La robotique mobile est un domaine en plein essor. L'un des domaines de recherche consiste à permettre à un robot de cartographier son environnement tout en se localisant dans l'espace. Les techniques couramment employées de SLAM (Simultaneous Localization And Mapping) restent généralement coûteuses en termes de puissance de calcul. La tendance actuelle vers la miniaturisation des systèmes impose de restreindre les ressources embarquées. L'ensemble de ces constatations nous ont guidés vers l'intégration d'algorithmes de SLAM sur des architectures adéquates dédiées pour l’embarqué.Les premiers travaux ont consisté à définir une architecture permettant à un robot mobile de se localiser. Cette architecture doit respecter certaines contraintes, notamment celle du temps réel, des dimensions réduites et de la faible consommation énergétique.L’implantation optimisée d’un algorithme (EKF-SLAM), en utilisant au mieux les spécificités architecturales du système (capacités des processeurs, implantation multi-cœurs, calcul vectoriel ou parallélisation sur architecture hétérogène), a permis de démontrer la possibilité de concevoir des systèmes embarqués pour les applications SLAM dans un contexte d’adéquation algorithme architecture. Une seconde approche a été explorée ayant pour objectif la définition d’un système à base d’une architecture reconfigurable (à base de FPGA) permettant la conception d'une architecture fortement parallèle dédiée au SLAM. L'architecture définie a été évaluée en utilisant une méthodologie HIL (Hardware in the Loop).Les principaux algorithmes de SLAM sont conçus autour de la théorie des probabilités, ils ne garantissent en aucun cas les résultats de localisation. Un algorithme de SLAM basé sur la théorie ensembliste a été défini garantissant l'ensemble des résultats obtenus. Plusieurs améliorations algorithmiques sont ensuite proposées. Une comparaison avec les algorithmes probabilistes a mis en avant la robustesse de l’approche ensembliste.Ces travaux de thèse mettent en avant deux contributions principales. La première consiste à affirmer l'importance d'une conception algorithme-architecture pour résoudre la problématique du SLAM. La seconde est la définition d’une méthode ensembliste permettant de garantir les résultats de localisation et de cartographie. / Mobile robotics is a growing field. One important research area is Simultaneous Localization And Mapping (SLAM). Algorithms commonly used in SLAM are generally expensive in terms of computing power. The current trend towards miniaturization imposes to restrict the embedded processing units. All these observations lead us to integrate SLAM algorithms on dedicated architectures suitable for embedded systems.The first work was to define an architecture for a mobile robot to localize itself. This architecture must satisfy some constraints, including the real-time, small dimensions and low power consumption. The optimized implementation of a SLAM algorithm, using the best architectural characteristics of the system (capacity of processors, multi-core implementation, SIMD instructions or parallelization on heterogeneous architecture), has demonstrated the ability to design embedded systems for SLAM applications in the context of Hardware-Software codesign.A second approach has been explored with the aim of designing a system based on a reconfigurable architecture (FPGA-based) for a highly parallel architecture dedicated to SLAM. The defined architecture was evaluated using a HIL (Hardware in the Loop) methodology.The main SLAM algorithms use the probabilistic theories, they do not guarantee their localization results. A SLAM algorithm based on interval analysis is defined to guarantee the overall results. Several algorithmic improvements are then proposed. A comparison with probabilistic algorithms highlighted the robustness of the approach.This thesis put forward two main contributions. The first is to affirm the importance of the hardware software codesign to solve the problem of SLAM with real-time constraint. The second is the definition of a new algorithm to ensure the results of localization and mapping.

This PhD thesis treats some problems concerning nonlinear differential equations. In the first two papers computer-assisted proofs are used. The differential equations there are rewritten as fixed point problems, and the existence of solutions are proved. The problem in the first paper is one-dimensional; with one boundary condition given by an integral. The problem in the second paper is three-dimensional, and Dirichlet boundary conditions are used. Both problems have their origins in fluid dynamics. Paper III describes an inverse problem for the heat equation. Given the solution, a solution dependent diffusion coefficient is estimated by intervals at a finite set of points. The method includes the construction of set-valued level curves and two-dimensional splines. In paper IV we prove that there exists a unique, globally attracting fixed point for a differential equation system. The differential equation system arises as the number of peers in a peer-to-peer network, which is described by a suitably scaled Markov chain, goes to infinity. In the proof linearization and Dulac's criterion are used.

