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International audience; The aim of this article is the state estimation of uncertain polytopic dynamic systems. The parametric uncertainties affecting the system are time varying, unknown and bounded with known bounds. The objective is to determine the state estimates consisting in the smallest interval containing the real state value caused by the parametric uncertainties. This set will be characterized by the lower and upper bounds of the state trajectory. Given the uncertainty bounds, the set can be computed by a direct simulation of the system but a more accurate estimation is obtained with a Luenberger-type observer, fed with the system measurements. The proposed observer is designed to minimize the interval width of the estimates. The observer gains are obtained by solving an optimization problem under LMI constraints. The efficiency of the proposed approach is illustrated by numerical examples.

International audience; The detection of outliers in a series of measurements, but even more so their location, is a necessity when these measurements are to be used in a monitoring system. This detection/localization can only be done if redundant information is available, which may be based on the model of the system on which the measurements were collected.In some cases, however, it is not necessary to detect and locate outliers. Instead, a robust approach to their use may be preferred, one that minimizes the influence of these outliers, such as using a median rather than a mean.In this paper, the focus will be on the notion of robustness through a few examples and notably by proposing extensions to two well-known data processing techniques (data reconciliation and principal component analysis). The numerical examples proposed clearly show how to implement these two techniques and how to use them in a system monitoring procedure.

International audience; The purpose of detecting changes in the operating regime of a system is to identify abrupt changes from one regime to another. This paper proposes a new detection method which can detect regime change instants in sequential time series data. Our approach is based on a sensitivity study of a global model combining, with a multiplicative effect, local models describing the different operating modes without knowing their parameters. More precisely, the operating mode change detection indicator corresponds to the direction of the gradient of the global model of the system (i.e. including all its operating modes) with respect to the variables characterising the system. The proposed procedure is illustrated by the analysis of a dynamic system with several measurable inputs and outputs, which makes it possible to consider auto- and inter-redundancy relationships between inputs and outputs.

The objective of this study is the analysis of dynamic systems represented by multi-model with variable parameters. Changes in these parameters are unknown but bounded. Since it is not possible to estimate these parameters over time, the simulation of such systems requires to consider all possible values taken by these parameters. More precisely, the goal is to determine, at any moment, the smallest set containing all the possible values of the state vector simultaneously compatible with the state equations and with a priori known bounds of the uncertain parameters. This set will be characterized by two trajectories corresponding to the lower and upper limits of the state at every moment. This characterization can be realized by a direct simulation of the system, given the bounds of its parameters. It can also be implemented with a Luenberger type observer, fed with the system measurements.

Takagi-Sugeno (T-S) type of polytopic models have been used prominently in the literature to analyze nonlinear systems. With the sector nonlinearity approach, an exact representation of a nonlinear system within a sector could be obtained in a T-S form. Hence, a number of observer design strategies have been proposed for nonlinear systems using the T-S framework. In this work, a design strategy for adaptive observers is presented for a type of T-S systems with unknown parameters. The proposed approach improves upon the existing literature in two folds: reduce the computational burden and provide an algorithmic procedure that would seamlessly connect the state estimation and parameter estimation parts of the observer design. Lyapunov approach is used for the stability analysis and the design procedure. The results are illustrated on a simulation example.

In this paper, we propose a technique to reduce the complexity of an existing (initial) model via the Laguerre filters. We present an analytical method for the parameter identification of the Fourier coefficients of the Laguerre model. This technique is based on the bilinear discrete transformation and in which the Fourier coefficients are expressed in recurrent form in terms of the Laguerre pole. This latter is estimated by an iterative technique, based on the Newton algorithm. This identification technique is after extended to the case of the ARX-Laguerre model and the MISO-ARX-Laguerre model and its performances are illustrated by numerical simulations.

International audience; This paper proposes two improvements in the design of unknown input observers (UIO) for linear parameter varying (LPV) systems. First, the parameter dependency of the UIO is not restricted to mimic the one of the system in order to relax the existing decoupling conditions. Second, the output equation of the LPV systems is not supposed to be linear time invariant. Both perfect UI decoupling or mixed decoupling and attenuation are considered, whether the relaxed structural conditions are met or not.

