Cette thèse présente un nouveau cadre pour la conception de correcteurs à gain programmé. Une partie de ce cadre est une fusion novatrice de la théorie des systèmes et de la commande (la métrique ν-gap et sa variante fréquentiellle) et de l'analyse en grappes, technique commune en analyse de données statistiques, apprentissage automatique, fouille de données, etc. La combinaison des deux champs permet de subdiviser le domaine de fonctionnement d'un système non linéaire en secteurs afin de récupérer des informations sur le comportement en boucle fermée avant la conception de la commande. Chaque secteur représente une partie du domaine opérationnel ayant des propriétés de retour similaires, c'est-à-dire que les points de fonctionnement dans un secteur ont des comportements davantage similaires (mesurés par la mesure d'écart ponctuel) les uns des autres que les points de fonctionnement des autres secteurs. La solution de sectorisation est utilisée en vue de réaliser des correcteurs séquencés réglés à partir d'un modèle linéarisé. Par exemple, une distribution optimisée et parcimonieuse des points de synthèse pour les correcteurs LTI est sélectionnée et la distribution des secteurs est exploitée pour le mélange des correcteurs linéaires individuels en un correcteur non-linéaire couvrant l'ensemble du domaine de fonctionnement. L'avantage général de ce cadre est qu'il présente une procédure systématique qui réduit potentiellement le temps, les efforts et donc le coût global d'un projet de développement en réduisant les itérations inutiles au cours du cycle de conception. Le cadre proposé est évalué à partir d’un exemple générique de missile industriel. / This thesis presents a new framework for the design of gain-scheduled controllers. Part of this framework is a novel merging of system & control theory (the ν-gap and pointwise gap metric) and cluster analysis, a common technique in statistical data analysis, machine learning, data mining, etc. The combination of both fields allows for a subdivision of a nonlinear system's operating domain into sectors in order to retrieve information on the feedback behaviour before the actual control design. Each sector represents a part of the operating domain with similar feedback properties, i.e. operating points inside a sector are more similar (as measured by the pointwise gap metric) to each other than to operating points in other sectors. The sectoring solution is used in the proposed framework to support the design of a linearization-based gain-scheduled controller. For example, a reduced and optimized distribution of design points for the LTI controllers is selected and the sectors' distribution is exploited for the blending of the individual linear controllers into an operating domain wide nonlinear controller. The overall advantage of the framework is that it presents a systematic procedure that potentially reduces the overall time, effort, and therefore cost of a development project by preventing unnecessary iterations in the design cycle specifically associated with the control design. The proposed framework is verified at the example of a generic industrial missile benchmark.

Submitted by PPG Engenharia El?trica (engenharia.pg.eletrica@pucrs.br) on 2018-03-26T18:49:00Z No. of bitstreams: 1 MATHEUS_SENNA_OLIVEIRA_DIS.pdf: 2367932 bytes, checksum: 927039b4746ebdc5d7da25318435b24a (MD5) / Approved for entry into archive by Tatiana Lopes (tatiana.lopes@pucrs.br) on 2018-04-06T17:26:05Z (GMT) No. of bitstreams: 1 MATHEUS_SENNA_OLIVEIRA_DIS.pdf: 2367932 bytes, checksum: 927039b4746ebdc5d7da25318435b24a (MD5) / Made available in DSpace on 2018-04-06T17:38:56Z (GMT). No. of bitstreams: 1 MATHEUS_SENNA_OLIVEIRA_DIS.pdf: 2367932 bytes, checksum: 927039b4746ebdc5d7da25318435b24a (MD5) Previous issue date: 2018-01-31 / Coordena??o de Aperfei?oamento de Pessoal de N?vel Superior - CAPES / Este documento apresenta um trabalho de disserta??o sobre o estudo de estrat?gias de controle para o seguimento eficiente de padr?es espirais. Estes padr?es podem ser aplicados em muitas ?reas, como por exemplo, a Microscopia de For?a At?mica, onde padr?es de referenciais r?pidos e suaves s?o requeridos. Para realizar com sucesso o seguimento destas refer?ncias, que s?o compostas de sinais senoidais de amplitude e frequ?ncia vari?vel, estrat?gias de controle avan?adas foram investigadas. O Princ?pio do Modelo Interno ? uma abordagem tradicional para o seguimento de sinais, mas ele n?o pode ser aplicado diretamente em sinais