The Linear Quadratic Regulator (LQR) is an optimal control approach which aims to drive states of a linear system to its origin through the minimization of a quadratic cost functional. Such an approach has been widely successful for both theoretical and practical applications. However, when such controllers are subject to uncertainties, optimal closed-loop performance cannot be obtained since robustness properties are no longer guaranteed. Guaranteed Cost Controllers (GCC) presents robust asymptotic stability and provides a guaranteed upper bound to a quadratic cost function. Such method addresses the lack of performance guarantees of the LQR. Meanwhile, Model Predictive Control (MPC) is a class of optimization-based control algorithms that use an explicit model of the controlled system to predict its future states. The MPC can be as a generalization of the LQR for constrained linear systems. Therefore, it equally suffers from a lack of robustness guarantees when the system is subject to uncertainties. Robust MPC (RMPC) approaches were proposed to address MPCs poor closed-loop performance subject to uncertainties. Its objective is to obtain a control input sequence that simultaneously minimizes a cost function and guarantees the feasibility of system states and control inputs, for a system subject to the worst-case disturbance within an uncertainty set. Autonomous vehicles have gained increasing interest from both the industry and research communities in recent years. An essential aspect in the design of automotive control systems is to ensure the controller is stable and has acceptable performance within the entire operational envelope which it is designed to operate. In the case of autonomous vehicles, where there is no human driver as a fallback, it is of utmost importance to ensure the safe operations of the control system and its capability to avoid saturating the handling limits of the vehicle. In this thesis, we propose Guaranteed Cost Controller approaches for both unconstrained and constrained linear systems subject to multiplicative structured norm-bounded uncertainties and present the application of such a controller to the lateral control problem of autonomous vehicles up to the tire saturation limits. / O Regulador Quadrático Linear (Linear Quadratic Regulator, LQR) é uma abordagem de controle ótimo que visa conduzir estados de um sistema linear à sua origem através da minimização de um custo funcional quadrático. Tal abordagem tem sido amplamente bem sucedida para aplicações teóricas e práticas. No entanto, não é possível obter o desempenho ótimo de malha fechada quando esses controladores são sujeitos a incertezas no sistema em decorrência de suas propriedades de robustez não serem garantidas. Controladores de Custo Garantido (Guaranteed Cost Control, GCC) visam abordar a falta de garantia de desempenho do LQR, neste caso. Esses controladores apresentam estabilidade assintótica robusta e fornecem um custo garantido de pior caso para uma função de custo quadrático. O Controle Preditivo de Modelo (Model Predictive Control, MPC) é uma classe de algoritmos de controle baseados em otimização que usa um modelo explícito do sistema controlado para prever seus estados futuros. Uma possível interpretação do MPC é uma generalização do LQR para sistemas lineares com restrições de estado e entrada de controle. Portanto, essa abordagem sofre igualmente da falta de garantias de robustez quando o sistema é sujeito a incertezas. As abordagens de MPC Robustas (Robust MPC, RMPC) foram propostas para abordar o desempenho de malha fechada do MPC sujeito a incertezas no sistema. Seu objetivo é obter uma sequência de entrada de controle que minimize simultaneamente uma função de custo e garanta que os estados do sistema e as entradas de controle estão contidos dentro das restrições para um sistema sujeito à pior das perturbações dentro de um conjunto admissível de incertezas. Pesquisas voltadas para veículos autônomos ganharam crescente interesse nos últimos anos, tanto da indústria automobilística quanto da comunidade acadêmica. Um aspecto essencial no projeto de sistemas de controle automotivo é a garantia de estabilidade e desempenho do controlador dentro de todo o envelope operacional ao qual ele foi projetado para operar. No caso de veículos autônomos, onde não há motoristas humanos para lidar com casos de falha do sistema, é de suma importância assegurar as operações seguras do sistema de controle e sua capacidade de evitar a saturação dos limites de manuseio do veículo. Nesta tese, propomos abordagens GCC para sistemas lineares restritos e irrestritos, sujeitos a incertezas estruturadas contidas por norma e apresentamos a aplicação de tais controladores ao problema de controle lateral de veículos autônomos até os limites de saturação dos pneus.

