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In this paper, we present a method that utilizes support vector machines (SVM) to identify linear parameter-varying (LPV) auto-regressive exogenous input (ARX) models corrupted by not only noise, but also uncertainties in the LPV scheduling variables. The proposed method employs SVM and takes advantage of the so-called 'kernel trick' to allow for the identification of the LPV-ARX model structure solely based on the input-output data. The objective function, as defined in this paper, allows to consider uncertainties related to the LPV scheduling parameters, and hence results in a new formulation that provides a more accurate estimation of the LPV model in the presence of scheduling uncertainties. We further demonstrate the viability of the proposed LPV identification method through numerical examples, where we show that higher best fit rate (BFR) can be achieved under realistic noise conditions using the proposed method compared to the method initially proposed in [6]. 2014 EUCA. Qatar National Research Fund Scopus

A large variety of natural, industrial, and environmental systems involves phenomena that are continuous functions not only of time, but also of other independent variables, such as space coordinates. Typical examples are transportation phenomena of mass or energy, such as heat transmission and/or exchange, humidity diffusion or concentration distributions. These systems are intrinsically distributed parameter systems whose description usually requires the introduction of partial differential equations. There is a significant number of phenomena that can be simulated and explained by partial differential equations. Unfortunately all phenomena are not likely to be represented by a single equation. Also, it is necessary to model the largest possible number of behaviors to consider several classes of partial differential equations. The most common are linear equations, but the most representative are non-linear equations. The nonlinear equations can be formulated in many different ways, the interest in nonlinear equations with linear parameters varying is studied. The aim of the thesis is to develop new estimators to identify the systems described by these partial differential equations. These estimators must be adapted with the actual data obtained in experiments. It is therefore necessary to develop estimators that provide convergent estimates when one is in the presence of missing data and are robust to measurement noise. In this thesis, identification methods are proposed for partial differential equation parameter estimation. These methods involve the introduction of estimators based on the instrumental variable technique, Les systèmes décrits par les équations aux dérivées partielles, appartiennent à la classe des systèmes dynamiques impliquant des fonctions dépendantes de plusieurs variables, comme le temps et l'espace. Déjà fortement répandus pour la modélisation mathématique de phénomènes physiques et environnementaux, ces systèmes ont un rôle croissant dans les domaines de l'automatique. Cette expansion, provoquée par les avancées technologiques au niveau des capteurs facilitant l'acquisition de données et par les nouveaux enjeux environnementaux, incite au développement de nouvelles thématiques de recherche. L'une de ces thématiques, est l'étude des problèmes inverses et plus particulièrement l'identification paramétrique des équations aux dérivées partielles. Tout abord, une description détaillée des différentes classes de systèmes décrits par ces équations est présentée puis les problèmes d'identification qui leur sont associés sont soulevés. L'accent est mis sur l'estimation paramétrique des équations linéaires, homogènes ou non, et sur les équations linéaires à paramètres variant. Un point commun à ces problèmes d'identification réside dans le caractère bruité et échantillonné des mesures de la sortie. Pour ce faire, deux types d'outils principaux ont été élaborés. Certaines techniques de discrétisation spatio-temporelle ont été utilisées pour faire face au caractère échantillonné des données; les méthodes de variable instrumentale, pour traiter le problème lié à la présence de bruit de mesure. Les performances de ces méthodes ont été évaluées selon des protocoles de simulation numérique reproduisant des situations réalistes de phénomènes physique et environnementaux, comme la diffusion de polluant dans une rivière

International audience; This article addresses the problem of designing a robust fault detection filter (RFDF) for a class of nonlinear descriptor systems whose nonlinear term is globally Lipschitz and linear term is described by a linear parameter varying form. The effect of perturbations on the residuals is minimised using the ∞ norm while the sensitivity performance is guaranteed using the − index. Thanks to a particular Lyapunov function: which depends on the faults and the filter design problem is formulated as a convex optimisation problem solved via linear matrix inequality techniques. Performances of the proposed filter are shown through the application of an activated sludge process model.