com frequ?ncia variante. Logo, o presente trabalho prop?s uma estrat?gia de controle robusto onde o Princ?pio do Modelo Interno foi aplicado como um Controlador Ressonante em uma estrutura aumentada e variante no tempo. O sistema aumentado e os valores da frequ?ncia foram organizados usando uma representa??o polit?pica e estruturados como um problema de otimiza??o sujeito a restri??es na forma de Desigualdades Matriciais Lineares. Esta s?ntese foi avaliada atrav?s de um conjunto de simula??es, usando um modelo num?rico de um Microsc?pio de For?a At?mica e um novo padr?o de refer?ncia para escaneamento apropriado. Al?m disso, usando a premissa que estes sinais de refer?ncia s?o aplicados m?ltiplas vezes, um Controle por Aprendizagem Iterativa tamb?m foi projetado para melhorar o desempenho do seguimento da estrat?gia principal proposta. Resultados num?ricos demonstraram que o controlador projetado atingiu resultados satisfat?rios, em compara??o com o controlador tradicional dispon?vel na ?rea. / This document presents a dissertation work regarding the study of control strategies for the efficient tracking of spiral patterns. Such patterns arise in many areas, as for example the Atomic Force Microscopy, where fast and smooth reference signals are required. In order to successfully track the above mentioned references, which are composed of amplitude and frequency-varying sinusoidal signals, advanced control strategies were investigated. The Internal Model Principle is a traditional approach to track reference signals, but it cannot be directly applied in frequency-varying signals. Therefore, the present work proposed a robust control strategy where the Internal Model Principle was applied as a Resonant Control in an augmented time-varying structure. The augmented system and the reference frequency values were organized using a polytopic representation and structured as an optimization problem subject to constraints in the form of Linear Matrix Inequalities. This synthesis was evaluated through a set of simulations, using a numerical model of an Atomic Force Microscope and a new suitable scanning reference pattern. Moreover, using the premise that the same reference signals are tracked multiple times, an Iterative Learning Controller was also designed in order to improve the tracking performance of the proposed main strategy. Numerical results demonstrated that the designed controller achieved satisfactory results, in comparison to the traditional controller available in the area.

Cette thèse porte sur les problèmes de stabilité en fréquence et en tension des microréseaux isolés avec forte pénétration d'énergies renouvelables en utilisant des dispositifs de stockage d'énergie, et se divise en deux parties principales.Dans la première partie, nous proposons une conception systématique d'une structure de commande robuste multi-variable pour le réglage de fréquence dans un système de génération de puissance hybride diesel-photovoltaïque-supercondensateur fonctionnant en mode autonome. La structure de commande proposée repose sur une architecture à deux niveaux: les contrôleurs d'asservissement de courant basés sur commande PI classique sont placés sur le niveau de commande inférieur et reçoivent des références d'un niveau supérieur qui, lui, est basé sur commande H-infini. Une méthodologie compréhensive qui traduit les demandes d'ingénierie spécifiques de l'opération du microréseau dans le formalisme de commande H-infini est détaillée. Nous montrons également comment les spécifications de performance dynamiques en boucle fermée doivent à leur tour être prises en compte dans la configuration et le dimensionnement initiaux du microréseau, c'est-à-dire en choisissant de manière appropriée et en évaluant le système de stockage d'énergie. Ensuite, une analyse de performance robuste du contrôleur H-infini synthétisé en présence de diverses perturbations de charge, des variations de puissance active de la source photovoltaïque, et des incertitudes du modèle est effectuée afin de déterminer la plage de variation maximale des paramètres pour laquelle les performances de commande imposées sont respectées pour le point de fonctionnement considéré. Les simulations numériques réalisées avec MATLAB/Simulink montrent l'efficacité de la stratégie de commande robuste de fréquence proposée sur un microréseau d'ordre de quelques MVA. Un banc de test de prototypage rapide, qui est composé d'un système de stockage d'énergie réel à base de supercondensateurs et un