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Les avancements récents dans les technologies sans fil ont vu l'émergence de techniques de localisation qui constitue une base utile et rentable pour offrir des nouveaux services. Ces services topo-dépendants ont été de plus en plus bénéfiques pour les opérateurs et les entreprises de télécommunications. Divers services topo-dépendants peuvent être offerts 'a l'utilisateur tels que le suivi, la publicité, la sécurité, et la gestion. Les réseaux sans fil eux-mêmes peuvent bénéficier de l'information de localisation pour améliorer les performances de leurs différentes couches. Le routage, la synchronisation et l'annulation d'interférences sont quelques exemples o'u l'information de localisation peut être fructueuse. Un système de localisation doit être capable d'exécuter deux tâches principales : la mesure des paramètres topo-dépendants (RSSI, TOA, et TDOA) et l'estimation de la position en utilisant des estimateurs appropriés. L'objectif principal de cette thèse est l'étude de différentes techniques d'estimation de la position: algébriques et géométriques. Les techniques algébriques étudiées sont les moindres carrés, le maximum de vraisemblance, et la programmation semi-définie. La technique géométrique RGPA proposée est basée sur l'analyse par intervalles et la représentation géométrique des paramètres topo-dépendants. L'accent est mis sur la fusion de différents paramètres topo-dépendants et son influence sur la précision de positionnement. L'estimation et la mesure des paramètres topo-dépendants sont également étudiées en utilisant une campagne de mesures ULB afin d'avoir une compréhension complète du domaine de localisation.

Les maladies cardiovasculaires sont l'une des principales causes de mortalité chez l'homme. Une façon de diagnostiquer des maladies cardiaques et des anomalies est le traitement de signaux cardiaques tels que le ECG. Dans beaucoup de ces traitements, des caractéristiques inter-battements et intra-battements de signaux ECG doivent être extraites. Ces caractéristiques comprennent les points de repère des ondes de l’ECG (leur début, leur fin et leur point de pic), les intervalles significatifs et les segments qui peuvent être définis pour le signal ECG. L'extraction des points de référence de l'ECG consiste à identifier l'emplacement du pic, de début et de la fin de l'onde P, du complexe QRS et de l'onde T. Ces points véhiculent des informations cliniquement utiles, mais la segmentation precise de chaque battement de l'ECG est une tâche difficile, même pour les cardiologues expérimentés.Dans cette thèse, nous utilisons un cadre bayésien basé sur le modèle dynamique d'ECG proposé par McSharry. Depuis ce modèle s'appuyant sur la morphologie des ECG, il peut être utile pour la segmentation et l'analyse d'intervalles d'ECG. Afin de tenir compte de la séquentialité des ondes P, QRS et T, nous utiliserons également l'approche de Markov et des modèles de Markov cachés (MMC). En bref dans cette thèse, nous utilisons un modèle dynamique (filtre de Kalman), un modèle séquentiel (MMC) et leur combinaison (commutation de filtres de Kalman (SKF)). Nous proposons trois méthodes à base de filtres de Kalman, une méthode basée sur les MMC et un procédé à base de SKF. Nous utilisons les méthodes proposées pour l'extraction de points de référence et l'analyse d'intervalles des ECG. Le méthodes basées sur le filtrage de Kalman sont également utilisés pour le débruitage d'ECG, la détection de l'alternation de l'onde T, et la détection du pic R de l'ECG du foetus.Pour évaluer les performances des méthodes proposées pour l'extraction des points de référence de l'ECG, nous utilisons la base de données "Physionet QT", et une base de données "Swine" qui comprennent ECG annotations de signaux par les médecins. Pour le débruitage d'ECG, nous utilisons les bases de données "MIT-BIH Normal Sinus Rhythm", "MIT-BIH Arrhythmia" et "MIT-BIH noise stress test". La base de données "TWA Challenge 2008 database" est utilisée pour la détection de l'alternation de l'onde T. Enfin, la base de données "Physionet Computing in Cardiology Challenge 2013 database" est utilisée pour la détection du pic R de l'ECG du feotus. Pour l'extraction de points de reference, la performance des méthodes proposées sont évaluées en termes de moyenne, écart-type et l'erreur quadratique moyenne (EQM). Nous calculons aussi la sensibilité des méthodes. Pour le débruitage d'ECG, nous comparons les méthodes en terme d'amélioration du rapport signal à bruit. / Cardiovascular diseases are one of the major causes of mortality in humans. One way to diagnose heart diseases and