Mathematical models of physical systems are pervasive in engineering. These models can be used to analyze properties of the system, to simulate the system, or synthesize controllers. However, many of these models are too complex or too large for standard analysis and synthesis methods to be applicable. Hence, there is a need to reduce the complexity of models. In this thesis, techniques for reducing complexity of large linear time-invariant (lti) state-space models and linear parameter-varying (lpv) models are presented. Additionally, a method for synthesizing controllers is also presented. The methods in this thesis all revolve around a system theoretical measure called the H2-norm, and the minimization of this norm using nonlinear optimization. Since the optimization problems rapidly grow large, significant effort is spent on understanding and exploiting the inherent structures available in the problems to reduce the computational complexity when performing the optimization. The first part of the thesis addresses the classical model-reduction problem of lti state-space models. Various H2 problems are formulated and solved using the proposed structure-exploiting nonlinear optimization technique. The standard problem formulation is extended to incorporate also frequency-weighted problems and norms defined on finite frequency intervals, both for continuous and discrete-time models. Additionally, a regularization-based method to account for uncertainty in data is explored. Several examples reveal that the method is highly competitive with alternative approaches. Techniques for finding lpv models from data, and reducing the complexity of lpv models are presented. The basic ideas introduced in the first part of the thesis are extended to the lpv case, once again covering a range of different setups. lpv models are commonly used for analysis and synthesis of controllers, but the efficiency of these methods depends highly on a particular algebraic structure in the lpv models. A method to account for and derive models suitable for controller synthesis is proposed. Many of the methods are thoroughly tested on a realistic modeling problem arising in the design and flight clearance of an Airbus aircraft model. Finally, output-feedback H2 controller synthesis for lpv models is addressed by generalizing the ideas and methods used for modeling. One of the ideas here is to skip the lpv modeling phase before creating the controller, and instead synthesize the controller directly from the data, which classically would have been used to generate a model to be used in the controller synthesis problem. The method specializes to standard output-feedback H2 controller synthesis in the lti case, and favorable comparisons with alternative state-of-the-art implementations are presented.

A large variety of natural, industrial, and environmental systems involves phenomena that are continuous functions not only of time, but also of other independent variables, such as space coordinates. Typical examples are transportation phenomena of mass or energy, such as heat transmission and/or exchange, humidity diffusion or concentration distributions. These systems are intrinsically distributed parameter systems whose description usually requires the introduction of partial differential equations. There is a significant number of phenomena that can be simulated and explained by partial differential equations. Unfortunately all phenomena are not likely to be represented by a single equation. Also, it is necessary to model the largest possible number of behaviors to consider several classes of partial differential equations. The most common are linear equations, but the most representative are non-linear equations. The nonlinear equations can be formulated in many different ways, the interest in nonlinear equations with linear parameters varying is studied. The aim of the thesis is to develop new estimators to identify the systems described by these partial differential equations. These estimators must be adapted with the actual data obtained in experiments. It is therefore necessary to develop estimators that provide convergent estimates when one is in the presence of missing data and are robust to measurement noise. In this thesis, identification methods are proposed for partial differential equation parameter estimation. These methods involve the introduction of estimators based on the instrumental variable technique., Les systèmes décrits par les équations aux dérivées partielles, appartiennent à la classe des systèmes dynamiques impliquant des fonctions dépendantes de plusieurs variables, comme le temps et l'espace. Déjà fortement répandus pour la modélisation mathématique de phénomènes physiques et environnementaux, ces systèmes ont un rôle croissant dans les domaines de l'automatique. Cette expansion, provoquée par les avancées technologiques au niveau des capteurs facilitant l'acquisition de données et par les nouveaux enjeux environnementaux, incite au développement de nouvelles thématiques de recherche. L'une de ces thématiques, est l'étude des problèmes inverses et plus particulièrement l'identification paramétrique des équations aux dérivées partielles. Tout abord, une description détaillée des différentes classes de systèmes décrits par ces équations est présentée puis les problèmes d'identification qui leur sont associés sont soulevés. L'accent est mis sur l'estimation paramétrique des équations linéaires, homogènes ou non, et sur les équations linéaires à paramètres variant. Un point commun à ces problèmes d'identification réside dans le caractère bruité et échantillonné des mesures de la sortie. Pour ce faire, deux types d'outils principaux ont été élaborés. Certaines techniques de discrétisation spatio-temporelle ont été utilisées pour faire face au caractère échantillonné des données; les méthodes de variable instrumentale, pour traiter le problème lié à la présence de bruit de mesure. Les performances de ces méthodes ont été évaluées selon des protocoles de simulation numérique reproduisant des situations réalistes de phénomènes physique et environnementaux, comme la diffusion de polluant dans une rivière.

