La qualité de la dérivation numérique en ligne d’un signal bruité joue un rôle primordial dans diverses applications touchant différents domaines (1D et 2D). Dans le travail présenté, nous nous sommes intéressés aux dérivateurs type "signal". Nos travaux s’inscrivent dans ce contexte et abordent des aspects théoriques et applicatifs. Du point de vue théorique, une étude de deux familles de dérivateurs a été effectuée. En premier lieu, nous avons étudié les dérivateurs de nature algébrique [travaux du projet INRIA-Non-A] et en deuxième lieu les différentiateurs modes glissants d’ordre supérieur [travaux de Levant]. Cette étude nous a permis de décrire les points forts et les points faibles de chacune de ces approches. Suite à cette étude, une nouvelle version des dérivateurs modes glissants a été proposée. Du point de vue applicatif, une première application dans le domaine 1D est présentée et qui consiste à utiliser le dérivateur proposé pour l’identification paramétrique en ligne d’un robot SCARA à deux axes. La méthode d’identification est validée expérimentalement par comparaison des résultats obtenus avec ceux donnés par d’autres méthodes (méthode en ligne et hors ligne). La deuxième application touche au domaine 2D. Dans ce cas, nous proposons l’application du différentiateur pour la détection des contours dans une image. Pour la validation des résultats, différents essais sont réalisés pour différents types de bruits. Une étude comparative avec des méthodes classiques est effectuée. Pour pouvoir tester l’efficacité du différentiateur dans des boucles de commande nous nous sommes intéressés aux systèmes électrohydrauliques. Le système physique étudié est un servo-vérin électrohydraulique à hautes performances ayant différents modes de fonctionnement. Après une succession d’hypothèses effectuées sur le modèle de simulation, des modèles de commande sont fournis. La dernière partie de ces travaux est dédiée à la synthèse de stratégie de commande via la technique du Backstepping pour le positionnement de l’axe électrohydraulique afin de tester l’efficacité l’algorithme proposé dans des boucles de commande. Comme base de comparaison, la version classique des algorithmes modes glissants est aussi utilisée. / The quality of the on-line differentiation with a noisy signal plays an important role in various applications involving different areas (1D and 2D). In the present work, we were interested particularly to differentiation method which requires a minimal knowledge on the noise and/or the input signal. Our work is registred in this context and address both aspects theoretical and applications. From the theoretical point of view, a study of two families of differentiation algorithm was performed. Firstly, we studied the algorithm based on the algebraic development [the work of the project INRIA-ALIEN] and secondly the differentiators of higher order sliding modes [work Levant] for detailed study. This study allowed us to describe the advantages and disadvantages of each approach. Following this study, a new version of sliding modes differentiator was proposed, this last one being the main theoretical contribution of this thesis. To test the efficiency of the proposed version, differents applications were carried out. The first application in 1D is shown, which consists in use the proposed differentiator for online parametric identification of a two-axis SCARA robot. The identification method is validated experimentally by comparing the results obtained with those given by other methods (method online and offline). The second application relates to the 2D domain. In this case, we propose the implementation of the differentiator for the edge detection in an image. To validate the results, various tests are carried out for different types of noise. In order to have some comparison basis, we use the filter Canny and Prewitt masks and the gradient. To test the effectiveness of the differentiator in control loops we are interested in electrohydraulic systems. For this, a model of the hydraulic and mechanical system is made. After a consideration of some assumptions on the simulation model, the control models are provided. To separate the dynamic servovalve/ actuator, a local study is performed. The last part of this work is dedicated to the synthesis of control strategy through the backstepping technique for the positioning of the electro-hydraulic axis in order to test the effectiveness of the proposed algorithm in the control loop. As a basis for comparison, the classic version of sliding mode algorithm is also used.