Les énergies renouvelables représentent aujourd'hui un domaine de développement de plus en plus important, au vu de la consommation énergétique mondiale et de ses conséquences désastreuses sur l'environnement. Les différents accords politiques, notamment l'accord de Paris, ne peuvent à eux seuls apporter une solution définitive au changement climatique actuel. Les contraintes imposées par la réduction des émissions de CO_2 et l’augmentation du prix du pétrole dans l’industrie maritime ont poussé Yves Parlier à lancer le projet « beyond the sea » dans le but de développer des cerfs-volants (kites) dédiés à la propulsion auxiliaire des navires. L'objectif principal de cette étude est donc la modélisation et la commande robuste d'une aile de kite en vol dynamique. Le but à terme étant l'élaboration d'un pilote automatique dédié à la traction d'un navire par kite. Un modèle « point-masse » du kite est proposé afin de comprendre et contrôler sa dynamique. Les différents paramètres du modèle sont estimés à partir de données expérimentales obtenues lors d’essais en conditions réelles. Des simulations en boucle ouverte sont proposées afin de valider la cohérence du modèle. Pour effectuer un vol dynamique, une trajectoire en forme de huit est définie dans la fenêtre de vol. La position, la taille et l’orientation de cette trajectoire sont des paramètres ajustables par l’utilisateur. Un algorithme de suivi de trajectoire est développé permettant ensuite de synthétiser une loi de commande robuste intégrant le modèle du kite. Ce pilote automatique permet donc d’effectuer une grande variété de trajectoires pour toute une gamme de vitesses de vent. Enfin, des simulations en boucle fermée montrant les performances théoriques du système mettent en évidence l’intérêt de la propulsion auxiliaire des navires par kite. / The need in reducing the CO_2 emissions and the increase of oil prices affect all transportation industries and especially the maritime industry. This has led to the search for more energy-saving ship propulsion systems. Taking advantage of wind energy by using tethered wings, or kites, as an alternative propulsion source can be an effective solution. The "beyond the sea" project, led by Yves Parlier, aims to provide ships an alternative green energy source. In most wind conditions, compared to a static flight, a dynamic motion of a tethered wing with an eight-shaped pattern can provide sufficient force through traction to tow a ship. Therefore, the main objective of this study is the modeling and robust control of a tethered kite in dynamic flight. To this end, a point mass model is first used to describe the kite dynamics. The model parameters are estimated from experimental data and the aerodynamic coefficients are identified using data from a quasi-static flight. Open loop simulations are conducted to verify the kite behavior and the overall coherence of the model. To ensure a dynamic flight, an eight-shaped trajectory is defined within the wind window. Its position, size, orientation and direction are all adjustable parameters. A path-following strategy is then developed in order to design a robust control law including the kite model. This allows the system to be used in different trajectories with a wide range of wind speeds. Closed-loop simulations are presented to show the efficiency of the path-following algorithm, and the various theoretical performances obtained shows the efficiency of a kite dedicated to vessels auxiliary propulsion.