International audience; This paper proposes a new Proportional Integral Derivative (PID) control algorithm based on the Meixner-like model. The Meixner-like functions are an extension of Laguerre functions and are convenient when the system has a slow start. The parameters of the PID controller are auto adjusted by the model predictive control (MPC) technique. To improve system performance, the resolution of the problem of saturation of the control signal is proposed. A numerical example of a variable parameter system is given to illustrate the effectiveness of the proposed control approach.

International audience; This work is dedicated to the synthesis of a new fault detection and identification scheme for the actuator and/or sensor faults modeled as unknown inputs of the system. The novelty of this scheme consists in the synthesis of a new structure of proportional-integral observer (PIO) reformulated from the new linear ARX-Laguerre representation with filters on system input and output in order to estimate the unknown inputs presented as faults. The designed observer exploits the input/output measurements to reconstruct the Laguerre filter outputs where the stability and the convergence properties are ensured by using Linear Matrix Inequality. However, a significant reduction of this model is subject to an optimal choice of both Laguerre poles which is achieved by a new proposed identification approach based on a genetic algorithm. The performances of the proposed identification approach and the resulting PIO are tested on numerical simulation and validated on a 2nd order electrical linear system.

We propose a new observer where the model, decomposed in generalized canonical form of regulation described by Fliess, is dissociated from the part assuring error correction. The obtained stable exact estimates give direct access to state variables in the form of successive derivatives. The dynamic response of the observer converges exponentially, as long as the nonlinearities are locally of Lipschitz type. In this case, we demonstrate that a quadratic Lyapunov function provides a number of inequalities which guarantee at least local stability. A synthesis of gains is proposed, independent of the observation time scale. Simulations of a Düffing system and a Lorenz strange attractor illustrate theoretical developments.

International audience; In this paper, the problem of observers for Takagi-Sugeno (TS) models with unmeasurable premise variables is investigated and a new design approach is proposed. The idea, is motivated by the immersion techniques and auxiliary dynamics generation, and consists in the transformation of the TS system with state dependent weighting functions in a new TS system with weighting functions depending only on the measured variables. This result aims to relax the strong conditions used in the design of observers for TS systems with unmeasurable premise variables. Illustrative examples are provided to discuss the performances of the proposed approach.

Air Handling Units (AHU) are responsible for efficiently transferring the energy produced for heating or cooling to the occupant area in the building. This energy transfer dynamics is modeled as a bilinear system. Such a structure poses problems to develop observers either with asymptotically vanishing error or with guaranteed error bounds. Takagi-Sugeno based polytopic models allow modeling of such nonlinear systems as well as to extend the results from linear system theory. Parameter estimation of such models with guaranteed error bounds is presented in Bezzaoucha et al. (2013). The present work applies this nonlinear parameter estimation technique on the energy balance model of a heat exchanger, the key component in an AHU. Three parameter estimation scenarios are proposed and extension to the theoretical results in the reference from an implementation point of view are given. Simulation results are provided to show the feasibility of the approach.

International audience; This paper presents an observer based sensor faultdiagnosis for 2-D systems. Firstly, a state observer is designed bytaking into account the measurements in a fixed length slidingwindow. Secondly, structured residual signals are generated bya bench of finite memory state observers which allow to detectand isolate sensor faults affecting the system. Finally, simulationresults are given to illustrate the proposed approach.

International audience; In this paper, a new strategy to cope with unmeasurable premise variables in observer design for Takagi-Sugeno (TS) models is proposed. The guiding principles are the immersion techniques and auxiliary dynamics generation, allowing to immerge a given TS system with unmeasured state dependent weighting functions into a larger TS system with weighting functions depending only on measured variables. This result relaxes the strong conditions used in the design of observers for TS systems with unmeasurable premise variables. An example is provided to illustrate the performances of the proposed approach.

International audience; In this article, the Meixner-like model is used to represent the linear discrete-time system in comparison with the Laguerre model. Furthermore, wepropose from input/output measurements a new recursive representation of the Meixner-like model. However, a significant approximation of thismodel is subject to an optimal choice of Meixner-like parameters: pole, order of generalization and Fourier coefficients. The present research yields aseries of computational experiments, through a simulation example of a linear parameter varying (LPV) system. This study tests this approach, verifiesthe theoretical results and points out the positive outcomes of using the Meixner-like model in comparison with the Laguerre model.