Le principe du contrôle par flux de fuite magnétique (Magnetic Flux Leakage MFL) consiste à aimanter la pièce à contrôler par un champ magnétique et à détecter à l'aide d'un capteur magnétique les fuites des lignes du champ qui résultent de la présence d'un défaut dans la pièce. Dans le but d'améliorer les performances d'un dispositif de détection, le CEA et la société Vallourec collaborent pour développer un modèle numérique dédié au contrôle virtuel des défauts longitudinaux dans les tubes ferromagnétiques. Le dispositif expérimental comprend un circuit magnétique tournant à une vitesse constante autour du tube qui défile. Dans le cadre de cette thèse, on débute le problème de la modélisation sans tenir compte des effets de la vitesse de rotation, il s'agit donc de résoudre un problème d'électromagnétisme en régime magnétostatique.Pour résoudre ce problème, on propose de comparer une approche semi-analytique basée sur le formalisme des équations intégrales (EI) et une approche purement numérique utilisant les éléments finis (EF).Dans la première partie de cette thèse, après avoir établi le formalisme théorique par EI, un premier modèle considérant des matériaux ferromagnétiques à perméabilité magnétique constante (régime linéaire) a été mis en œuvre en 2D. Ce modèle a été appliqué pour un exemple de système extrait de la littérature et validé numériquement par une comparaison des résultats EI/EF. Pour une meilleure détection, il est opportun de saturer magnétiquement la pièce. Le matériau ferromagnétique est alors caractérisé par une courbe B(H) non-linéaire. Par conséquent, la deuxième partie de la thèse a été consacrée à la mise en œuvre du modèle en régime non linéaire qui tient compte de cette caractéristique.Différentes méthodes de discrétisation ont été étudiées afin de réduire le nombre d'inconnues et le temps de calcul. L'originalité de la thèse réside dans l'utilisation des fonctions d'interpolation d'ordre élevé (polynôme de Legendre) pour une discrétisation des équations intégrales par une approche de type Galerkin. Les premiers essais de validation numérique de ce modèle ont été effectués sur un système MFL simplifié. Des premiers essais de validation expérimentale pour des données obtenues par EF ont été effectués en deux phases : La première a consisté à vérifier le distribution du champ magnétique pour un tube sain et en régime magnétostatique. La deuxième phase a consisté à calculer la réponse d'un défaut dans le tube ferromagnétique en tenant en compte les effets éventuels de la rotation du circuit magnétique par rapport au tube. / The principle of the non destructive testing by magnetic flux leakage (MFL) is to magnetize the part to be inspected by a magnetic field and to detect a flaw thanks to magnetic leakage field lines due to the strong decreasing of the magnetic permeability in the flawed region. In order to improve the performance of detection, the CEA and the Vallourec society collaborate to develop a numerical model dedicated to the virtual NDT of longitudinal defects in ferromagnetic tubes. The experimental system includes a magnetic circuit rotating at a constant speed around the tube to be inspected. The modeling task is started without considering the effects of the rotational speed, so the magnetostatic regime is considered to solve the modeling problem. In the framework of this thesis, we propose to compare a semi-analytical approach based on the formalism of integral equations method (IEM) and a purely numerical approach using finite element method (FEM).In the first part of this thesis, the theoretical formalism was established. A first simple discretization scheme is been implemented in the linear regime considering a constant magnetic permeability. This first numerical model has been validated for a simplified MFL configuration extracted and modified from the literature.For better detection, it is wishable to magnetically saturate the piece under-test. The ferromagnetic material is then characterized by a B(H) curve. Therefore, the second part of the thesis was devoted to the implementation of the model in the non-linear regime that takes into account this non-linear characteristic. Different discretization schemes have been studied in order to reduce the number of unknowns and the computational time. The originality of the thesis lies in the use of basis function of high order (Legendre polynomials) associated to a Galerkin approach for the discretization of integral equations. The first numerical result has been validated on a simplified MFL system. The first results of the experimental validation based on simulated data obtain by FEM have been performed in two steps. The first one consists to verify the distribution of the magnetic field for a ferromagnetic tube without any defect and in the magnetostatic regime. The objective of the second one was to compute the response of the flaw and to evaluate the effects of the rotational speed of the magnetic circuit around the tube.