abnormalities is processing of cardiac signals such as ECG. In many of these processes, inter-beat and intra-beat features of ECG signal must be extracted. These features include peak, onset and offset of ECG waves, meaningful intervals and segments that can be defined for ECG signal. ECG fiducial point (FP) extraction refers to identifying the location of the peak as well as the onset and offset of the P-wave, QRS complex and T-wave which convey clinically useful information. However, the precise segmentation of each ECG beat is a difficult task, even for experienced cardiologists.In this thesis, we use a Bayesian framework based on the McSharry ECG dynamical model for ECG FP extraction. Since this framework is based on the morphology of ECG waves, it can be useful for ECG segmentation and interval analysis. In order to consider the time sequential property of ECG signal, we also use the Markovian approach and hidden Markov models (HMM). In brief in this thesis, we use dynamic model (Kalman filter), sequential model (HMM) and their combination (switching Kalman filter (SKF)). We propose three Kalman-based methods, an HMM-based method and a SKF-based method. We use the proposed methods for ECG FP extraction and ECG interval analysis. Kalman-based methods are also used for ECG denoising, T-wave alternans (TWA) detection and fetal ECG R-peak detection.To evaluate the performance of proposed methods for ECG FP extraction, we use the "Physionet QT database", and a "Swine ECG database" that include ECG signal annotations by physicians. For ECG denoising, we use the "MIT-BIH Normal Sinus Rhythm", "MIT-BIH Arrhythmia" and "MIT-BIH noise stress test" databases. "TWA Challenge 2008 database" is used for TWA detection and finally, "Physionet Computing in Cardiology Challenge 2013 database" is used for R-peak detection of fetal ECG. In ECG FP extraction, the performance of the proposed methods are evaluated in terms of mean, standard deviation and root mean square of error. We also calculate the Sensitivity for methods. For ECG denoising, we compare methods in their obtained SNR improvement.

Dans ce travail, nous proposons deux nouvelles approches ensemblistes pourl’estimation d’état basées sur la caractérisation explicite des bornes d’erreur d’estimation. Ces approches peuvent être vues comme la combinaison entre un observateur ponctuel et une caractérisation ensembliste de l’erreur d’estimation. L’objectif est de réduire la complexité de leur implémentation, de réduire le temps de calcul en temps réel et d’améliorer la précision et des encadrements des vecteurs d’état.La première approche propose un observateur ensembliste basé sur des ensembles invariants ellipsoïdaux pour des systèmes linéaires à temps-discret et aussi des systèmes à paramètres variables. L’approche proposée fournit un intervalle d’état déterministe qui est construit comme une somme entre le vecteur état estimé du système et les bornes de l’erreur d’estimation. L’avantage de cette approche est qu’elle ne nécessite pas la propagation des ensemble d’état dans le temps.La deuxième approche est une version intervalle de l’observateur d’état de Luenberger, pour les systèmes linéaires incertains à temps-discret, basés sur le calcul d’intervalle et les ensembles invariants. Ici, le problème d’estimation ensembliste est considéré comme un problème d’estimation d’état ponctuel couplé à une caractérisation intervalle de l’erreur d’estimation. / In This work, we propose two main new approaches for the set-membershipstate estimation problem based on explicit characterization of the estimation error bounds. These approaches can be seen as a combination between a punctual observer and a setmembership characterization of the observation error. The objective is to reduce the complexity of the on-line implimentation, reduce the on-line computation time and improve the accuracy of the estimated state enclosure.The first approach is a set-membership observer based on ellipsoidal invariant sets for linear discrete-time systems and also for Linear Parameter Varying systems. The proposed approach provides a deterministic state interval that is build as the sum of the estimated system states and its corresponding estimation error bounds. The important feature of the proposed approach is that does not require propagation of sets.The second approach is an interval version of the Luenberger state observer for uncertain discrete-time linear systems based on interval and invariant set computation. The setmembership state estimation problem is considered as a punctual state estimation issue coupled with an interval characterization of the estimation error.