L'architecture modulaire est une caractéristique distinctive des circuits cérébraux. En particulier, il a été observé l'existence de connexions réciproques entre des zones fonctionnellement interconnectées dans le cortex, et qui par ailleurs sont hiérarchiquement organisées. De plus, le développement évolutif est une autre caractéristique distinctive des espèces vivantes ; même les virus sont capables d'adaptation pour mieux répondre à de nouvelles conditions environnementales. En tenant compte de ces deux importants aspects, nous avons construit un nouvel et unique outil de simulation permettant de modéliser et d'étudier l'évolution des circuits multi-modulaires hiérarchiques. Dans ce modèle, chaque module est représenté par des réseaux de neurones impulsionels et caractérisé à la fois par des changements d'activités neurales imbriquées et par la plasticité synaptique. La morte cellulaire, la plasticité synaptique et l'apoptose intégrés dans le modèle créent des liens auto-associatifs au sein des modules. Ces liens peuvent générer une activité zonale qui reflète l'évolution de la connectivité fonctionnelle à l'intérieur comme à l'extérieur des modules, et donc entre les plusieurs modules neuronaux. L'activité bioélectrique de chaque module est enregistrée au moyen des électrodes virtuelles. Les signaux, electrochipogrammes (EChG), sont analysés par les méthodes fréquentiels et les méthodes de potentiels évoqués afin de trouver des généralités dans le comportement émergeant. En plus de ces méthodes conventionnelles, nous proposons une nouvelle approche de régression non-linéaire structurelle afin de fournir des outils plus puissants et mieux adaptés aux données habituellement analysées dans ce domaine. Nous avons donc testé l'effet d'un stimulus externe sur le développement de liens fonctionnels d'un réseau neuronaux. Le circuit est structuré hiérarchiquement avec un unique module sensoriel et d'autres modules constitués de deux voies parallèles organisées aussi de façon hiérarchique. Nos résultats montrent que les circuits modélisés manifestent un comportement similaire que les circuits biologiques réels. En particulier, tous les éléments du circuit peuvent traiter et maintenir des patterns d'activité liés à la disparition du stimulus. Les résultats obtenus dans nos expériences apportent un éclairage sur les processus émergents et coordonnés de l'activité électrique enregistrée par des EEG de circuits inter-corticaux hiérarchiques et évolutifs qui sont artificiels ou réels. Plus généralement, notre approche concernant les signaux EEG pourrait être étendue à la modélisation d'une vaste variété des processus cognitifs et comportementaux. / Modular architecture is a hallmark of many brain circuits. Particularly, in the cerebral cortex it has been observed that reciprocal connections are often present between functionally interconnected areas that are hierarchically organized. Evolutionary development is another distinctive characteristic of living species, even the simplest viruses are capable to adapt to better fit new environmental conditions. Having hierarchical architectures and evolutionary features in mind, we build unique and novel simulation framework, which allows us to model and to study evolving hierarchically organized circuits of modules of spiking neural networks. Each module is characterized by embedded neural development and expression of spike timing dependent plasticity. Cell death, synaptic plasticity and projection pruning, embedded in the neural model, drive the build-up of auto-associative links within each module, which generate an areal activity that reflect the changes in the corresponding functional connectivity within and between neuronal modules. Bio-electric activity of each module is recorded by means of virtual electrodes and these signals, called electrochipograms (EChG), are analyzed by time and frequency domain methods in order to find general patterns of emerging behavior. Beside time and frequency domain analysis methods, a novel robust non-linear structural regression approach is proposed to provide researchers with more powerful tools specially adapted to the data typically used in the domain. We tested the effect of an external stimulus at fixed frequency fed to a sensory module, which pro jecting its activity to two hierarchically organized parallel pathways. We found that modeled circuits manifest behavior similar in certain aspects to that of real brains. We show evidence that all networks of modules are able to maintain long patterns of activity associated with the stimulus offset. These findings bring new insights to the understanding of EEG-like signals, both real and virtual. The findings prove that the approach is successful and could be extended to model cognitive and behavioral processes in the brains.