Orientador: Samuel da Silva / Resumo: Muitas aplicações da engenharia envolvem estruturas essencialmente não-lineares onde várias técnicas têm sido recentemente estudadas e investigadas por muitos pesquisadores. Dentre as várias abordagems, as que usam séries de Volterra têm apresentado propriedades úteis para fornecer um melhor entendimento para identificação e análise. Neste contexto, a presente tese propõem novas contribuições em como usar as séries de Volterra para caracterização, identificação e análise dinâmica de sistemas não-lineares usando sinais de entrada e saída e sinais somente de saída. Inicialmente, apresenta-se uma metodologia para análise de sistemas mecânicos não-lineares através das funções de resposta em frequência de alta-ordem (HOFRFs) e o conceito de HOFRFs estendidas com dados apenas de saída é introduzido e descrito em detalhes. Após isso, uma abordagem para identificação de sistemas não-lineares com base nas séries de Volterra através da expansão na base ortonormal de Kautz é proposta. Essa técnica permite identificar os seus núcleos mais facilmente e permite separar as contribuições dos termos lineares e não-lineares usando somente sinais de saída. Além disso, uma metodologia para análise modal de sistemas fracamente não-lineares sujeito a excitações com vários níveis de amplitude é também apresentada. A contribuição desse novo método reside no fato de que as HOFRFs são simplesmente estimadas como função das FRFs lineares. Basicamente, essa metodologia estende o conceito ... (Resumo completo, clicar acesso eletrônico abaixo) / Abstract: Most recent engineering applications involve structures essentially nonlinear where several techniques have been recently studied and investigated by many researchers. Among them, the methods based on Volterra series expansion have presented powerful properties to provide a better understanding for identification and analysis. In this context, the present thesis proposes new contributions in how to use Volterra series for characterization, identification and dynamical analysis of nonlinear systems based on input and output signals and output-only signals. Initially, a methodology for analysis of nonlinear mechanical systems through higher-order frequency response functions (HOFRFs) is presented and the concept of extended HOFRFs based on output-only is introduced and described in detail. Afterwards, an approach for identification of nonlinear systems based on Volterra series through the expansion onto orthonormal Kautz basis is proposed. This technique allows to identify the Volterra kernels easily and enable to split the contribution of the linear and nonlinear terms using input-output as well as output-only signals. Furthermore, a methodology for modal analysis of weakly nonlinear systems under multilevel excitation is also proposed. The contribution of this new approach lies in the fact that HOFRFs are simply computed as functions of the linear FRFs. Basically, it extends the conventional experimental modal analysis methods in order to characterize and treat no... (Complete abstract click electronic access below) / Doutor

CoordenaÃÃo de AperfeÃoamento de Pessoal de NÃvel Superior / Conselho Nacional de Desenvolvimento CientÃfico e TecnolÃgico / In this work we approach four research lines, where we began with the study of isometrically immersed hypersurfaces in a horoball. Next we studied Liouville type theorems in a complete Riemannian manifold for general operators. After we studied hypersurfaces f-minimal closed on a manifold with density, and nally we studied properly embedded minimal hypersurfaces with free boundary in a n-dimensional compact Riemannian manifold. Continuing, we obtain under a more general class operator than '-Laplacian, a Liouville type theorem for a complete Riemannian manifold, so that, prove a classication theorem for Killing graph of a foliation. Firstly, we are going to assume a weak maximum principle and that immersion is contained