In the present paper, a Takagi-Sugeno TS model is used to simultaneously represent the behaviour of a nonlinear system and its saturated actuators. With the TS formalism and the Lyapunov approach, stabilization conditions are expressed as linear matrix inequalities for different controller designs. Static parallel distributed compensation PDC state feedback and static and dynamic PDC output feedback controllers for nonlinear saturated systems are proposed. The descriptor approach is used to obtain relaxed conditions to compute the controller gains. The nonlinear cart-pendulum system is used to illustrate the proposed control laws. Copyright © 2015 John Wiley & Sons, Ltd.

Summary This paper presents a new scheme for sensor fault tolerant control for nonlinear systems based on the Takagi–Sugeno modeling. First, a structured residual generator aimed at detecting and isolating sensor faults is designed. A bank of observers controlled either by only one system output or a set of outputs is then implemented, leading to a set of state estimates. The parallel distributed compensation structure is adopted to design the fault tolerant controller. The novelty in this paper is that the estimated state used in the controller is a weighted state vector obtained from all the estimated states provided by the different observers. The weighting functions depend on the residual vector signals delivered by the residual generator. They are designed to avoid crisp switches in the control law. Indeed, the interesting feature of the proposed approach is to avoid the commonly used switching strategy. For each residual component, the greater its magnitude is, the less the weight affected to the corresponding state estimate is. Consequently, the controller only uses estimations computed on the basis of healthy measurements. The closed-loop stability is studied with the Lyapunov theory, and the obtained conditions are expressed as a set of linear matrix inequalities. The proposed residual generation and fault tolerant controller are applied to a vehicle lateral dynamics affected by sensor faults. Copyright © 2015 John Wiley & Sons, Ltd.

International audience; This paper proposes a new predictive controller approach for nonlinear process based on a reduced complexity homogeneous, quadratic discretetime Volterra model called quadratic S-PARAFAC Volterra model. The proposed model is yielded by using the symmetry property of the Volterra kernels and their tensor decomposition using the PARAFAC technique which provide a parametric reduction compared to the conventional Volterra model. This property allows synthesizing a new nonlinear model based predictive control (NMBPC). We develop the general form of a new predictor and so, we propose an optimization algorithm formulated as a Quadratic Programming (QP) under linear and nonlinear constraints. The performances of the proposed quadratic S-PARAFAC Volterra model and the developed NMBPC algorithm are illustrated on a numerical simulation and validated on a benchmark as a continuous Stirred Tank Reactor (CSTR) system. Moreover the efficiency of the proposed quadratic SPARAFAC Volterra model and the NMBPC approach are validated on an experimental Communicating Two Tank system (CTTS).

Published in IFAC-PaperOnLine, 50(1):1025-1030; International audience; The principal component analysis (PCA) is a linear technique widely used to retrieve a subspace that maximizes the variance of the data, making the presence of a fault easy to detect. Nevertheless, the real systems are nonlinear. To this end, we propose in this paper to use a kernel-based technique known as kernel principal component analysis (KPCA) for fault diagnosis. The main idea is to use a nonlinear transformation that projects data into a higher dimensional feature space, where conventional PCA is applied. Although detection can be defined in this space, the estimation of the fault requires the map back to the input space. In this sense, we derive an iterative pre-image technique. A study on possible initial points is done. Three initialization techniques based on different properties are presented. The relevance of the proposed technique is illustrated on simulated data.

In this paper, a novel method is constructed for model predictive control (MPC) of multi-input multi-output (MIMO) systems. The latter are represented by a discrete-time MIMO ARX model expansion on Laguerre orthonormal bases. The resulting model, entitled the MIMO ARX-Laguerre model, provides a recursive representation with parameter number reduction. This reduction is strongly linked to the choice of Laguerre poles, and therefore we propose a new algorithm to optimize the Laguerre poles of the resulting model. The recursive formulation of the MIMO ARX-Laguerre model is used to obtain the MPC strategy. An [Formula: see text]-norm finite moving horizon cost function is used to obtain a control law which is implemented as a quadratic programming (QP) problem. The effectiveness of the proposed controller that takes into account physical constraints is illustrated by a numerical simulation example and by a practical validation on an experimental communicating two-tank system (CTTS).

