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Indirect wind estimation onboard unmanned aerial systems (UASs) can be accomplished using existing air vehicle sensors along with a dynamic model of the UAS augmented with additional wind-related states. It is often desired to extract a mean component of the wind the from frequency fluctuations (i.e. turbulence). Commonly, a variation of the KALMAN filter is used, with explicit or implicit assumptions about the nature of the random wind velocity. This dissertation presents an H-infinity (H∞) filtering approach to wind estimation which requires no assumptions about the statistics of the process or measurement noise. To specify the wind frequency content of interest a low-pass filter is incorporated. We develop the augmented UAS model in continuous-time, derive the H∞ filter, and introduce a KALMAN-BUCY filter for comparison. The filters are applied to data gathered during UAS flight tests and validated using a vaned air data unit onboard the aircraft. The H∞ filter provides quantitatively better estimates of the wind than the KALMAN-BUCY filter, with approximately 10-40% less root-mean-square (RMS) error in the majority of cases. It is also shown that incorporating DRYDEN turbulence does not improve the KALMAN-BUCY results. Additionally, this dissertation describes the theory and process for using generalized polynomial chaos (gPC) to re-cast the dynamics of a system with non-deterministic parameters as a deterministic system. The concepts are applied to the problem of wind estimation and characterizing the precision of wind estimates over time due to known parametric uncertainties. A novel truncation method, known as Sensitivity-Informed Variable Reduction (SIVR) was developed. In the multivariate case presented here, gPC and the SIVR-derived reduced gPC (gPCr) exhibit a computational advantage over Monte Carlo sampling-based methods for uncertainty quantification (UQ) and sensitivity analysis (SA), with time reductions of 38% and 98%, respectively. Lastly, while many estimation approaches achieve desirable accuracy under the assumption of known system parameters, reducing the effect of parametric uncertainty on wind estimate precision is desirable and has not been thoroughly investigated. This dissertation describes the theory and process for combining gPC and H-infinity (H∞) filtering. In the multivariate case presented, the gPC H∞ filter shows superiority over a nominal H∞ filter in terms of variance in estimates due to model parametric uncertainty. The error due to parametric uncertainty, as characterized by the variance in estimates from the mean, is reduced by as much as 63%. / Doctor of Philosophy / On unmanned aerial systems (UASs), determining wind conditions indirectly, without direct measurements, is possible by utilizing onboard sensors and computational models. Often, the goal is to isolate the average wind speed while ignoring turbulent fluctuations. Conventionally, this is achieved using a mathematical tool called the KALMAN filter, which relies on assumptions about the wind. This dissertation introduces a novel approach called H-infinity (H∞) filtering, which does not rely on such assumptions and includes an additional mechanism to focus on specific wind frequencies of interest. The effectiveness of this method is evaluated using real-world data from UAS flights, comparing it with the traditional KALMAN-BUCY filter. Results show that the H∞ filter provides significantly improved wind estimates, with approximately 10-40% less error in most cases. Furthermore, the dissertation addresses the challenge of dealing with uncertainty in wind estimation. It introduces another mathematical technique called generalized polynomial chaos (gPC), which is used to quantify and manage uncertainties within the UAS system and their impact on the indirect wind estimates. By applying gPC, the dissertation shows that the amount and sources of uncertainty can be determined more efficiently than by traditional methods (up to 98% faster). Lastly, this dissertation shows the use of gPC to provide more precise wind estimates. In experimental scenarios, employing gPC in conjunction with H∞ filtering demonstrates superior performance compared to using a standard H∞ filter alone, reducing errors caused by uncertainty by as much as 63%.

Text in Afrikaans / A study of the philosophical and historical foundations of infinity highlights the problematic development of infinity. Aristotle distinguished between potential and actual infinity, but rejected the latter. Indeed, the interpretation of actual infinity leads to contradictions as seen in the paradoxes of Zeno. It is difficult for a human being to understand actual infinity. Our logical schemes are adapted to finite objects and events. Research shows that students focus primarily on infinity as a dynamic or neverending process. Individuals may have contradictory intuitive thoughts at different times without being aware of cognitive conflict. The intuitive thoughts of students about both the actual (at once) infinite and potential (successive) infinity are very complex. The problematic nature of actual infinity and the contradictory intuitive cognition should be the starting point in the teaching of the concept infinity. / Educational Studies / M.Ed. (Mathematic Education)

The existence of pathwise stationary solutions of this stochastic partial differential equation (SPDE, for abbreviation) is demonstrated. In Part II, a connection between certain kind of state constrained controlled Forward-Backward Stochastic Differential Equations (FBSDEs) and Hamilton-Jacobi-Bellman equations (HJB equations) are demonstrated. The special case provides a probabilistic representation of some geometric flows, including the mean curvature flows. Part II includes also a probabilistic proof of the finite time existence of the mean curvature flows.