in a horoball, i.e., the set of bounded above Bussemann functions . We obtain an estimate for the highest quotient of r-curvatures. Moreover, under certain conditions on sectional curvature and assuming that the immersion is contained in a horoball, we forced the validity of the weak maximum principle and obtain the same estimates. Next, we establish a Choi-Wang type estimate for the rst eigenvalue of the weighter Laplacian on spaces with density in responding partially to Yau's conjecture for the rst eigenvalue weighter Laplacian for spaces with density, and moreover, we obtain an inequality Poincare type. With the estimates obtained, we establish an estimate of volume for a closed surface immersed in a space with density. Still following the study of spaces with density, we obtain a type Hientze-Karcher inequality for a compact manifold with nonempty boundary , so that, we obtain that if holds the equality than the manifold is isometric to a Euclidian ball. As consequence, we obtain under same conditions that if the f-mean curvature satisfy a bounded below than the manifold is isometric to a Euclidian ball. Finally, we obtain an estimate for the nonzero rst Steklov eigenvalue, where we are giving a answer partial to a conjecture by Fraser and Li. Moreover, as a consequence we establish an estimate for the total length of the boundary of the properly embedded minimal surfaces with free boundary in terms of its topology, thus, we proved the same when the surface is embedded in the Euclidean ball 3-dimensional. / Neste trabalho, abordamos quatro linhas de estudo, onde iniciamos com o estudo de hipersuperfcies isometricamente imersas sobre uma horobola. Em seguida estudamos Teoremas tipo Liouville para uma variedade Riemanniana completa em operadores mais gerais que o Laplaciano. Alem disso, estudamos hipersuperfcies f-mÃnimas fechadas em uma variedade com densidade e, por fim, estudamos hipersuperfÃcies mÃnimas com bordo livre, propriamente imersas em uma variedade Riemanniana compacta n-dimensional. Primeiramente, assumindo um princpio do maximo fraco e que a imersÃo està contida em uma horobola, i.e., um conjunto em que a funcÃo de Busemann à limitada superiormente, obtemos uma estimativa para o supremo do quociente das r-Ãsimas curvaturas. AlÃm disso, sob certas condiÃÃes sobre as curvaturas seccionais e assumindo que a imersÃo està contida em uma horobola, forÃamos a validade do princÃpio do mÃximo fraco e obtemos as mesmas estimativas. Prosseguindo, obtemos, para um operador mais geral que o '-Laplaciano, um teorema tipo-Liouville para uma variedade Riemanniana completa. Como aplicaÃÃo provamos um teorema de classificaÃÃo para grÃficos de Killing de uma folheaÃÃo. Em seguida, estabelecemos uma estimativa tipo Choi e Wang para o primeiro autovalor do f-Laplaciano em espaÃos com densidade, no sentido de responder parcialmente à conjectura de Yau para o primeiro autovalor do Laplaciano; alÃm disso, obtemos uma desigualdade tipo Poincarà para esse operador. Com a estimativa obtida, pudemos estabelecer uma estimativa de volume para uma superfÃcie fechada mergulhada em um espaÃo com densidade. Ainda seguindo o estudo de espaÃos com densidade, obtemos uma desigualdade tipo Heintze-Karcher para uma variedade compacta com bordo e verificamos que, se vale a igualdade, entÃo a variedade à isomÃtrica a uma bola Euclidiana. Como consequÃncia, obtemos que, nas mesmas condiÃÃes, e se a f-curvatura mÃdia satisfizer uma certa limitaÃÃo inferior, entÃo a variedade ainda à isometrica a uma bola Euclidiana. Finalmente, obtemos uma estimativa para o primeiro autovalor de Steklov, dando uma resposta parcial a uma conjectura devida a Fraser e Li. AlÃm disso, como consequÃncia, estabelecemos uma estimativa para o comprimento do bordo de uma superfÃcie mÃnima, compacta e propriamente megulhada com bordo livre em termos de sua topologia; assim, provamos o mesmo resultado quando a superfÃcie està mergulhada em uma bola Euclidiana 3-dimensional.