In this paper, a Fault Tolerant Control (FTC) strategy for Linear Parameter Varying (LPV) systems that can be used in the case of actuator faults is proposed. The idea of this FTC method is to adapt the faulty plant instead of adapting the controller to the faulty plant. This approach can be seen as a kind of virtual actuator. An integrated FTC design procedure for the fault identification and fault-tolerant control schemes using LPV techniques is provided as well. Fault identification is based on the use of an Unknown Input Observer (UIO). The FTC controller is implemented as a state feedback controller and designed using polytopic LPV techniques and Linear Matrix Inequality (LMI) regions in such a way as to guarantee the closed-loop behavior in terms of several LMI constraints. To assess the performance of the proposed approach, a two degree of freedom helicopter is used., This work has been partially funded by the grant CICYT DPI2008-01996 of the Spanish Ministry of Education, by the Research Commission of Generalitat de Catalunya (SAC group ref. 2005SGR00537), by a grant from Consejo Nacional de Ciencia y Tecnologia de México (CONACyT), and by the grant N N514 678440 of the Ministry of Science and Higher Education in Poland (within the science funds for the years 2011–2014).

Model predictive control (MPC) of a class of nonlinear systems is considered in this paper. We will use Linear Parameter Varying (LPV) model of the nonlinear system. By taking the advantage of having future values of the scheduling variable, we will simplify state prediction. Consequently the control problem of the nonlinear system is simplied into a quadratic programming. Wind turbine is chosen as the case study and we choose wind speed as the scheduling variable. Wind speed is measurable ahead of the turbine, therefore the scheduling variable is known for the entire prediction horizon.

Two controllers for an automotive suspensions with Magneto-Rheological (MR) dampers are proposed. One is a model-based using the Linear Parameter Varying (LPV) approach, and the other is a model-free controller with a Frequency Estimation Based (FEB) principle. The LPV controller includes an experimental nonlinear model of an MR damper using only one scheduling parameter. A comparison with a several semiactive controllers for comfort and road holding is discussed. The FEB controller is the best option based on frequency and time response analysis for comfort (1020), suspension deflection (3050), and road holding (15). © 2012 Jorge de Jesús Lozoya-Santos et al.

Robust model predictive control (RMPC) of a class of nonlinear systems is considered in this paper. We will use Linear Parameter Varying (LPV) model of the nonlinear system. By taking the advantage of having future values of the scheduling variable, we will simplify state prediction. Because of the special structure of the problem, uncertainty is only in the B matrix (gain) of the state space model. Therefore by taking advantage of this structure, we formulate a tractable minimax optimization problem to solve robust model predictive control problem. Wind turbine is chosen as the case study and we choose wind speed as the scheduling variable. Wind speed is measurable ahead of the turbine, therefore the scheduling variable is known for the entire prediction horizon.

The development and application of Linear Parameter Varying (LPV) control system for robust longitudinal control system on an Autonomous Underwater Vehicle (AUV) are presented. The LPV system is represented as Linear Fractional Transformation (LFT) on its parameter set. The LPV control system combines LPV theory based upon Linear Matrix Inequalities (LMIs) and - synthesis to form a robust LPV control system. The LPV control design is applied for a pitch control of the AUV to fulfill control design criteria on frequency and time domain. The final closed-loop system is tested for robust stability throughout the operational envelope.

International audience; In this paper, an approach to design an Admissible Model Matching (AMM) Fault Tolerant Control (FTC) based on Linear Parameter Varying (LPV) techniques is proposed. The main contribution of the proposed approach consists in the on-line reconfiguration of the controller based on the use of LPV gain-scheduling techniques that allow to take into account changes in the system parameters due to changes in the operating point and faults. The proposed strategy is an active FTC strategy that requires the fault to be detected, isolated and estimated by the FDI scheme. The formulation of AMM is based on establishing a set of admissible behaviors by specifying the region where the closed-loop should lie through LMIs. To select the best controller, the notion of quadratic H2/H∞ performance is used in the FTC design. The effectiveness and performance of proposed approach have been illustrated using a two degree of freedom helicopter.