Les problématiques de recherche abordées dans cette thèse concernent la conceptualisation, la modélisation et la commande générique des robots mobiles lors de leur évolution en milieux extérieurs et en présence de glissement pour des applications de suivi de précision. Ainsi, ce mémoire synthétise dans un premier temps les développements et résultats obtenus lors du suivi de trajectoire (localisation absolue), puis synthétise ensuite ceux obtenus lors de suivi de structure et de cible (localisation relative). Une dernière partie introduit un concept de plateforme robotique reconfigurable et sa commande associée pour adapter l’assiette et les dimensions du châssis en fonction de la topographie du terrain.Pour chaque application de suivi, ce mémoire présente un panel de lois de commande originales pour des robots différentiels, à un train et à deux trains directeurs. Chaque modalité de commande est présentée en quatre étapes : modélisation, estimation, commande et expérimentations. La première contribution majeure de la thèse concerne l’estimation du glissement. Cette dernière est adaptative et basée modèle. Elle intègre la modélisation cinématique étendue seule ou couplée à la modélisation dynamique du robot mobile pour assurer une estimation intègre quels que soient la vitesse, les phénomènes dynamiques rencontrés et la nature du sol. La seconde contribution majeure concerne le développement d’une stratégie de commande générique pour les robots mobiles. Cette stratégie est basée sur le principe de la commande en cascade (ou par backstepping) et est déclinée dans ce mémoire à travers un panel de lois de commande. Cette méthodologie de commande, lorsqu’elle est associée à l’observation du glissement précédent, permet d’obtenir des performances de suivi accrues quel que soit le contexte rencontré. L’ensemble des algorithmes ont été validés en simulation et/ou expérimentalement à l’aide de différentes plateformes robotiques en contextes réels. / This work is focused on the conceptualization, the modeling and the genericcontrol of mobile robots when moving in off-road contexts and facing slipperyterrains, especially for very accurate tracking and following applications. Thisthesis summarizes the proposed methods and the obtained results to addressthis research issue, first for path following applications (absolute localization)and then for edge and target tracking applications (relative localization). A finalsection of this thesis introduces an adaptive robotic concept and its associatedcontroller allowing the adaptation of the pose (position and orientation) of thechassis with respect to the environment topography.For each application, this thesis introduces a panel of innovative control algorithmsfor controlling skid-steering, two-wheel steering and four-wheel steeringmobile robots. Each algorithm of the panel is described, in this thesis, infour steps : modeling, estimation, control and experiments.The first main contribution of this thesis deals with the slippage estimation.The latter is adaptive and model-based. It also includes the extended kinematicmodeling only or together with the dynamic modeling of the mobile robot toensure a robust estimation of the slippage whatever the speed of the robot, encountereddynamic phenomena or even ground characteristics.The second main contribution deals with the design of a generic control approachfor mobile robots when path following and target tracking. The proposedstrategy is mostly based on a backstepping method and is illustrated inthis thesis via a panel of control laws. When combining this proposed controlapproach with the slippage estimation described above, significant improvedtracking and following performances are obtained (in term of stability, repeatability,accuracy and robustness) whatever the encountered context.All algorithms have been tested and validated through simulations and/orfull-scale experiments, indoor and off-road, with different mobile robots.

Le travail présenté dans cette thèse s'inscrit dans le cadre de l'étude de l'efficacité de la commande CRONE avec effet anticipatif robuste dans les problèmes de poursuite et de régulation pour les systèmes monovariables et multivariables. L'objectif de l'anticipation est de concevoir des algorithmes de commande capables de minimiser un critère quadratique basé sur l'erreur entre la sortie du système et le signal de référence avec modération du niveau du signal de commande. La solution proposée repose sur l'association d'une commande robuste de type feedback à une commande anticipative de type feedforward. L'action feedforward utilise un filtre anticipatif synthétisé dans le domaine fréquentiel en utilisant des critères d'optimalité et de contraintes de type $mathcal{H}_2$ et $mathcal{H}_infty$. La réduction du nombre de paramètres du filtre anticipatif en utilisant une période d'échantillonnage plus lente a été traitée. Des exemples académiques illustrent les développements théoriques. Une application pratique sur un système de régulation hydraulique a montré la pertinence de cette nouvelle approche. / The work presented in this thesis is part of the study of the effectiveness of CRONE control with anticipative effect in the problems of tracking and control for monovariable and multivariable systems. The anticipation objective is to design a control algorithm that minimizes a quadratic error between the reference and the output of the system and at the same time achieve a good level of the control signal. The proposed solution combines a robust feedback control with a feedforward control. The feedforward action uses optimality criteria and an anticipative filter which is designed in the frequency domain using a mix of $mathcal{H}_2$ et $mathcal{H}_infty$ constraints. The reduction of the number of parameters of the anticipative filter by using a slower sampling period for the anticipative filter is treated. Academic examples highlight the theoretical developments. A practical application on a hydraulic control system has shown the efficiency of the developed approach.