Esta Tese propõe uma nova ferramenta para Otimização Robusta Multiobjetivo por Análise de Intervalo Não Probabilística (Non-probabilistic Interval Analysis for Multiobjective Robust Design Optimization ou NPIA-MORDO). A ferramenta desenvolvida visa à otimização dos parâmetros concentrados de suspensão em um modelo veicular completo, submetido a uma manobra direcional percorrendo diferentes perfis de pista, a fim de garantir maior conforto e segurança ao motorista. O modelo multicorpo possui 15 graus de liberdade (15-GDL), dentre os quais onze pertencem ao veículo e assento, e quatro, ao modelo biodinâmico do motorista. A função multiobjetivo é composta por objetivos conflitantes e as suas tolerâncias, como a raiz do valor quadrático médio (root mean square ou RMS) da aceleração lateral e da aceleração vertical do assento do motorista, desenvolvidas durante a manobra de dupla troca de faixa (Double Lane Change ou DLC). O curso da suspensão e a aderência dos pneus à pista são tratados como restrições do problema de otimização. As incertezas são quantificadas no comportamento do sistema pela análise de intervalo não probabilística, por intermédio do Método dos Níveis de Corte-α (α-Cut Levels) para o nível α zero (de maior dispersão), e realizada concomitantemente ao processo de otimização multiobjetivo. Essas incertezas são aplicáveis tanto nos parâmetros do problema quanto nas variáveis de projeto. Para fins de validação do modelo, desenvolvido em ambiente MATLAB®, a trajetória do centro de gravidade da carroceria durante a manobra é comparada com o software CARSIM®, assim como as forças laterais e verticais dos pneus. Os resultados obtidos são exibidos em diversos gráficos a partir da fronteira de Pareto entre os múltiplos objetivos do modelo avaliado Os indivíduos da fronteira de Pareto satisfazem as condições do problema, e a função multiobjetivo obtida pela agregação dos múltiplos objetivos resulta em uma diferença de 1,66% entre os indivíduos com o menor e o maior valor agregado obtido. A partir das variáveis de projeto do melhor indivíduo da fronteira, gráficos são gerados para cada grau de liberdade do modelo, ilustrando o histórico dos deslocamentos, velocidades e acelerações. Para esse caso, a aceleração RMS vertical no assento do motorista é de 1,041 m/s² e a sua tolerância é de 0,631 m/s². Já a aceleração RMS lateral no assento do motorista é de 1,908 m/s² e a sua tolerância é de 0,168 m/s². Os resultados obtidos pelo NPIA-MORDO confirmam que é possível agregar as incertezas dos parâmetros e das variáveis de projeto à medida que se realiza a otimização externa, evitando a necessidade de análises posteriores de propagação de incertezas. A análise de intervalo não probabilística empregada pela ferramenta é uma alternativa viável de medida de dispersão se comparada com o desvio padrão, por não utilizar uma função de distribuição de probabilidades prévia e por aproximar-se da realidade na indústria automotiva, onde as tolerâncias são preferencialmente utilizadas. / This thesis proposes the development of a new tool for Non-probabilistic Interval Analysis for Multi-objective Robust Design Optimization (NPIA-MORDO). The developed tool aims at optimizing the lumped parameters of suspension in a full vehicle model, subjected to a double-lane change (DLC) maneuver throughout different random road profiles, to ensure comfort and safety to the driver. The multi-body model has 15 degrees of freedom (15-DOF) where 11-DOF represents the vehicle and its seat and 4-DOF represents the driver's biodynamic model. A multi-objective function is composed by conflicted objectives and their tolerances, like the root mean square (RMS) lateral and vertical acceleration in the driver’s seat, both generated during the double-lane change maneuver. The suspension working space and the