The main goal of our research is to control the output voltage of electrical embedded networks. The first part of this manuscript presents a detailed description of the model and behaviour of these systems. Under some working conditions, they can be written as Linear Parameter Varying (LPV) models. It is then possible to prove stability and performance with well established theoretical tools. These systems present very rich dynamics, and, in some situations, it is very hard to control them. A dynamical analysis is presented, and a classification of the systems based on the connected loads is proposed. From this classification it is possible to decide which control strategy should be used to control them. The second part of this manuscript proposes a technique for controlling electrical embedded networks. Usually, to deal with load commutations, a noise-rejection approach is used: the system is in its steady-state working status, and a commutation happens. As output voltage deviates from its nominal value, the controller has to bring it back. Our approach is different: before commutation happens, the system is led to a more suited stated for it. This way the control signal used during the load impact allows us to better attenuate it. As the system's model varies for each different load, the controller's gains will adapt to this variation. This way, for each load an optimal controller is used to drive the system. Hence the denomination: "Anticipative Gain-Scheduling Control".; Le but principal de nos travaux est de commander la tension de sortie de réseaux électriques embarqués. La première partie de ce manuscrit étudie en détail la modélisation et le comportement de ces systèmes. Sous certaines conditions de fonctionnement, ils peuvent être représentés comme des modèles Linéaires à Paramètres Variants (LPV). Il est ainsi possible de prouver la stabilité et la performance des systèmes avec des outils théoriques bien établis. Ces systèmes présentent des dynamiques très riches, et il est, dans certaines situations, très difficile de les commander. Une analyse dynamique est présentée, et une classification des systèmes en fonction des charges connectées est proposée. A partir de cette classification, il est possible de décider quelle stratégie de commande doit être utilisée pour les piloter. La deuxième partie de ce manuscrit apporte une contribution à la commande des réseaux électriques embarqués. Classiquement, une approche basée sur le ``rejet de perturbation'' est utilisée : le système subit l'impact de charge et le régulateur de tension doit ramener cette grandeur à sa valeur nominale. Notre stratégie est différente : avant que l'impact ne se produise, le système est amené à un état plus favorable à celui-ci. De cette façon la commande utilisée au moment de l'impact permet alors de mieux l'atténuer. Comme le modèle du système varie pour chaque charge différente, les gains des régulateurs que nous avons développés s'adaptent à cette variation. De cette façon, pour toute charge, un régulateur optimal est utilisé pour commander le système. D'où la dénomination de "Commande Anticipative à Gains Programmés".

The main goal of our research is to control the output voltage of electrical embedded networks. The first part of this manuscript presents a detailed description of the model and behaviour of these systems. Under some working conditions, they can be written as Linear Parameter Varying (LPV) models. It is then possible to prove stability and performance with well established theoretical tools. These systems present very rich dynamics, and, in some situations, it is very hard to control them. A dynamical analysis is presented, and a classification of the systems based on the connected loads is proposed. From this classification it is possible to decide which control strategy should be used to control them. The second part of this manuscript proposes a technique for controlling electrical embedded networks. Usually, to deal with load commutations, a noise-rejection approach is used: the system is in its steady-state working status, and a commutation happens. As output voltage deviates from its nominal value, the controller has to bring it back. Our approach is different: before commutation happens, the system is led to a more suited stated for it. This way the control signal used during the load impact allows us to better attenuate it. As the system's model varies for each different load, the controller's gains will adapt to this variation. This way, for each load an optimal controller is used to drive the system. Hence the denomination: "Anticipative Gain-Scheduling Control".; Le but principal de nos travaux est de commander la tension de sortie de réseaux électriques embarqués. La première partie de ce manuscrit étudie en détail la modélisation et le comportement de ces systèmes. Sous certaines conditions de fonctionnement, ils peuvent être représentés comme des modèles Linéaires à Paramètres Variants (LPV). Il est ainsi possible de prouver la stabilité et la performance des systèmes avec des outils théoriques bien établis. Ces systèmes présentent des dynamiques très riches, et il est, dans certaines situations, très difficile de les commander. Une analyse dynamique est présentée, et une classification des systèmes en fonction des charges connectées est proposée. A partir de cette classification, il est possible de décider quelle stratégie de commande doit être utilisée pour les piloter. La deuxième partie de ce manuscrit apporte une contribution à la commande des réseaux électriques embarqués. Classiquement, une approche basée sur le ``rejet de perturbation'' est utilisée : le système subit l'impact de charge et le régulateur de tension doit ramener cette grandeur à sa valeur nominale. Notre stratégie est différente : avant que l'impact ne se produise, le système est amené à un état plus favorable à celui-ci. De cette façon la commande utilisée au moment de l'impact permet alors de mieux l'atténuer. Comme le modèle du système varie pour chaque charge différente, les gains des régulateurs que nous avons développés s'adaptent à cette variation. De cette façon, pour toute charge, un régulateur optimal est utilisé pour commander le système. D'où la dénomination de "Commande Anticipative à Gains Programmés".