[pt] Em meados do século XIX, G. Boole mostrou que a transformação x -> x − 1/x, definida em R − {0}, preserva a medida de Lebesgue (Ble). Mais de um século depois, R. Adler e B.Weiss mostraram que essa aplicação, chamada de transformação de Boole, é, de fato, ergódica com respeito à medida de Lebesgue (Adl). Nesse trabalho, apresentaremos o conceito de sistemas alternantes, definido recentemente por S. Muñoz (Mun), que consiste numa grande classe de aplicações na reta que generaliza a transformação de Boole e que torna possível uma análise abrangente de propriedades como transitividade robusta e ergodicidade. Para mostrar que, sob certas condições, sistemas alternantes são ergódicos com relação à medida de Lebesgue, mostraremos, usando o Teorema do Folclore, que a transformação induzida do sistema alternante é ergódica. / [en] In the middle of the 19th century, G. Boole proved that the transformation x -> x − 1/x, defined on R − {0}, is a Lebesgue measure preserving transformation (Ble). Over one hundred years later, R. Adler and B.Weiss proved that this map, called Boole`s map, is, in fact, ergodic with respect to the Lebesgue measure (Adl). In this work, we present the notion of alternating systems, recently introduced by S. Mu`noz (Mun), which is a large class of functions on the real line that generalizes the Boole`s map and allows us to make a wide analysis on certain properties such as robust transitivity and ergodicity. In order to show that, under certain conditions, alternating systems are ergodic with respect to the Lebesgue measure, we show, using the Folklore Theorem, that the induced transformation of an alternating system is ergodic.

Ces travaux ont pour application la détection l'identification des signaux audio et particulièrement les signaux d'alarmes de voitures prioritaires. Dans un premier temps, nous proposons une méthode de détection des signaux d'alarme dans un environnement bruité, fondée sur des techniques d'analyse temps-fréquence des signaux. Cette méthode permet de détecter et d'identifier des signaux d'alarmes noyés dans du bruit, y compris pour des rapports signal à bruit négatifs. Puis nous proposons une quantification des signaux robuste aux bruits de transmission. Il s'agit de remplacer chaque niveau de bit d'un vecteur d'échantillons temporels ou fréquentiels par un mot binaire de même longueur fourni par un codeur correcteur d'erreur. Dans une première approche, chaque niveau de bits est quantifié indépendamment des autres selon le critère de minimisation de la distance de Hamming. Dans une seconde approche, pour réduire l'erreur de quantification à robustesse égale, les différents niveaux de bits sont quantifiés successivement selon un algorithme de type matching pursuit. Cette quantification donne aux signaux une forme spécifique permettant par la suite de les reconnaitre facilement parmi d'autres signaux. Nous proposons donc enfin deux méthodes de détection et d'identification des signaux fondées sur la quantification robuste, opérant dans le domaine temporel ou dans le domaine fréquentiel, par minimisation de la distance entre les signaux reçus restreints à leurs bits de poids fort et les signaux de référence. Ces méthodes permettent de détecter et d'identifier les signaux dans des environnements à rapport signal à bruit très faible et ceci grâce à la quantification. Par ailleurs, la première méthode, fondée sur la signature temps-fréquence, s'avère plus performante avec les signaux quantifiés. / This work targets the detection and identification of audio signals and in particular alarm signals from priority cars. First, we propose a method for detecting alarm signals in a noisy environment, based on time-frequency signal analysis. This method makes it possible to detect and identify alarm signals embedded in noise, even with negative signal-to-noise ratios. Then we propose a signal quantization robust against transmission noise. This involves replacing each bit level of a vector of time or frequency samples with a binary word of the same length provided by an error- correcting encoder. In a first approach, each bit level is quantized independently of the others according to the Hamming distance minimization criterion. In a second approach, to reduce the quantization error at equal robustness, the different bit levels are quantized successively by a matching pursuit algorithm. This quantization gives the signals a specific shape that allows them to be easily recognized among other signals. Finally, we propose two methods for detecting and identifying signals based on robust quantization, operating in the time domain or in the frequency domain, by minimizing the distance between the received signals restricted to their high-weight bits and the reference signals. These methods make it possible to detect and identify signals in environments with very low signal-to-noise ratios, thanks to quantization. In addition, the first method, based on the time-frequency signature, is more efficient with quantized signals.