International audience; Multiple models are recognised by their abilities to accurately describe nonlinear dynamic behaviours of a wide variety of nonlinear systems with a tractable model in control engineering problems. Multiple models are built by the interpolation of a set of submodels according to a particular aggregation mechanism, among them heterogeneous multiple model is of particular interest. This multiple model is characterized by the use of heterogeneous submodels in the sense that their state spaces are not the same and consequently they can be of various dimensions. Thanks to this feature, the complexity of the submodels can be well adapted to the complexity of the nonlinear system introducing flexibility and generality in the modelling stage. This paper deals with the off-line identification of nonlinear systems based on heterogeneous multiple model. Three optimisation criteria (global, local and combined) are investigated to obtain the submodel parameters according to the expected modelling performances. Particular attention is paid to the potential problems encountered in the identification procedure with a special focus on an undesirable phenomenon called no output tracking effect. The origin of this problem is explained and an effective solution is suggested to overcome this problem in the identification task. The abilities of this model are finally illustrated via relevant identification examples showing the effectiveness of the proposed methods.

Published in Journal of Physics: Conference Series, 783:012016, 2017; International audience; Takagi-Sugeno (T-S) models have been popular in analyzing nonlinear systems. Observer designs for T-S models have focused on both cases with measured and unmeasured premise variables. However, the unmeasured premise variables have to be one of the states of the system. If one of the inputs is a premise variable, these approaches are not applicable. A recent literature proposed a joint state and parameter estimation for time-varying unknown parameters in systems of a special type [1]. A discrete-time version of the results is developed in this paper. The modeling approach is described and the stability analysis of the estimation is given using the Lyapunov method with the L2 approach handling the uncertainties.

International audience; The complexity problem of nonlinear dynamic systems appears in a great number of scientific and engineering fields. The multi-model, also known as polytopic approach, constitutes an interesting tool for modeling dynamic nonlinear systems, in the framework of stability analysis and controller/observer design. A systematic procedure to transform a nonlinear system into a polytopic one will be briefly presented and illustrated by an academical example. This procedure gives the possibility of choosing between different polytopic structures, which is a degree of freedom used to ease the controllability, observability, stability analysis studies. In addition to that, the system transformation into polytopic form does not cause any information loss, contrarily to most existing studies in the field. In the second part of this chapter, a discussion about multiple time scale nonlinear systems, also known as singularly perturbed systems is proposed, by eliminating some structural constraints and by performing the identification and the separation of the time-scales. Robust observer synthesis with respect to internal/external perturbations, modeling parametrization errors and unknown inputs are presented for the estimation of different variables of interest, the state variables. The above-mentioned points will be applied to an activated sludge wastewater treatment plant (WWTP), which is a complex chemical and biological process. The variations in wastewater flow rate/composition and the time-varying bio-chemical reactions make this process nonlinear. Despite the process nonlinearity and complexity, there is a need to control the quality of the water rejected in the nature by the WWTPs in order to achieve the requirements of the European Union in terms of environmental protection. To this end, a Benchmark, proposed by the European program COST 624 to asses the control strategies of WWTPs, is used as an example in the present chapter.

In this paper, we present the synthesis of a robust controller for uncertain discrete systems. The synthesis method of such a robust controller is the generalization of the Loop Shaping Design Procedure (LSDP) approach of McFarlane and Glover in the discrete case based on the work of Gu et al. We exploit the bilinear transform known as Tustin’s method in order to formulate the discrete loop shaping technique. A discrete weighting filter and a shaped discrete plant result from this technique. By taking into account the coprime factor uncertainty representation for the resulting shaped plant and by applying the small gain theorem, we define the concept of the robust stabilization of the discrete LSDP approach. This concept is based on the resolution of an optimization problem characterized by the maximum stability margin for the synthesis of the robust controller. To calculate the robust controller we transform this problem to a standard robust [Formula: see text] controller design based on the resolution of the Riccati equations. Also, we present the gap metric theory to characterize the controller’s robustness. We note that the resulting final controller is the combination of the discrete weighting filter and the robust controller. We propose then to exploit the recent work of Bouzrara et al. in order to develop a reduced robust controller by expanding the final controller on two independent Laguerre orthonormal bases. The discrete LSDP and the reduced controller approaches were validated on a Continuous Stirred Tank Reactor chemical reactor for a set of different equilibrium points in order to take into account the nonlinearities.