Em Complexidade Descritiva investigamos o uso de logicas para caracterizar classes problemas pelo vies da complexidade. Desde 1974, quando Fagin provou que NP e capturado pela logica existencial de segunda-ordem, considerado o primeiro resultado da area, outras relac~oes entre logicas e classes de complexidade foram estabelecidas. Os resultados mais conhecidos normalmemte envolvem logica de primeira-ordem e suas extens~oes, e classes de complexidade polinomiais em tempo ou espaco. Alguns exemplos sÃo que a logica de primeira-ordem estendida com o operador de menor ponto xo captura a clsse P e que a logica de segunda-ordem estendida com o operador de fecho transitivo captura a classe PSPACE. Nesta dissertaÃÃo, analisaremos inicialmente a expressividade de algumas logicas modais com relacÃo ao problema de decisÃo REACH e veremos que e possvel expressa-lo com as logicas temporais CTL e CTL. Analisaremos tambem o uso combinado de logicas de ordem superior com o operador de menor ponto xo e obteremos como resultado que cada nvel dessa hierarquia captura cada nvel da hierarquia determinstica em tempo exponencial. Como corolario, provamos que a hierarquia de HOi(LFP) nÃo colapsa, ou seja, HOi(LFP) HOi+1(LFP) / In Descriptive Complexity, we investigate the use of logics to characterize computational classes os problems through complexity. Since 1974, when Fagin proved that the class NP is captured by existential second-order logic, considered the rst result in this area, other relations between logics and complexity classes have been established. Wellknown results usually involve rst-order logic and its extensions, and complexity classes in polynomial time or space. Some examples are that the rst-order logic extended by the least xed-point operator captures the class P and the second-order logic extended by the transitive closure operator captures the class PSPACE. In this dissertation, we will initially analyze the expressive power of some modal logics with respect to the decision problem REACH and see that is possible to express it with temporal logics CTL and CTL. We will also analyze the combined use of higher-order logics extended by the least xed-point operator and obtain as result that each level of this hierarchy captures each level of the deterministic exponential time hierarchy. As a corollary, we will prove that the hierarchy of HOi(LFP), for i 2, does not collapse, that is, HOi(LFP) HOi+1(LFP)

Several active learning strategies have been used when increasing the structure of a course as increasing course structure has been known to improve student learning in introductory STEM courses. Much has been studied on the value of frequent formative assessment; however, few studies have evaluated the effective modes of delivering summative assessment. This study examines the use of summative assessment as an inclusive teaching practice to improve first generation college student success in introductory biology and also uses faculty surveys to find out how instructors structure their introductory biology course and why they are structured that way. Final exams were evaluated by Bloom’s Taxonomy of Learning. Survey results showed that many instructors used online activities most of the time to supplement face-to-face courses. However, student and faculty viewpoints on assessments offer many interesting insights into how instructors may modify teaching strategies to increase the success of diverse student populations.

Gegenstand dieser Dissertation sind die Auswirkungen von Unsicherheit, die hohe Aufmerksamkeit unter Akademikern und Politikern erregt hat. Der erste Aufsatz beschäftigt sich mit den Folgen von Unsicherheit, die von Finanzmärkten ausgeht. Zu diesem Zweck belege ich die empirische Relevanz von Finanzmarktunsicherheit mithilfe von SVAR Methoden. Anschließend benutze ich das von Gertler and Karadi (2011) entwickelte DSGE-Modell, um den Transmissionsmechanismus aufzudecken. Im Einklang mit der empirischen Evidenz impliziert das Modell einen Rückgang der Wirtschaftsleistung als Reaktion auf einen Anstieg der Finanzmarktunsicherheit. Dieses Ergebnis entsteht hauptsächlich aufgrund einer Verschärfung der endogenen Leverage-Beschränkung, die den finanziellen Akzelerator auslöst. Im zweiten Aufsatz schlage ich eine asymptotische Perturbationsmethode vor, um DSGE Modelle mit endogener Portfolioentscheidung zu lösen. Im Gegensatz zu existierenden Verfahren kann sie benutzt werden, um Approximationen höheren Grades von Bruttovermögenswerten zu