus, necessary and sufficient conditions for Laguerre series convergence are computed. Laguerre functions are considered in their general definition : orthogonal w.r.t. an exponential weight function.