International audience; Variable Air Volume (VAV) based Heating Ventilation and Air Conditioning (HVAC) systems are common in large non-residential buildings. The dynamic model of a VAV system along with the Air Handling Unit (AHU) and the zones has a nonlinear characteristic. In this paper, a nonlinear model based joint state and parameter observer is proposed to estimate the VAV damper position in such systems. First, a Takagi-Sugeno (T-S) equivalent model for the AHU-VAV-Zone model is obtained using sector nonlinearity approach. The damper position estimation problem is then posed as a time varying parameter estimation problem. A procedure based on existing literature results on T-S joint state and parameter estimation is implemented. Simulation results show the effectiveness of this approach. A bank of observers based approach is then described that can help in detecting and isolating VAV damper faults in the system using the state and parameter estimates.

International audience; A new actuator fault diagnosis and estimation approach is proposed for dynamical systems. The main contribution consists in enhancing the fault detection with a new observer that takes into account the relative degree of the output of the system with respect to the fault. The Single Input Single Fault (SIFO) case is considered to present the approach and an extension to systems with multiple outputs and multiple faults. The convergence of the proposed residual generator is analyzed using the Lyapunov theory which can be expressed straightforwardly in terms of Linear Matrix Inequalities (LMIs). Numerical examples are provided in order to illustrate the proposed approach.

International audience; This paper presents two approaches of observer based stabilization for Takagi-Sugeno (T-S) systems with immeasurable premise variables in continuous time case. These approaches are based on the description of the state estimation error by a T-S model. To design the observer based stabilization law, the concept of PDC (Parallel Distributed Compensation) is employed, the sufficient stabilization conditions are proved and expressed in the form of Linear Matrix Inequalities (LMI). The perform-ances of these approaches are tested by simulation for an illustrate example and a physical system representing a two-link robot.

International audience; In this paper, we propose a new reduced complexity model by expanding a discrete-time ARX model on Laguerre orthonormal bases. To ensure an efficient complexity reduction, the coefficients associated to the input and the output of the ARX model are expanded on independent Laguerre bases, to develop a new black-box linear ARX-Laguerre model with filters on model input and output. The parametric complexity reduction with respect to the classical ARX model is proved theoretically. The structure and parameter identification of the ARX-Laguerre model is achieved by a new proposed approach which consists in solving an optimization problem built from the ARX model without using system input/output observations. The performances of the resulting ARX-Laguerre model and the proposed identification approach are illustrated by numerical simulations and validated on benchmark manufactured by Feedback known as Process Trainer PT326. A possible extension of the proposed model to a multivariable process is formulated.

International audience; This paper presents a new robust filter structure to solve the simultaneous state and fault estimation problem of linear stochastic discrete-time systems with unknown disturbance. The method is based on the assumption that the fault and the unknown disturbance affect both the system state and the output, and no prior knowledge about their dynamical evolution is available. By making use of an optimal three-stage Kalman filtering method, an augmented fault and unknown disturbance models, an augmented robust three-stage Kalman filter (ARThSKF) is developed. The unbiasedness conditions and minimum-variance property of the proposed filter are provided. An illustrative example is given to apply this filter and to compare it with the existing literature results.

International audience; This study addresses the problem of parameters estimation for switched regression models used to represent systems with multiple operating modes or regimes. For the identification of such models, the collected data are from different operating modes and there is no a priori information holding on the partitioning of the data in regard to the different operating modes. The essential contributions of this paper lie first in the estimation procedure of the model parameters that provides an analytical solution, second in the simultaneous resolution of the problem of estimating the model parameters and allocating the data points to the different local models, and finally the robustness of the estimation procedure regarding the presence of outliers in the identification dataset.