ermitteln. Der vorgeschlagene Lösungsalgorithmus wird evaluiert, indem ich ein Lucas-Tree-Modell mit Portfolioentscheidung löse. Der Schwerpunkt liegt dabei auf den Folgen von struktureller Heterogenität in der Unsicherheit zwischen den Ländern. Die vorgeschlagene Methode erfasst diese Asymmetrie und kann zu einer Verbesserung von der Qualität der Approximation führen. Der dritte Aufsatz untersucht die Folgen von globalen Unsicherheitsschocks für die Bankenportfolios und die makroökonomischen Aggregate. Zu diesem Zweck benutze ich ein Zwei-Länder DSGE Modell mit endogener Portfolioentscheidung und Bilanzrestriktionen im Bankensektor. Die Bankenportfolios sind charakterisiert durch einen Home Bias, der mit den Daten konsistent ist. Außerdem führt ein Anstieg der Finanzmarktunsicherheit zum Rückgang der grenzüberschreitenden Bruttoanlagen und der Wirtschaftsleistung weltweit. Dies entspricht den Entwicklungen während der globalen Finanzkrise. / This thesis examines the macroeconomic implications of uncertainty which has attracted attention within both the academic literature and policy community. The first essay investigates the effects of uncertainty originating in financial markets. To this end, I first document empirical relevance of financial uncertainty using SVAR methods. Second, I employ the DSGE framework developed by Gertler and Karadi (2011) to uncover the underlying transmission mechanism. In line with the empirical evidence, the model generates a decline in economic activity in response to an increase in financial uncertainty. This outcome arises mainly because of tightening of leverage constraints which in turn triggers the financial accelerator mechanism. In the second essay, I propose an asymptotic perturbation method to solve DSGE models with endogenous portfolio choice. In contrast to existing local techniques, it can be used to compute a higher-order approximation of gross asset holdings. I evaluate the proposed method by solving a Lucas tree model with portfolio choice. The focus lies on implications of cross-country structural heterogeneity in economic uncertainty for international asset holdings. The proposed method accounts for these asymmetries and can consequently lead to an improvement in quality of the approximation. Finally, the third essay examines the consequences of global uncertainty shocks for banking portfolios and macroeconomic aggregates. To this end, I employ a two-country DSGE model with balance-sheet constrained financial intermediaries and endogenous portfolio choice. Countries are assumed to be ex-ante asymmetric, which allows me to consider both developed and emerging economies. The model implies a home bias in banking assets that is consistent with the data. Moreover, an increase in financial uncertainty leads to a decline in cross-border portfolios and a worldwide reduction in economic activity, which is consistent with dynamics observed during the global financial crisis.

Cette thèse concerne le problème de désocclusion d'images, au moyen des équations aux dérivées partielles. Dans la première partie de la thèse, la désocclusion est modélisée par un problème de Cauchy qui consiste à déterminer une solution d'une équation aux dérivées partielles avec des données aux bords accessibles seulement sur une partie du bord de la partie à recouvrir. Ensuite, on a utilisé des algorithmes de minimisation issus de la théorie des jeux, pour résoudre ce problème de Cauchy. La deuxième partie de la thèse est consacrée au choix des paramètres de régularisation pour des EDP d'ordre deux et d'ordre quatre. L'approche développée consiste à construire une famille de problèmes d'optimisation bien posés où les paramètres sont choisis comme étant une fonction variable en espace. Ceci permet de prendre en compte les différents détails, à différents échelles dans l'image. L'apport de la méthode est de résoudre de façon satisfaisante et objective, le choix du paramètre de régularisation en se basant sur des indicateurs d'erreur et donc le caractère à posteriori de la méthode (i.e. indépendant de la solution exacte, en générale inconnue). En outre, elle fait appel à des techniques classiques d'adaptation de maillage, qui rendent peu coûteuses les calculs numériques. En plus, un des aspects attractif de cette méthode, en traitement d'images est la récupération et la détection de contours et de structures fines. / Image inpainting refers to the process of restoring a damaged image with missing information. Different mathematical