A robust linear parameter varying (LPV) identification/invalidation method is presented. Starting from a given initial model, the proposed method modifies it and produces an LPV model consistent with the assumed uncertainty/noise bounds and the experimental information. This procedure may complement existing nominal LPV identification algorithms, by adding the uncertainty and noise bounds which produces a set of models consistent with the experimental evidence. Unlike standard invalidation results, the proposed method allows the computation of the necessary changes to the initial model in order to place it within the consistency set. Similar to previous LPV identification procedures, the initial parameter dependency is fixed in advance, but here a methodology to modify this dependency is presented. In addition, all calculations are made on state-space matrices which simplifies further controller design computations. The application of the proposed method to the identification of nonlinear systems is also discussed. Fil: Bianchi, Fernando Daniel. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Politécnica de Catalunya; España Fil: Sanchez Peña, Ricardo Salvador. Universidad Politécnica de Catalunya; España. Institució Catalana de Recerca i Estudis Avancats; España. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina

International audience; In this paper, a new approach to design a Fault- Tolerant Control (FTC) based on Linear Parameter Varying (LPV) Admissible Model Matching (AMM) is proposed. The suggested strategy is an active technique that requires the fault to be detected and estimated by the FDI scheme. Then, the controller is redesigned accordingly. In this work, faults are expressed as a change in the system dynamics (in particular, in the model parameters). The main contribution of the proposed approach is to consider the fault as a scheduling variable in the LPV model that allows the controller reconfiguration. The range of the scheduling variables (fault magnitude and system operating point) allow to specify the set of admissible behaviors. The effectiveness and performances of the method have been illustrated in a two degree of freedom helicopter.

Methods for direct data-driven tuning of the parameters of precompensators for LPV systems are developed. Since the commutativity property is not always satisfied for LPV systems, previously proposed methods for LTI systems that use this property cannot be directly adapted. When the ideal precompensator giving perfect mean tracking exists in the proposed parameterisation of the precompensator, the LPV transfer operators do commute and an algorithm using only two experiments on the real system is proposed. It is shown that this algorithm gives consistent estimates of the ideal parameters despite the presence of stochastic disturbances. For the more general case, when the ideal precompensator does not belong to the set of parameterised precompensators, another technique is developed. This technique requires a number of experiments equal to twice the number of precompensator parameters and it is shown that the calculated parameters minimise the mean squared tracking error.

International audience; In this paper, the problem of comfort and handling improvements of a ground vehicle is treated through the joint control of the suspension and braking systems. Two Hinf gain-scheduled controllers are synthesized to achieve, attitude and yaw performances according to the driving situation, observed through of a simple vehicle monitor. The proposed strategy tackles the nonlinear tire braking force in an original way and meets the situation dependent objectives of the vehicle in a unied framework. Simulations on a complex nonlinear full vehicle model, validated using experimental data obtained on a real vehicle, illustrate the improvements brought by the proposed approach.