réseau diesel-photovoltaïque-charge émulé, est développé afin de valider expérimentalement cette stratégie de commande.La deuxième partie de cette thèse se concentre sur le calcul d'un contrôleur de tension multi-variable basé sur commande H-infini afin de forcer robustement l'amplitude de tension du point de couplage commun à satisfaire des spécifications dynamiques. La même idée de la structure de commande à deux niveaux en cascade - où ce contrôleur est placé sur un niveau de commande supérieur et fournit les références de courant aux contrôleurs de courant placés sur un niveau inférieur - est également adoptée. Ensuite, la performance et la robustesse du contrôleur H-infini proposé en présence de diverses perturbations de puissance réactive de la charge et de la source photovoltaïque, ainsi que des incertitudes du modèle, sont étudiées en utilisant des simulations temporelles MATLAB/Simulink. / This thesis addresses the frequency and voltage stability issues of stand-alone microgrids with high penetration of renewable energy by making use of energy storage devices, and is divided into two main parts.In the first part, we propose a systematic design of a multi-variable robust control structure for frequency regulation in a diesel-photovoltaic-supercapacitor hybrid power generation system operating in stand-alone mode. The proposed control structure relies on a two-level architecture: classical PI-based current tracking controllers are placed on the low control level and receive references from an H-infinity-control-based upper level. A comprehensive methodology that casts the specific engineering demands of microgrid operation into H-infinity control formalism is detailed. It is also shown how closed-loop dynamic performance requirements must at their turn be taken into account in the initial microgrid setup and sizing, namely in appropriately choosing and rating the energy storage system. Then, a robust performance analysis of the synthesized H-infinity controller in the presence of various load disturbances, photovoltaic output active power variations, and model uncertainties is carried out in order to determine the maximum parameter variation range for which the imposed control performances are respected for the considered operating point. Numerical simulations performed with MATLAB/Simulink show the effectiveness of the proposed frequency robust control strategy on a MVA-rated microgrid. A rapid-prototyping test bench, which is composed of a real supercapacitor-based energy storage system and an emulated diesel-photovoltaic-load grid, is developed in order to experimentally validate this control strategy.The second part of this thesis focuses on computing an H-infinity-based multi-variable voltage controller in order to robustly force the voltage magnitude of the point of common coupling to satisfy dynamic specifications. The same idea of cascaded two-level control structure - where this controller is placed on an upper control level and provides the references to current controllers placed on a lower level - is aslo adopted. Then, the performance and robustness of the proposed H-infinity controller in the presence of various load and photovoltaic reactive power disturbances, as well as model uncertainties, are studied based on MATLAB/Simulink time-domain simulations.

Estuda-se o problema de sintonia de controladores, objetivando-se a formulação do problema de sintonia ótima de controladores. Busca-se uma formulação que seja geral, ou seja, válida para qualquer estrutura de controlador e qualquer conjunto de especificações. São abordados dois temas principais: especificação de controladores e sintonia ótima de controladores. São compiladas as principais formas de especificação e avaliação de controladores e é feita a formulação do problema de sintonia de controladores como um problema padrão de otimização. A abordagem proposta e os conceitos apresentados são então aplicados em um conjunto de exemplos. / The problem of control tuning is studied, aiming the formulation of the optimal control tuning problem. A general formulation, valid for any controller structure and any set of specifications, is sought. Two main themes are addressed: controller specification and optimal controller tuning. The main ways of controller specification and assessment are compiled and the optimal controller tuning problem is formulated as a standard optimization problem. The proposed approach and the presented concepts are then applied in a set of examples.