approaches were suggested to deal with this problem. In particular, partial differential diffusion equations are extensively used. The underlying idea of PDE-based approaches is to fill-in damaged regions with available information from their surroundings. The first purpose of this Thesis is to treat the case where this information is not available in a part of the boundary of the damaged region. We formulate the inpainting problem as a nonlinear boundary inverse problem for incomplete images. Then, we give a Nash-game formulation of this Cauchy problem and we present different numerical which show the efficiency of the proposed approach as an inpainting method.Typically, inpainting is an ill-posed inverse problem for it most of PDEs approaches are obtained from minimization of regularized energies, in the context of Tikhonov regularization. The second part of the thesis is devoted to the choice of regularization parameters in second-and fourth-order energy-based models with the aim of obtaining as far as possible fine features of the initial image, e.g., (corners, edges, … ) in the inpainted region. We introduce a family of regularized functionals with regularization parameters to be selected locally, adaptively and in a posteriori way allowing to change locally the initial model. We also draw connections between the proposed method and the Mumford-Shah functional. An important feature of the proposed method is that the investigated PDEs are easy to discretize and the overall adaptive approach is easy to implement numerically.

Les effets d’extrémité jouent un rôle important dans la modélisation et la commande de la Machine Linéaire à Induction (MLI). Ces phénomènes augmentent significativement la non-linéarité du modèle de la machine et génèrent plusieurs difficultés pour contrôler et observer ses états avec de bonnes performances. Cette thèse aborde trois problématiques distinctes : la commande robuste de la MLI, l’estimation de la vitesse et du flux de la MLI et le contrôle robuste à base d’observateur en utilisant la théorie du mode glissant d’ordre supérieur.Dans la première partie de la thèse, trois contrôleurs robustes assurant la poursuite de trajectoire de la vitesse et du flux pour la MIL ont été développés : le Super Twisting (ST), le Super Twisting Adaptatif (STA) et le Twisting Adaptatif (TA). Ces commandes ont été testées en simulations et leurs performances ont été démontrées. Ainsi, le ST assure un contrôle continu avec convergence à temps fini de l’erreur à zéro malgré les perturbations, sous l’hypothèse que les bornes des incertitudes sont connues. Cette hypothèse est relaxée dans le cas du TA et du STA grâce à leurs propriétés adaptatives.Dans la deuxième partie de la thèse, un nouveau modèle du MLI a été proposé et son observabilité a été démontrée. Ensuite un Observateur par Mode Glissant d’Ordre Deux (MGOD) et un Observateur par Mode Glissant d’Ordre Supérieur (MGOS) ont été synthétisé afin d’estimer la vitesse et le flux du MLI, uniquement en utilisant la mesure des tensions et des courants statorique. La stabilité des deux observateurs a été prouvée par une approche de Lyapunov et leurs performances ont été démontrées à travers des simulations.Dans la dernière partie de la thèse, deux commandes par rejet actif des perturbations sont synthétisées. Ainsi et dans un premier temps, le modèle de la MLI est décomposé en deux sous-systèmes du second ordre. Ensuite, deux contrôleurs (le twisting et le super-twsiting) ont été synthétisés afin d’assurer la poursuite du flux et de la vitesse. Le MGOS est utilisé pour estimer les dérivées du flux et de la vitesse, ainsi que pour l’estimation en temps réel de la perturbation. Les contrôleurs quant à eux assurent la compensation des perturbations et la poursuite des trajectoires du flux et de la vitesse. La stabilité et la convergence des deux commandes proposées ont été prouvées et leurs performances démontrées par simulation. / Dynamic end effects play an important role in the Linear Induction Machine (LIM) control. They increase significantly the nonlinearity of the machine model and generate several difficulties to control and observe states with good performances. This thesis addresses three distinctissues: LIM robust control, LIM speed and flux estimation and observer-based robust control using higher order sliding mode theory.In the first part, to achieve speed and flux tracking,Super Twisting Controller (STC), Adaptive Super Twisting Controller (ASTC), and Adaptive Twisting