road holding capacity are used as constraints for the optimization problem. On the other hand, the uncertainties in the system are quantified using a non-probabilistic interval analysis with the α-Cut Levels Method for zero α-level (the most uncertainty one), performed concurrently in the multi-objective optimization process. These uncertainties are both applied to the system parameters and design variables to ensure the robustness in results. For purposes of validation in the model, developed in MATLAB®, the path of the car’s body center of gravity during the maneuver is compared with the commercial software CARSIM®, as well as the lateral and vertical forces from the tires. The results are showed in many graphics obtained from the Pareto front between the multiple conflicting objectives of the evaluated model. The obtained solutions from the Pareto Front satisfy the conditions of the evaluated problem, and the aggregated multi-objective function results in a difference of 1.66% for the worst to the best solution. From the design variables of the best solution choose from the Pareto front, graphics are created for each degree of freedom, showing the time histories for displacements, velocities and accelerations. In this particular case, the RMS vertical acceleration in the driver’s seat is 1.041 m/s² and its tolerance is 0.631 m/s², but the RMS lateral acceleration in the driver’s seat is 1.908 m/s² and its tolerance is 0.168 m/s². The overall results obtained from NPIA-MORDO assure that is possible take into account the uncertainties from the system parameters and design variables as the external optimization loop is performed, reducing the efforts in subsequent evaluations. The non-probabilistic interval analysis performed by the proposed tool is a feasible choice to evaluate the uncertainty if compared to the standard deviation, because there is no need of previous well-known based probability distribution and because it reaches the practical needs from the automotive industry, where the tolerances are preferable.

CAPES / O ensino tradicional da matemática leva os estudantes a resolverem problemas a partir de algoritmos e fórmulas. Este trabalho apresenta a matemática intervalar como importante ferramenta pedagógica para o desenvolvimento da capacidade de raciocínio dos estudantes. Neste sentido, um questionário sobre matemática intervalar, com exercícios que abordam diferentes áreas da matemática, foi aplicado a estudantes do ensino médio e feito uma análise dos resultados obtidos. / The traditional teaching of mathematics leads students to solve problems from algorithms and formulas. This work present interval mathematics as an important educational tool for the development of thinking ability of students. In this direction, a problem set on interval mathematics, with exercices that address different areas of mathematics, was applied to high school students. The results are analized.

CAPES / O ensino tradicional da matemática leva os estudantes a resolverem problemas a partir de algoritmos e fórmulas. Este trabalho apresenta a matemática intervalar como importante ferramenta pedagógica para o desenvolvimento da capacidade de raciocínio dos estudantes. Neste sentido, um questionário sobre matemática intervalar, com exercícios que abordam diferentes áreas da matemática, foi aplicado a estudantes do ensino médio e feito uma análise dos resultados obtidos. / The traditional teaching of mathematics leads students to solve problems from algorithms and formulas. This work present interval mathematics as an important educational tool for the development of thinking ability of students. In this direction, a problem set on interval mathematics, with exercices that address different areas of mathematics, was applied to high school students. The results are analized.