This article proposes a linear parameter varying (LPV) switching tracking control scheme for a flexible air-breathing hypersonic vehicle (FAHV). First, a polytopic LPV model is constructed to represent the complex nonlinear longitudinal model of the FAHV by using Jacobian linearization and tensor-product (T-P) model transformation approach. Second, for less conservative controller design purpose, the flight envelope is divided into four sub-regions and a non-fragile LPV controller is designed for each parameter sub-region. These non-fragile LPV controllers are then switched in order to guarantee the closed-loop FAHV system to be asymptotically stable and satisfy a specified performance criterion. The desired non-fragile LPV switching controller is found by solving a convex constraint problem which can be efficiently solved using available linear matrix inequality (LMI) techniques, and robust stability analysis of the closed-loop FAHV system is verified based on multiple Lypapunov functions (MLFs). Finally, numerical simulations have demonstrated the effectiveness of the proposed approach.

This thesis presents Adaptive Model Predictive Control approach for a two-wheeled robot manipulator with varying mass. The mass variation corresponds to the robot picking and placing objects or loads from one place to another. A Linear Parameter Varying model of the system is derived consisting of local linear models of the system at different values of the varying parameter. An Adaptive Model Predictive Control controller is designed to control the fast-varying center of gravity angle in the inner loop. The reference for the inner loop is generated by a slower outer loop controlling the linear position using an Linear Quadratic Gaussian regulator. The control system is simulated on the nonlinear model of the robot, and the closed-loop performance of the proposed scheme is compared with a system having Proportional Derivative Integral controllers for both loops, Feedback Linearization Controller for inner loop, as well as one having Linear Quadratic Gaussian controllers for both loops. It is seen that Adaptive Model Predictive Control shows mostly superior and otherwise very good performance when compared to these two benchmarks in terms of reference tracking and robustness to mass parameter variations. Finally, comparison of two controllers Adaptive Model Predictive Control and Model Predictive Control comparison is presented in order to verify the leadership of the adaptive one for the future real-time implementation., Bu tez çalışması değişken kütle koşulu altında Uyarlamalı Model Tabanlı Öngörücü Kontrol yaklaşımının İki-Tekerlekli Gezer Robot Platform sistemine uygulanmasını ele almaktadır. Sistemdeki kütle değişimi robotun bir yerden başka bir yere taşıdığı nesneleri alırken ve bırakırken ortaya çıkmaktadır. Değişken kütleli yapıyı tasvir edebilmek için farklı kütleler için tanımlanmş doğrusal denklemlerden meydana gelen Doğrusal Değişken Değişimli sistem türetilmiştir. Sistemin hızlı (kütle merkezi açısı) dinamiklerini kontrol edebilmek için Uyarlamalı Model Tabanlı Öngörücü Kontrol yaklaşımı tasarlanmıştır. Hızlı dinamikler için istenen açısal değerler, daha yavaş olan dış (doğrusal konum) kontrolcüsü Doğrusal Kuadratik Gauss kontrolcüsü tarafından yapılmaktadır. Kontrol sistemi doğrusal olmayan dinamik sistem üzerinde benzetim çalışmaları yapılmıştır. Bu kontrol yaklaşımı her iki dinamikleri de Oransal Integral Türevsel kontrol ile kontrol edilen kapalı çevrim sistemle karşılaştırılmış, daha sonra iç çevrimi Geribeslemeli Doğrusallaştırma ve dış çevrimi Doğrusal Kuadratik Gauss kontrolcüsü ile gerçeklenen kapalı çevrim yapıyla da sonrasında karşılaştırılmıştır. Bu karşılaştırmalar neticesinde görüldüğü üzere Uyarlamalı Model Tabanlı Öngörücü Kontrol yaklaşımının bahsedilen üç adet referans kontrol yöntemine göre gezinge takibi ve kütle değişimine karşı olan gürbüzlük açısından üstünlüğü gözler önüne serilmiştir. Son olarak Model Tabanlı Öngörücü Kontrol ile karşılaştırma yapılarak uyarlamalı olanın ileride yapılacak olan uygulamalar için üstünlüğü kesinleştirilmiştir.