Controller (ATC) were proposed and implemented into LIM system with great performance, i.e. finite time convergence and robustness properties. Among them, STC ensures continuous control with finite time convergence of the error to zero despite disturbances, under the assumption that their bounds are known. ATC and ASTC can deal with unknown bounded disturbance thanks to their adaptive properties.In the second part, a novel simplified LIM model was proposed and its observability has been proved. Then, Second Order Sliding Mode Observer (SOSMO) and Adaptive High Order Sliding Mode Observer (HOSMO) were proposed to estimate LIM speed, only by using the measured stator voltages and stator currents. SOSMO observer is based on the super twisting algorithm and its stability has been proved with Lyapunov’s theory, which can guarantee finite time convergence with less chattering. Adaptive HOSMO strategy combines speed adaptive algorithm and HOSMO method together to estimate rotor fluxes and speed simultaneously.In the third part, the LIM is viewed as two second order subsystems. Moreover, only the speed and the flux are supposed to be measured. Based on that two differentcontrollers based on HOSMO were presented in order to achieve flux and speed tracking. In both controllers, the idea of active disturbance rejection control is applied. Hence, the HOSMO is used to estimate the derivatives of the flux and the speed, as well as the disturbance. Then, in order to deal with the uncertainty in the measured variables, two different SM controllers are proposed. Firstly, the TC is applied in the LIM. However, the control signal in this case is discontinuous. Then, in order to provide a continuous control signal, the TC is replaced with STC. The stability and convergence of proposed TC-HOSMO and STC-HOSMO approaches were given and simulation validated their performances.

Cette thèse porte sur le développement de nouvelles stratégies de commande et d’observation adaptatives par Modes Glissants (MG) et par Modes Glissants d’Ordres Supérieurs (MGOS). En effet, la mise en œuvre des commandes par MG et MGOS classiques nécessite la connaissance des limites supérieures des perturbations ou de leurs dérivées, souvent inconnues. Le premier apport de cette thèse est la synthèse d’une stratégie d’adaptation permettant d'assurer la convergence de la variable de glissement vers un voisinage prédéfini de zéro sans nécessiter d'informations sur les perturbations ou leurs dérivées et sans surestimation du gain. Cette stratégie est ensuite déclinée pour concevoir : deux commandes par MG d’ordre 1 et 2, une commande par mode glissant intégral, ainsi qu’une version du différenciateur de Levant. La deuxième contribution de la thèse est la mise au point de deux commandes adaptatives par MGOS discontinues. Ces deux algorithmes assurent un mode glissant d'ordre n en s’affranchissant de la connaissance de la limite supérieure de la perturbation et de sa dérivée. Enfin, afin de montrer l’efficacité des algorithmes proposés, ils sont appliqués avec succès à travers des simulations pour la commande d’un système de conversion de l’énergie éolienne et la commande d’un moteur à induction linéaire pour la cogénération. / This thesis deals with the development of novel strategies to adapt higher order sliding mode controllers and observers. The implementation of classics first order and higher order sliding mode controllers requires the knowledge of the upper bound of the disturbance or its derivative, which are often not known. The first contribution of this thesis is the design of an adaptive strategy that can ensure the convergence of the sliding variable to a predefined neighborhood of zero without requiring any information of the disturbance or its derivative and without overestimating the adaptive gain. This adaptive strategy is then declined for the design of the first order, second order and integral sliding mode controllers, and for the Levant's differentiator. The second contribution of the thesis is the development of two adaptive strategies for discontinuous higher order sliding mode control. The proposed two algorithms can provide the achievement of n-order sliding mode despite disturbances with unknown upper bounds or with unknown upper bounds of their derivatives. Finally, in order to show the effectiveness of the proposed algorithms, they are successfully applied through simulations to control the wind energy conversion system and the linear induction motor system for cogeneration.