Neste trabalho foram desenvolvidas duas técnicas de sintonia para controladores preditivos por modelo. Ambas visam minimizar a soma do erro quadrático entre respostas do sistema em malha fechada e trajetórias de referência pré-definidas; a primeira resolve um problema de otimização lexicográfica enquanto a segunda resolve um problema de otimização de compromisso. As vantagens dos métodos apresentados são: maior automatização, definição de objetivos de sintonia intuitiva que considera especificações na dinâmica do processo, uma métrica no domínio do tempo e é capaz de incluir o conhecimento do engenheiro de controle em uma técnica de sintonia confiável. Um estudo de caso no sistema de craqueamento catalítico ilustrou a flexibilidade de definição dos objetivos da técnica lexicográfica. Um estudo de caso sobre uma coluna de fracionadora de óleo pesado em malha fechada com um controlador preditivo por modelo comparou ambas as estratégias de sintonia desenvolvidas aqui e pode-se concluir que a técnica lexicográfica dá prioridade aos objetivos importantes enquanto a técnica de compromisso calcula uma solução média, com respeito aos objetivos. A técnica de compromisso foi comparada a um método de sintonia da literatura quanto a aplicação em um controlador preditivo de horizonte infinito com targets para as entradas e controle por faixas das saídas com uma coluna de destilação. Observou-se que a técnica desenvolvida aqui é computacionalmente mais rápida e não requer a escolha de uma solução não-dominada dentre um conjunto de soluções de Pareto. Aplicações reais de controle preditivo são severamente afetadas por incerteza de modelo. Estendeu-se as técnicas desenvolvidas aqui para considerar o caso de incerteza multi-planta, calculando parâmetros de sintonia robustos para controladores nominais, visando tratar o compromisso entre performance e estabilidade e robustez da malha fechada. Um controlador preditivo de horizonte infinito foi sintonizado de forma robusta e comparado com um controlador preditivo robusto em malha fechada com um modelo de separadora C3/C4. Observou-se que este consegue controlar melhor o processo, entretanto, tem um tempo de computação duas ordens de grandeza maior que o controlador nominal, em operação on-line. / Two multi-objective optimization based tuning techniques for Model Predictive Control (MPC) were developed. Both take into account the sum of the squared errors between closed-loop trajectories and reference responses based on pre-defined goals as tuning objectives; one solves a lexicographic optimization to obtain an optimum set of tuning parameters (LTT), whereas the other solves a compromise optimization problem (CTT). The main advantages are an automated framework, and straightforward goal definition, which are capable of taking into account a specification on the process dynamics, a time-domain metrics, and of embedding the control engineers knowledge into a reliable approach. A fluid catalytic cracking tuning case study unveiled the goal definition flexibility of the LTT, with respect to output tracking and variable coupling. A heavy oil fractionator in closed-loop with a MPC case study compared both tuning techniques developed here, and it was observed that the LTT in fact prioritizes the main objectives, whereas the CTT yields an average solution, in terms of the tuning objectives. The CTT was compared to another multi-objective tuning technique from the literature, in the tuning of a MPC with input targets and output zone control in closed-loop with a crude distillation unit model. The simulation results showed that the CTT allows for faster results, regarding the computational time to compute the tuning parameters and there is no need of a posteriori decisions to select the best non-dominated solution. Real MPC applications are strongly hindered by model uncertainty. This limitation was addressed by the extension of the tuning techniques to account for multi-plant model uncertainty, thus obtaining optimum robustly tuned parameters for nominal controllers, addressing the trade-off between robustness and performance. A robustly tuned Infinite Horizon MPC (IHMPC) was compared to a Robust IHMPC, in closed-loop with a C3/C4 splitter system model. It was observed in a simulation that even though the latter yields better output responses, it is two orders of magnitude slower than the former in online operation.