International audience; This study addresses the analysis and design of unknown input observer in order to provide both state and unknown input estimations of complex systems modelled with the help of a particular class of multiple model. The proposed observer uses the multi-integral strategy successfully employed in the classic linear control theory and known for its robustness properties. The observer design is based on the representation of the system via a particular multiple model, known as 'decoupled multiple model'. This structure of multiple model allows to use submodels with different number of states and this feature constitutes the main advantage of the proposed observer with respect to the classic multiple model structure where the submodels have the same dimension. It is shown how the gains of the suggested observer can be obtained by solving a linear matrix inequality optimal problem. An academic example is also proposed in order to illustrate the proposed methodology.

This paper addresses the design of an unknown input fuzzy observer for Takagi-Sugeno (T-S) fuzzy model subject to unknown inputs. The main contribution of the paper is the development of a robust fuzzy observer in presence of disturbances. Based on Lyapunov function, it is shown how to determine observers gains in linear matrix inequalities (LMI). The proposed T-S observer is used for detection and isolation of faults which can affect a nonlinear models. The validity of the proposed methodology is illustrated by estimating the yaw rate and the fault of automatic steering vehicle.

International audience; This paper addresses a new scheme for fault diagnosis in nonlinear systems described by Takagi-Sugeno multiple models. Two cases are considered, the first one concerns the T-S models with known premise variables (the input or the output of the system). For the second case it is supposed that the weighting functions depend on unmeasurable premise variables (state of the system). The approach is based on the design of observer-based residual generator by minimization of the disturbances effect and maximizing the effects of the faults. The synthesis is based on the L2 formalism developed for linear systems. The convergence conditions are given in LMI formulation.

This paper presents a method for state-estimation of Takagi-Sugeno descriptor systems (TSDS) affected by unknown inputs (UI). For ease of implementation's sake, the proposed observers are not in descriptor form but in usual form. Sufficient existence conditions of the unknown input observers are given and strict linear matrix inequalities (LMI) are solved to determine the gain of the observers. If the perfect unknown input decoupling is not possible, the UI observer is designed in order to minimise the L2-gain from the UI to the state estimation error. The two previous objectives can be mixed in order to decouple the estimation to a subset of the UI, while attenuating the L2 gain from the other UI to the estimation. The proposed UI observers are used for robust fault diagnosis. Fault diagnosis for TSDS is performed by designing a bank of observers. A simple decision logic and thresholds setting allow to determine the occurring fault. The results are established for both the continuous and the discrete time cases. The proposed method is illustrated by a numerical example.

International audience; This paper addresses a discussion about Unknown Input Observers (UIO) for Linear Parameter Varying (LPV) systems designed classically by using the polytopic representation. It is illustrated that even if the rank conditions ensuring the existence of an UIO are satisfied, the design may fail, due to the polytopic representation of the LPV system. In this paper a new design approach is proposed via two different UIOs for a class of LPV systems with parameter dependent output equation. It is based on parameter algebraic matrix equations and LMI conditions. Examples are provided in order to illustrate the performances of the proposed approach.

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.

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.

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 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 article is dedicated to the problem of fault detection, isolation and estimation for nonlinear systems described by a Takagi-Sugeno (T-S) model. One of the interests of this type of models is the possibility to extend some tools and methods from the linear system case to the nonlinear one. The principle of the proposed strategy is to transform the problem of simultaneously minimizing the perturbation effect and maximizing the fault effect, on the residual vector, in a simple problem of L2-norm minimization. A linear system is used to define the ideal response of the residual signal to the fault. Then the aim is to synthesize a residual generator that both minimizes the difference between real and ideal responses and the influence of the disturbance. The minimization problem is formulated by using the bounded real lemma (BRL) and linear matrix inequality (LMI) formalism. After studying the general framework, a special case of systems with actuator and sensor faults is considered where the fault incidence matrix is not full column rank. Simulation examples are given to illustrate the proposed method. Finally, Polya's theorem is used to reduce the conservatism of the proposed result. The obtained relaxation is also illustrated by a numerical example.

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.

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.

International audience; The robust stability of systems with structured uncertain parameters is investigated. Using the generalized Lyapunov method, the present study shows how the domain of tolerable uncertain parameters for which the system stability is guaranteed can be determined.

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.

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; 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.