"Side channel attacks (SCA) pose a serious threat on many cryptographic devices and are shown to be effective on many existing security algorithms which are in the black box model considered to be secure. These attacks are based on the key idea of recovering secret information using implementation specific side-channels. Especially active fault injection attacks are very effective in terms of breaking otherwise impervious cryptographic schemes. Various countermeasures have been proposed to provide security against these attacks. Double-Data-Rate (DDR) computation, dual-rail encoding, and simple concurrent error detection (CED) are the most popular of these solutions. Even though these security schemes provide sufficient security against weak adversaries, they can be broken relatively easily by a more advanced attacker. In this dissertation, we propose various error detection techniques that target strong adversaries with advanced fault injection capabilities. We first describe the advanced attacker in detail and provide its characteristics. As part of this definition, we provide a generic metric to measure the strength of an adversary. Next, we discuss various techniques for protecting finite state machines (FSMs) of cryptographic devices against active fault attacks. These techniques mainly depend on nonlinear robust codes and physically unclonable functions (PUFs). We show that due to the nonuniform behavior of FSM variables, securing FSMs using nonlinear codes is an important and difficult problem. As a solution to this problem, we propose error detection techniques based on nonlinear codes with different randomization methods. We also show how PUFs can be utilized to protect a class of FSMs. This solution provides security on the physical level as well as the logical level. In addition, for each technique, we provide possible hardware realizations and discuss area/security performance. Furthermore, we provide an error detection technique for protecting elliptic curve point addition and doubling operations against active fault attacks. This technique is based on nonlinear robust codes and provides nearly perfect error detection capability (except with exponentially small probability). We also conduct a comprehensive analysis in which we apply our technique to different elliptic curves (i.e. Weierstrass and Edwards) over different coordinate systems (i.e. affine and projective). "

The primary goal of this thesis is to evaluate vibration control of an all-clamped plate having an unknown disturbance. The vibration control is implemented using a piezoelectric actuator placed at an optimal location. The first part of this thesis considers a robust actuator placement with respect to varying spatial distributions of disturbances. The treatment here, is different from performance-based LQR approaches, since it is based on minimizing the effect of the disturbance distributions. The second part of this thesis addresses a more general case where the plate is under an unknown disturbance. An unknown disturbance is also characterized by the case where the disturbance signal moves randomly over the entire spatial domain. An optimal switching controller algorithm is developed, based on LQR performance, which switches between piezoelectric actuators employed for the vibration control of the plate. A single actuator is selected from the various actuator locations during each time interval, which leads to performance enhancement.

Over the last two decades, the field of educational data mining (EDM) has been focusing on predicting the correctness of the next student response to the question (e.g., [2, 6] and the 2010 KDD Cup), in other words, predicting student short-term performance. Student modeling has been widely used for making such inferences. Although performing well on the immediate next problem is an indicator of mastery, it is by far not the only criteria. For example, the Pittsburgh Science of Learning Center's theoretic framework focuses on robust learning (e.g., [7, 10]), which includes the ability to transfer knowledge to new contexts, preparation for future learning of related skills, and retention - the ability of students to remember the knowledge they learned over a long time period. Especially for a cumulative subject such as mathematics, robust learning, particularly retention, is more important than short-term indicators of mastery. The Automatic Reassessment and Relearning System (ARRS) is a platform we developed and deployed on September 1st, 2012, which is mainly used by middle-school math teachers and their students. This system can help students better retain knowledge through automatically assigning tests to students, giving students opportunity to relearn the skill when necessary and generating reports to teachers. After we deployed and tested the system for about seven months, we have collected 287,424 data points from 6,292 students. We have created several models that predict students' retention performance using a variety of features, and discovered which were important for predicting correctness on a delayed test. We found that the strongest predictor of retention was a student's initial speed of mastering the content. The most striking finding was that students who struggled to master the content (took over 8 practice attempts) showed very poor retention, only 55% correct, after just one week. Our results will help us advance our understanding of learning and potentially improve ITS.