In this paper, a model reference fault tolerant control (FTC) strategy based on a reconfiguration of the reference model, with the addition of a virtual actuator block, is presented for linear parameter varying (LPV) systems. The advantage of the proposed FTC method is that the control system is reconfigured in such a way that the nominal controller is used without the need of retuning it. Moreover, the presence of saturations is taken into account through their incorporation in the reference model, and the introduction of additional varying parameters, such that the system exhibits some graceful performance degradation when the system could not achieve the desired state because of the actuator limits. The design of the control scheme is based on linear matrix inequalities (LMIs) and polytopic LPV techniques. In order to implement the proposed active FTC strategy, a fault estimation is required. In this paper, the fault estimation is formulated as a parameter estimation problem, which is solved using a set-membership approach. An aeronautical application is used to assess the performance of the proposed approach.

International audience; In this paper, an approach to design an Admissible Model Matching (AMM) Fault Tolerant Control (FTC) based on Linear Parameter Varying (LPV) fault representation is proposed. The main contribution of this approach is to consider the fault as a scheduling variable that allows the controller reconfiguration online. The fault is expressed as a change in the system dynamics (in particular, in the model parameters). The suggested strategy is an active technique that requires the fault to be detected, isolated and estimated by the FDI scheme. In case the fault estimation is not available, a passive strategy based on a single AMM FTC controller could be designed. The FTC controller is designed using LMI regional pole placement. The effectiveness and performances of the method have been illustrated in simulation considering a thermal hydraulic system.

This thesis focuses on the development of some fixed-order controller design methods in the gain-scheduling/Linear Parameter Varying (LPV) framework. Gain-scheduled controllers designed using frequency-domain Single Input Single Output (SISO) models are considered first, followed by LPV controller design in the SISO transfer function setting and, finally, by Multiple Input Multiple Output (MIMO) LPV controller design in the state-space setting. In addition to the guarantee of closed-loop stability, each of the methods optimizes some classical performance measure, such as the $\mathscr{H}_\infty$ or $\mathscr{H}_2$ performance metrics. In the LPV state-space setting, the practical assumption of bounded scheduling parameter variations is taken into account in order to allow a higher performance level to be achieved. The fixed-order gain-scheduled controller design method is based on frequency-domain models dependent on the scheduling parameters. Based on the linearly parameterized gain-scheduled controllers and desired open-loop transfer functions, the $\mathscr{H}_\infty$ performance of the weighted closed-loop transfer functions is presented in the Nyquist diagram as a set of convex constraints. No a posteriori interpolation is needed, so the stability and performance level are guaranteed for all values of scheduling parameters considered in the design. Controllers designed with this method are successfully applied to the international benchmark in adaptive regulation. These low-order controllers ensure good rejection of the multisinusoidal disturbance with time-varying frequencies on the active suspension testbed. One issue related to the gain-scheduled controller design using the frequency response model is the computational burden due to the constraint sampling in the frequency domain. The other is a guarantee of stability and performance for all the values of scheduling parameters, not just those treated in design. To overcome these issues, a method for the design of fixed-order LPV controllers with the transfer function representation is proposed. The LPV controller parameterization considered in this approach leads to design variables in both the numerator and denominator of the controller. Stability and $\mathscr{H}_\infty$ performance conditions for all fixed values of scheduling parameters are presented in terms of Linear Matrix Inequalities (LMIs). With a problem of rejection of a multisinusoidal disturbance with time-varying frequencies in mind, LPV controller is designed for an LTI plant with a transfer function model. The extension of these methods from SISO to MIMO systems is far from trivial. The state-space setting is used for this reason, as there the transition from SISO to MIMO systems is natural. A method for fixed-order output-feedback LPV controller design for continuous-time state-space LPV plants with affine dependence on scheduling parameters is proposed. Bounds on the scheduling parameters and their variation rates are exploited in design through the use of affine Parameter Dependent Lyapunov Functions (PDLFs). The exponential decay rate, induced $\mathscr{L}_2$-norm and $\mathscr{H}_2$ performance constraints are expressed through a set of LMIs. The proposed method is applied to the 2DOF gyroscope experimental setup. In practice control is performed using digital computers, so some effort needs to be put into the LPV controller discretization. If the discrete-time LPV model of the system is available [...]