O planejamento da produção em indústrias moveleiras de pequeno porte é comumente constituído por decisões referentes ao volume de produção e à política de estoque, com o objetivo de minimizar o desperdício de material, os atrasos e as horas-extras utilizadas ao longo do horizonte de planejamento. Administrar tais decisões de uma maneira tratável e eficiente é, em geral, um desafio, especialmente considerando a natureza incerta dos dados. Nessa tese, são desenvolvidos modelos de otimização para apoiar tais decisões no contexto do problema combinado de dimensionamento de lotes e corte de estoque sob incertezas que surge em indústrias moveleiras. Para lidar com as incertezas dos dados, são investigadas duas metodologias: programação estocástica e otimização robusta. Dessa maneira, são propostos modelos de programação estocástica de dois estágios com recurso, assim como modelos estocásticos robustos que incorporam aversão ao risco. A motivação em também desenvolver modelos baseados em otimização robusta é considerar casos práticos em que não há uma descrição probabilística explícita dos dados de entrada, assim como evitar trabalhar com numerosos cenários, o que pode tornar o modelo estocástico computacionalmente intratável. Os experimentos numéricos baseados em exemplares reais de uma empresa moveleira de pequeno porte mostram que as soluções obtidas pelos modelos de programação estocástica fornecem planos de produção robustos e que o (a) decisor (a) pode designar suas preferências em relação ao risco aos modelos, assim como controlar o tradeoff entre o custo total esperado e a robustez da solução. Em relação aos resultados dos modelos de otimização robusta, são obtidos alguns insights entre os chamados budgets de incerteza, as taxas de atendimento da demanda e os valores ótimos. Além disso, evidências numéricas indicam que budgets de incerteza menos conservadores resultam em níveis de serviço razoáveis com baixos custos globais, enquanto a abordagem de pior caso gera, relativamente, boas taxas de atendimento da demanda, mas com custos globais elevados / Production planning procedures in small-size furniture companies commonly consist of decisions with respect to production level and inventory policy, while attempting to minimize trim-loss, backlogging and overtime usage throughout the planning horizon. Managing these decisions in a tractable and efficient way is often a challenge, especially when the uncertainty of data is taken into account. In this thesis, we develop optimization models to support these decisions in the context of the combined lot-sizing and cutting-stock problem that arises in furniture companies. To deal with data uncertainty, we investigate two methodologies: stochastic programming and robust optimization. In the former case, we propose two-stage stochastic programming models with recourse, as well as robust stochastic models to incorporate risk-aversion. In the latter case, our motivation to investigate robust optimization models is the lack of an explicit probabilistic description of the input data. Furthermore, we want to avoid dealing with a large number of scenarios, which typically lead to computationally intractable stochastic programming models. Numerical experiments based on real data from a small-size furniture plant show that the solutions of the stochastic programming models provide robust production plans so that the decision-maker can assign his or her risk preferences to the model and control the tradeoff between the expected total cost and solution robustness. Regarding the results from the robust optimization models, we provide some insights into the relationship among budgets of uncertainty, fill rates and optimal values. Moreover, numerical evidence indicate that less conservative budgets of uncertainty result in reasonable service levels with cheaper global costs, while worst case deterministic approaches lead to relatively good fill rates, but with prohibitive global costs

Nesta dissertação é apresentado um estudo comparativo entre seis controladores H \'infinito\' não lineares aplicados em um robô móvel com rodas. Três estratégias de controle são avaliadas. Na primeira, o modelo do robô é considerado completamente conhecido. Na segunda, o modelo matemático é considerado desconhecido e é realizada uma estimativa baseada em métodos inteligentes. E finalmente, na terceira estratégia, o modelo nominal é conhecido e técnicas inteligentes são usadas para estimar somente incertezas paramétricas do robô. As técnicas inteligentes usadas são baseadas em redes neurais e em lógica fuzzy. Esses controladores são resolvidos através de desigualdades matriciais lineares (DMLs) e equações algébricas de Riccati. Todos os resultados obtidos são baseados em dados experimentais. / This dissertation is present a comparative study between six nonlinear H \'infinity\' controllers applied to a wheeled mobile robot. Three control strategies are adopted. In the first, the model of the robot is considered completely known. In the second, the mathematical model is considered unknown and is accomplished an estimate based on intelligent methods. And finally, in the third strategy, the nominal model is known and intelligent techniques are used only to estimate parametric uncertainties of the robot. The intelligent techniques used are based in neural networks and in fuzzy logic. These controllers are solved via linear matrix inequalities (LMIs) and algebraic Riccati equations. All results obtained are based in experimental data.