"The goal of this thesis is to extend the theory and practice of matrix completion algorithms, and how they can be utilized, improved, and scaled up to handle large data sets. Matrix completion involves predicting missing entries in real-world data matrices using the modeling assumption that the fully observed matrix is low-rank. Low-rank matrices appear across a broad selection of domains, and such a modeling assumption is similar in spirit to Principal Component Analysis. Our focus is on large scale problems, where the matrices have millions of rows and columns. In this thesis we provide new analysis for the convergence rates of matrix completion techniques using convex nuclear norm relaxation. In addition, we validate these results on both synthetic data and data from two real-world domains (recommender systems and Internet tomography). The results we obtain show that with an empirical, data-inspired understanding of various parameters in the algorithm, this matrix completion problem can be solved more efficiently than some previous theory suggests, and therefore can be extended to much larger problems with greater ease. "

Recent advances in robust subspace estimation have made dimensionality reduction and noise and outlier suppression an area of interest for research, along with continuous improvements in computer vision applications. Due to the nature of image and video signals that need a high dimensional representation, often storage, processing, transmission, and analysis of such signals is a difficult task. It is therefore desirable to obtain a low-dimensional representation for such signals, and at the same time correct for corruptions, errors, and outliers, so that the signals could be readily used for later processing. Major recent advances in low-rank modelling in this context were initiated by the work of Cand`es et al. [17] where the authors provided a solution for the long-standing problem of decomposing a matrix into low-rank and sparse components in a Robust Principal Component Analysis (RPCA) framework. However, for computer vision applications RPCA is often too complex, and/or may not yield desirable results. The low-rank component obtained by the RPCA has usually an unnecessarily high rank, while in certain tasks lower dimensional representations are required. The RPCA has the ability to robustly estimate noise and outliers and separate them from the low-rank component, by a sparse part. But, it has no mechanism of providing an insight into the structure of the sparse solution, nor a way to further decompose the sparse part into a random noise and a structured sparse component that would be advantageous in many computer vision tasks. As videos signals are usually captured by a camera that is moving, obtaining a low-rank component by RPCA becomes impossible. In this thesis, novel Approximated RPCA algorithms are presented, targeting different shortcomings of the RPCA. The Approximated RPCA was analysed to identify the most time consuming RPCA solutions, and replace them with simpler yet tractable alternative solutions. The proposed method is able to obtain the exact desired rank for the low-rank component while estimating a global transformation to describe camera-induced motion. Furthermore, it is able to decompose the sparse part into a foreground sparse component, and a random noise part that contains no useful information for computer vision processing. The foreground sparse component is obtained by several novel structured sparsity-inducing norms, that better encapsulate the needed pixel structure in visual signals. Moreover, algorithms for reducing complexity of low-rank estimation have been proposed that achieve significant complexity reduction without sacrificing the visual representation of video and image information. The proposed algorithms are applied to several fundamental computer vision tasks, namely, high efficiency video coding, batch image alignment, inpainting, and recovery, video stabilisation, background modelling and foreground segmentation, robust subspace clustering and motion estimation, face recognition, and ultra high definition image and video super-resolution. The algorithms proposed in this thesis including batch image alignment and recovery, background modelling and foreground segmentation, robust subspace clustering and motion segmentation, and ultra high definition image and video super-resolution achieve either state-of-the-art or comparable results to existing methods.