Esta Tese propõe uma nova ferramenta para Otimização Robusta Multiobjetivo por Análise de Intervalo Não Probabilística (Non-probabilistic Interval Analysis for Multiobjective Robust Design Optimization ou NPIA-MORDO). A ferramenta desenvolvida visa à otimização dos parâmetros concentrados de suspensão em um modelo veicular completo, submetido a uma manobra direcional percorrendo diferentes perfis de pista, a fim de garantir maior conforto e segurança ao motorista. O modelo multicorpo possui 15 graus de liberdade (15-GDL), dentre os quais onze pertencem ao veículo e assento, e quatro, ao modelo biodinâmico do motorista. A função multiobjetivo é composta por objetivos conflitantes e as suas tolerâncias, como a raiz do valor quadrático médio (root mean square ou RMS) da aceleração lateral e da aceleração vertical do assento do motorista, desenvolvidas durante a manobra de dupla troca de faixa (Double Lane Change ou DLC). O curso da suspensão e a aderência dos pneus à pista são tratados como restrições do problema de otimização. As incertezas são quantificadas no comportamento do sistema pela análise de intervalo não probabilística, por intermédio do Método dos Níveis de Corte-α (α-Cut Levels) para o nível α zero (de maior dispersão), e realizada concomitantemente ao processo de otimização multiobjetivo. Essas incertezas são aplicáveis tanto nos parâmetros do problema quanto nas variáveis de projeto. Para fins de validação do modelo, desenvolvido em ambiente MATLAB®, a trajetória do centro de gravidade da carroceria durante a manobra é comparada com o software CARSIM®, assim como as forças laterais e verticais dos pneus. Os resultados obtidos são exibidos em diversos gráficos a partir da fronteira de Pareto entre os múltiplos objetivos do modelo avaliado Os indivíduos da fronteira de Pareto satisfazem as condições do problema, e a função multiobjetivo obtida pela agregação dos múltiplos objetivos resulta em uma diferença de 1,66% entre os indivíduos com o menor e o maior valor agregado obtido. A partir das variáveis de projeto do melhor indivíduo da fronteira, gráficos são gerados para cada grau de liberdade do modelo, ilustrando o histórico dos deslocamentos, velocidades e acelerações. Para esse caso, a aceleração RMS vertical no assento do motorista é de 1,041 m/s² e a sua tolerância é de 0,631 m/s². Já a aceleração RMS lateral no assento do motorista é de 1,908 m/s² e a sua tolerância é de 0,168 m/s². Os resultados obtidos pelo NPIA-MORDO confirmam que é possível agregar as incertezas dos parâmetros e das variáveis de projeto à medida que se realiza a otimização externa, evitando a necessidade de análises posteriores de propagação de incertezas. A análise de intervalo não probabilística empregada pela ferramenta é uma alternativa viável de medida de dispersão se comparada com o desvio padrão, por não utilizar uma função de distribuição de probabilidades prévia e por aproximar-se da realidade na indústria automotiva, onde as tolerâncias são preferencialmente utilizadas. / This thesis proposes the development of a new tool for Non-probabilistic Interval Analysis for Multi-objective Robust Design Optimization (NPIA-MORDO). The developed tool aims at optimizing the lumped parameters of suspension in a full vehicle model, subjected to a double-lane change (DLC) maneuver throughout different random road profiles, to ensure comfort and safety to the driver. The multi-body model has 15 degrees of freedom (15-DOF) where 11-DOF represents the vehicle and its seat and 4-DOF represents the driver's biodynamic model. A multi-objective function is composed by conflicted objectives and their tolerances, like the root mean square (RMS) lateral and vertical acceleration in the driver’s seat, both generated during the double-lane change maneuver. The suspension working space and the road holding capacity are used as constraints for the optimization problem. On the other hand, the uncertainties in the system are quantified using a non-probabilistic interval analysis with the α-Cut Levels Method for zero α-level (the most uncertainty one), performed concurrently in the multi-objective optimization process. These uncertainties are both applied to the system parameters and design variables to ensure the robustness in results. For purposes of validation in the model, developed in MATLAB®, the path of the car’s body center of gravity during the maneuver is compared with the commercial software CARSIM®, as well as the lateral and vertical forces from the tires. The results are showed in many graphics obtained from the Pareto front between the multiple conflicting objectives of the evaluated model. The obtained solutions from the Pareto Front satisfy the conditions of the evaluated problem, and the aggregated multi-objective function results in a difference of 1.66% for the worst to the best solution. From the design variables of the best solution choose from the Pareto front, graphics are created for each degree of freedom, showing the time histories for displacements, velocities and accelerations. In this particular case, the RMS vertical acceleration in the driver’s seat is 1.041 m/s² and its tolerance is 0.631 m/s², but the RMS lateral acceleration in the driver’s seat is 1.908 m/s² and its tolerance is 0.168 m/s². The overall results obtained from NPIA-MORDO assure that is possible take into account the uncertainties from the system parameters and design variables as the external optimization loop is performed, reducing the efforts in subsequent evaluations. The non-probabilistic interval analysis performed by the proposed tool is a feasible choice to evaluate the uncertainty if compared to the standard deviation, because there is no need of previous well-known based probability distribution and because it reaches the practical needs from the automotive industry, where the tolerances are preferable.