In this thesis I explore the relation in Buber's and Levinas's understanding. Both of these Jew philosophers endeavoured to describe an essence of genuine dialogue and both saw in dialogue the word that turns to a Thou, the primal deed of spirit. Nevertheless in spite of these similarities there are also a differences in their understanding of a dynamics within the genuine dialogue. Whereas Buber talks about a reciprocity in such a relation Levinas asserts that there is an asymmetry there and therefore he radicalizes Buber's conception and responsibility towards the other. In the first part of my thesis I focus on important influences on Buber's and Levinas' lives and introduce a "poetics" of their understanding of a genuine dialogue based particularly on their main piece of work: Buber's I and Thou and Levinas's Totality and Infinity. Although there was a communication between these two thinkers according to some philosophers it often exhibited a lack of dialogue and a failure to understand each other. Therefore I outline the similarities and differences in detail in the final chapters. Keywords Buber, Levinas, Rosenzweig, I - Thou relationship, face, reciprocity, asymmetry, responsibility, ethics, infinity

Nos últimos anos, tem havido grande interesse em estudar manipuladores paralelos, aplicados principalmente em simuladores de voo, com seis graus de liberdade. O interesse em estruturas cinemáticas paralelas é motivado por sua alta rigidez e excelente capacidade de posicionamento em relação às estruturas cinemáticas seriais. Além disso, como os atuadores são posicionados em uma base, eles podem ser aplicados em cargas pesadas e ainda apresentam baixo consumo de energia, tendo em vista que vários atuadores atuam simultaneamente no mesmo corpo. A presente tese apresenta o projeto de três controladores, sendo eles, o controlador H infinito com realimentação de saída, o controlador PID e o controlador Fuzzy, com isto, esta metodologia poderá ser empregada na construção de um futuro simulador de voo. O modelo dos atuadores foi obtido através de uma entrada degrau de tensão nos motores, medindo os seus deslocamentos através dos encoders acoplados, individualmente, a cada um dos respectivos eixos dos motores. Sabendo-se a relação de transmissão do mecanismo de movimento entre o motor e cada haste dos atuadores obtém-se o deslocamento de cada haste a partir da rotação de cada motor medida pelo correspondente encoder e com isso obtém-se o modelo matemático de cada atuador em conjunto com seu sistema de transmissão. Entretanto, na prática, cada atuador é ligeiramente diferente dos outros, o que leva a comportamento e desempenho diferentes entre si. Isso afeta o comportamento da plataforma fazendo com que a trajetória final desejada não possa ser seguida adequadamente, algo que é extremamente necessário em simuladores de voo. Assim, uma das contribuições importantes deste trabalho é, em primeiro lugar, apresentar uma metodologia de padronização das respostas dos atuadores de modo a que todos eles tenham no final, um comportamento igual o mais próximo possível, particularmente em termos de velocidade e de posicionamento. Com os dados da cinemática e da dinâmica da plataforma compondo o modelo completo do sistema foram realizadas várias simulações que aplicadas na plataforma de Stewart real validaram o modelo e mostraram a eficiência das técnicas de controle aplicadas no controle de posição e orientação da plataforma. Para validar o projeto da Plataforma de Stewart como uma possível base de movimento de um simulador de voo, foi implementada a dinâmica longitudinal e lateral de um Boeing 747-100, e com o auxilio de um sensor inercial Xsens® MTi-G, foram realizadas as medições dos ângulos de Euler da Plataforma. Os resultados obtidos pelos três controladores foram satisfatórios e ilustram o desempenho e a robustez da metodologia proposta. / In recent years there has been great interest in studying parallel manipulators, mainly applied in flight simulators, with six degrees of freedom. The interest in parallel kinematic structures is motivated by its high stiffness and excellent positioning capability in relation to serial kinematic structures. Furthermore, since the actuators are positioned on a base, they can handle heavy loads and also have low power consumption, considering that several actuators act on the same platform. This thesis presents the design of three controllers, which are, H-infinity controller with output feedback, PID controller and Fuzzy controller, so that this methodology can be employed in building a future flight simulator. The actuators models were obtained by a step voltage input to the engines and measuring their displacements by the encoders that are coupled to each of the respective axes of the motors. Knowing the relation from the motion transmission mechanism between the motor and the spindle of each actuator, the displacement of each spindle is obtained from the rotation of each motor measured by the corresponding encoder and thus we obtain the mathematical model of each actuator together with its transmission system. However, in practice, each actuator is slightly different from others, which leads to different behavior and performance of each. This affects the behavior of the platform making the final desired trajectory cannot be properly followed something that is extremely necessary in flight simulators. Thus, one of the important contributions of this work is first to present a methodology to standardize the actuators responses so that they all have in the end a behavior equal a close as possible, particularly in terms of velocity and positioning. With the kinematics data and platform dynamics composing the complete system model, several simulations applied to the real Stewart Platform validate the model and show the effectiveness of control techniques applied to control the position and orientation of the platform. In order to validate the Stewart Platform design as a possible base for a motion flight simulator, the longitudinal and lateral dynamics of a Boeing 747-100 model were implemented, and with the aid of an inertial sensor Xsens® MTi-G, measurements of the Euler angles of the platform were performed. The results obtained by the three controllers were satisfactory and illustrate the performance and robustness of the proposed methodology.