Dans le secteur de l'automobile, les turbomachines sont des machines tournantes participant au refroidissement des moteurs des voitures. Leur performance dépend de multiples paramètres géométriques qui déterminent leur forme. Cette thèse s'inscrit dans le projet ANR PEPITO réunissant industriels et académiques autour de l'optimisation de ces turbomachines. L'objectif du projet est de trouver la forme du ventilateur maximisant le rendement en certains points de fonctionnement. Dans ce but, les industriels ont développé des codes CFD (computational fluid dynamics) simulant le fonctionnement de la machine. Ces codes sont très coûteux en temps de calcul. Il est donc impossible d'utiliser directement le résultat de ces simulations pour conduire une optimisation.Par ailleurs, lors de la construction des turbomachines, on observe des perturbations sur les paramètres d'entrée. Elles sont le reflet de fluctuations des machines de production. Les écarts observés sur la forme géométrique finale de la turbomachine peuvent provoquer une perte de performance conséquente. Il est donc nécessaire de prendre en compte ces perturbations et de procéder à une optimisation robuste à ces fluctuations. Dans ce travail de thèse, nous proposons des méthodes basées sur du krigeage répondant aux deux principales problématiques liées à ce contexte de simulations coûteuses :• Comment construire une bonne surface de réponse pour le rendement lorsqu'il y a beaucoup de paramètres géométriques ?• Comment procéder à une optimisation du rendement efficace tout en prenant en compte les perturbations des entrées ?Nous répondons à la première problématique en proposant plusieurs algorithmes permettant de construire un noyau de covariance pour le krigeage adapté à la grande dimension. Ce noyau est un produit tensoriel de noyaux isotropes où chacun de ces noyaux est lié à un sous groupe de variables d'entrée. Ces algorithmes sont testés sur des cas simulés et sur une fonction réelle. Les résultats montrent que l'utilisation de ce noyau permet d'améliorer la qualité de prédiction en grande dimension. Concernant la seconde problématique, nous proposons plusieurs stratégies itératives basées sur un co-krigeage avec dérivées pour conduire l'optimisation robuste. A chaque itération, un front de Pareto est obtenu par la minimisation de deux objectifs calculés à partir des prédictions de la fonction coûteuse. Le premier objectif représente la fonction elle-même et le second la robustesse. Cette robustesse est quantifiée par un critère estimant une variance locale et basée sur le développement de Taylor. Ces stratégies sont comparées sur deux cas tests en petite et plus grande dimension. Les résultats montrent que les meilleures stratégies permettent bien de trouver l'ensemble des solutions robustes. Enfin, les méthodes proposées sont appliquées sur les cas industriels propres au projet PEPITO. / The turbomachineries are rotary machines used to cool down the automotive engines. Their efficiency is impacted by a high number of geometric parameters that describe the shape.My thesis is fully funded by the ANR project PEPITO where industrials and academics collaborate. The aim of this project is to found the turbomachineries shape that maximizes the efficiency.That is why, industrials have developed numerical CFD (Computational fluid dynamics) codes that simulate the work of turbomachineries. However, the simulations are time-consuming. We cannot directly use the simulations provided to perform the optimization.In addition, during the production line, the input variables are subjected to perturbations. These perturbations are due to the production machineries fluctuations. The differences observed in the final shape of the turbomachinery can provoke a loss of efficiency. These perturbations have to be taken into account to conduct an optimization robust to the fluctuations. In this thesis, since the context is time consuming simulations we propose kriging based methods that meet the requirements of industrials. The issues are: • How can we construct a good response surface for the efficiency when the number of input variables is high?• How can we lead to an efficient optimization on the efficiency that takes into account the inputs perturbations?Several algorithms are proposed to answer to the first question. They construct a covariance kernel adapted to high dimension. This kernel is a tensor product of isotropic kernels in each subspace of input variables. These algorithms are benchmarked on some simulated case and on a real function. The results show that the use of this kernel improved the prediction quality in high dimension. For the second question, seven iterative strategies based on a co-kriging model are proposed to conduct the robust optimization. In each iteration, a Pareto front is obtained by the minimization of two objective computed from the kriging predictions. The first one represents the function and the second one the robustness. A criterion based on the Taylor theorem is used to estimate the local variance. This criterion quantifies the robustness. These strategies are compared in two test cases in small and higher dimension. The results show that the best strategies have well found the set of robust solutions. Finally, the methods are applied on the industrial cases provided by the PEPITO project.