Neste trabalho, o equacionamento dinâmico de um manipulador espacial de base livre flutuante é descrito a partir do conceito do manipulador dinamicamente equivalente para que as técnicas de controle desenvolvidas sejam experimentalmente validadas em um manipulador convencional de base fixa. Dois tipos de controle de movimento são considerados. O primeiro foi desenvolvido no espaço das juntas e realiza o comando direto de posicionamento das juntas do manipulador; o segundo foi desenvolvido no espaço inercial e o controle é direcionado para o posicionamento do efetuador no espaço Cartesiano. Nos dois casos, o problema de acompanhamento de trajetória de um manipulador espacial com base livre flutuante sujeito a incertezas na planta e perturbações externas é proposto e solucionado sob o ponto de vista do critério de desempenho H \'INFINITO\'. Considerando métodos de controle para sistemas subatuados, três técnicas adaptativas foram desenvolvidas a partir de um controlador H \'INFINITO\' não-linear baseado na teoria dos jogos. A primeira técnica foi proposta considerando a estrutura do modelo bem definida, porém calculada com base em parâmetros incertos. Uma lei adaptativa foi aplicada para estimar esses parâmetros utilizando parametrização linear. Redes neurais artificiais são aplicadas nas outras duas abordagens adaptativas. A primeira utiliza uma rede neural para aprender o comportamento dinâmico do sistema robótico, considerado totalmente desconhecido. Nenhum dado cinemático ou dinâmico da base é utilizado neste caso. A segunda abordagem considera a estrutura do modelo nominal do manipulador bem definida e a rede neural é aplicada para estimar o comportamento das incertezas paramétricas e da dinâmica não-modelada da base. O critério H \'INFINITO\' é aplicado nas três técnicas para atenuar o efeito dos erros de estimativa. Resultados experimentais foram obtidos com um robô manipulador de base fixa subatuado (UArmII) e apresentaram melhor desempenho no acompanhamento da trajetória e no consumo de energia para as abordagens baseadas em redes neurais. / In the present work, the dynamics of a free-floating space manipulator is described through the dynamically equivalent manipulator approach in order to obtain experimental results in a planar fixed base manipulator. Control in joint and Cartesian spaces are considered. The first acts directly on joints positioning; the second control scheme acts on positioning the end-effector in some inertially fixed position. In both cases, the problem of tracking control with a guaranteed H-infinity performance for free-floating manipulator systems with plant uncertainties and external disturbances is proposed and solved. Considering control methods for underactuated systems, three adaptive techniques were developed from a nonlinear H-infinity controller based on game theory. The first approach was proposed considering a well defined structure for the plant, however it was computed based on uncertain parameters. An adaptive law was applied to estimate these parameters using linear parametrization. Artificial neural networks were applied in the two other approaches. The first one uses a neural network to learn the dynamic behavior from the robotic system, which is considered totally unknown. No kinematics or dynamics data from the spacecraft are necessary in this case. The second approach considers the nominal model structure well defined and the neural network is applied to estimate the behavior of the parametric uncertainties and of the spacecraft non-modeled dynamics. The H-infinity criterion was applied to attenuate the effect of estimation errors in the three techniques. Experimental results were obtained with an underactuated fixed-base planar manipulator (UArmII) and presented better performance in tracking and energy consumption for the neural based approaches.

O uso de etanol combustível no Brasil é hoje considerado o mais importante programa de combustível comercial renovável do mundo, sendo um potencial substituto aos derivados de petróleo. O aumento de rendimento fermentativo e a diminuição das perdas são objetivos de estudo em diversos centros de pesquisa, sendo o estudo da modelagem matemática e simulação do processo de grande importância para tal. A presente pesquisa apresenta como função identificar um modelo matemático para a linhagem isolada de Saccharomyces cerevisiae PE-2, de maneira a otimizar a maneira como é realizada a sua alimentação através de um controle H∞ por representação quasi-LPV. São realizados 9 ensaios de fermentação em 3 temperaturas distintas sob mesmas condições de concentração de substrato entrante. Após a finalização dos experimentos e análises, realiza-se a estimativa dos parâmetros componentes das equações diferenciais que modelam a cinética fermentativa, através de um algoritmo Quasi-Newton. De posse do modelo matemático, desenvolve-se um controle otimizado para a temperatura de 33ºC (temperatura usual de controle no processo industrial), considerando os parâmetros \"s\" e \"v\" variantes no tempo e os parâmetros x = 150 g/L e p = 70 g/L fixados, sendo valores médios obtidos durante o experimento. A utilização do controle desenvolvido possibilita um aumento de produtividade na faixa de 10% com relação a alimentação realizada em laboratório. Os resultados finais comprovam a eficiência do modelo matemático desenvolvido, comparado a outros estudos semelhantes, a influência da temperatura nos parâmetros cinéticos e a possibilidade de otimizar o processo através de um controle avançado do processo. / The use of ethanol in Brazil is considered the most important commercial renewable fuel program in the world, with a potential substitute for oil products. The increase in fermentation yield and losses reduction are objectives of study in various research centers, where the study of mathematical modeling and simulation of the process is of significant importance. This research presents as function to identify a mathematical model for the isolated strain of Saccharomyces cerevisiae PE-2, in order to optimize the way their substrate is fed, through a H∞ control based on quasi-LPV representation. Nine fermentation tests are performed at three different temperatures under the same conditions for incoming substrate concentration. After the experiments and analysis, it is carried out the estimation of parameters which are components of the differential equations that explain the fermentation kinetics, through a Quasi-Newton algorithm. With the mathematical model obtained, it is developed an optimal control for temperature 33°C (usual temperature control in the industrial process), considering the parameters \"s\" e \"v\" variyng in time and the parameters x = 150 g/L e p = 70 g/L set, which are average values obtained over the tests. The use of the control developed, applied to the flow variation, allows increasing productivity in 10% when compared with the flow performed in the tests conditions. The final results demonstrated the efficacy of the developed mathematical model, compared to other similar studies, the influence of temperature on the kinetic parameters and the possibility to optimize the process through an advanced process control.

The thesis is called Emmanuel Lévinas Ethics and its aim is to explain the ethical concept of this original French philosopher. The first part of the thesis is focused on important influences that were important for Lévinas' philosophical work. The next part of the thesis deals with dialogical personalism as a philosophical direction into which Lévinas is most often classified. The third and most important part deals with the motives that led Lévinas to the elaboration of his ethical theses and subsequently parts of these theses are processed. It turns out that the basic aspect of his theory is the social relationship of the 'I' with the Second, through which the path to transcendence leads .Lévinas' conception is considered as a sort of ethical turn in philosophy and can be considered as a return to man. Properly conceived ethics based on respect, Levinas considers being "prima Philosophia".

Smooth manifolds have been always understood intuitively as spaces that are infinitesimally linear at each point, and thus infinitesimally affine when forgetting about the base point. The aim of this thesis is to develop a general theory of infinitesimal models of algebraic theories that provides us with a formalisation of these notions, and which is in accordance with the intuition when applied in the context of Synthetic Differential Geometry. This allows us to study well-known geometric structures and concepts from the viewpoint of infinitesimal geometric algebra. Infinitesimal models of algebraic theories generalise the notion of a model by allowing the operations of the theory to be interpreted as partial operations rather than total operations. The structures specifying the domains of definition are the infinitesimal structures. We study and compare two definitions of infinitesimal models: actions of a clone on infinitesimal structures and models of the infinitesimalisation of an algebraic theory in cartesian logic. The last construction can be extended to first-order theories, which allows us to define infinitesimally euclidean and projective spaces, in principle. As regards the category of infinitesimal models of an algebraic theory in a Grothendieck topos we prove that it is regular and locally presentable. Taking a Grothendieck topos as a base we study lifts of colimits along the forgetful functor with a focus on the properties of the category of infinitesimally affine spaces. We conclude with applications to Synthetic Differential Geometry. Firstly, with the help of syntactic categories we show that the formal dual of every smooth ring is an infinitesimally affine space with respect to an infinitesimal structure based on nil-square infinitesimals. This gives us a good supply of infinitesimally affine spaces in every well-adapted model of Synthetic Differential Geometry. In particular, it shows that every smooth manifold is infinitesimally affine and that every smooth map preserves this structure. In the second application we develop some basic theory of smooth loci and formal manifolds in naive Synthetic Differential Geometry using infinitesimal geometric algebra.