Infinite dimensional systems such as flexible airplane wings and Vertical Axis Wind Turbine (VAWT) blades may require control to improve performance. Traditional control techniques use position and velocity information feedback, but velocity information for infinite dimensional systems is not easily attained. This research investigates the use of reduced-sensing control for these applications. Reduced-sensing control uses feedback of position measurements and an associated filter state to stabilize the system dynamics. A filter state is a nonphysical entity that appends an additional ordinary differential equation to the system dynamics. Asymptotic stability of a system using this control approach is confirmed through a sequence of existing mathematical tools. These tools include equilibrium point solutions, Lyapunov functions for stability and control, and Mukherjee and Chen's Asymptotic Stability Theorem. This thesis research investigates the stability of a beam representing an airplane wing or a VAWT blade controlled using feedback of position and filter state terms only. Both of these infinite dimensional systems exhibit asymptotic stability with the proposed reduced-sensing control design. Additionally, the analytical stability response of the VAWT is verified through numerical simulation.

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / This study was carried out to estimate genetic parameters for scrotal circumference (SC) and weights (W) taken at different ages in Nelore male participants of a breeding program sponsored by National Association of Breeders and Researchers. In the first paper there were estimated genetic parameters for the characteristics of the SC and W at 210, 280, 365, and 450 days of age (SC210, SC280, SC365, SC450, W210, W280, W365 and W450 respectively). The components of (co)variances were estimated by Restricted Maximum Likelihood method under an animal model in multi-trait analysis. The heritability estimates for direct effect were: 0,45±0,05 (SC210); 0,34±0,02 (SC280), 0,35±0,02 (SC365); 0,45±0,02 (SC450); 0,39±0,05 (W210); 0,31±0,03 (W280); 0,23±0,02 (W365), and 0,20±0,02 (W450), while estimates of heritability for the maternal effect for the weights were 0,08±0,02; 0,05±0,01; 0,05±0,01, and 0,03±0,01, respectively, for W210, W280, W365, and W450. These results suggest that the use of the measure of the SC as a selection criterion may contribute to reproductive genetic gain. The genetic correlations between SC were positive and medium to high magnitude, as between the SC and W were positive and showed a smaller magnitude compared to the estimated between measures of SC at differents ages. These genetic correlations indicate that only one measurement of SC can be effective for selection, and older age for this evaluation is recommended at 450 days of age. In the second article, it was analyzed 29,691 SC measures taken between 134 and 495 days of age, by random regression models under uni-trait analysis. To model the mean population curve, was used a third order fixed regression on Legendre polynomials. There were considered three random effects and differents orders of polynomial fit. Residual variances were considered homogeneous or heterogeneous. The model chosen was the one with homogeneous residual variance (M45_1). The heritability estimates obtained from the 360 days were greater than 0.42, indicating that the selection in this period should provide better response. High and positive genetic correlations were estimated between measures of SC, being higher for the measurements at closer ages. Because of the genetic correlation estimates between the SC measured at different ages were positive and with high magnitudes, the selection can be done in only one age. The best age for the measurement of SC indicated by the less parameterized model is after 360 days, and the closer to 495 days, the higher estimates. In the third article the data were analyzed using a random regression model in bi-traits analysis to estimate genetic parameters for SC and W. The mean population curve was modeled using third order fixed regression using Legendre polynomials. The analysis model considered the residual effect as constant throughout the period of age evaluated. The highest estimate of SC heritability was found close to 495 days of age (0.52), while the maximum value for W (0.35) was observed at 290 and 495 days of age. These values suggest that selection for both traits should promote genetic gain. The values of genetic correlations between SC and W ranged from -0.22 to 0.59 over the period studied. These values suggest a correlated response of different magnitudes, depending on the selected characteristic and also the age at which the selection was performed. The measurement of scrotal circumference at 450 days can be used as selection criteria in the studied population. / O presente estudo foi desenvolvido com o objetivo de estimar parâmetros genéticos para perímetro escrotal (PE) e pesos (P) tomados em diferentes idades em bovinos machos da raça Nelore participantes do programa de melhoramento genético da Associação Nacional de Criadores e Pesquisadores. No primeiro artigo foram estimados parâmetros genéticos para as características de PE e P medidos aos 210, 280, 365 e 450 dias de idade (PE210, PE280, PE365, PE450, P210, P280, P365 e P450, respectivamente). Os componentes de (co)variâncias foram estimados pelo método da máxima verossimilhança restrita, sob modelo animal, em análises multi-características. As estimativas de herdabilidade para o efeito direto foram: 0,45±0,05 (PE210); 0,34±0,02 (PE280), 0,35±0,02 (PE365); 0,45±0,02 (PE450); 0,39±0,05 (P210); 0,31±0,03 (P280); 0,23±0,02 (P365) e 0,20±0,02 (P450), enquanto que as estimativas de herdabilidade para o efeito materno para os pesos foram 0,08±0,02; 0,05±0,01; 0,05±0,01 e 0,03±0,01, respectivamente, para P210, P280, P365 e P450. Esses resultados sugerem que a utilização da medida do PE como critério de seleção pode contribuir para o ganho genético reprodutivo dos animais. As correlações genéticas estimadas entre os PE foram todas positivas e de médias a altas magnitudes, já entre PE e P se apresentaram positivas e de menor magnitude em relação às estimadas entre as medidas de PE em diferentes idades. Essas correlações genéticas indicam que apenas uma mensuração de PE pode ser eficiente para seleção e a idade mais recomendada para essa avaliação é aos 450 dias de idade. No segundo artigo, foram analisadas 29.691 medidas de PE tomadas entre os 134 e os 495 dias de idade, através de modelos de regressão aleatória (RA) sob análise uni-característica. Para modelar a curva média populacional, foi utilizada uma regressão fixa de terceira ordem sob polinômios de Legendre. Foram considerados três efeitos aleatórios e diferentes ordens de ajuste de polinômios. As variâncias residuais foram consideradas homogêneas ou heterogêneas. O modelo escolhido foi o que apresentou variância residual homogênea (M45_1). As estimativas de herdabilidade obtidas a partir dos 360 dias foram maiores que 0,42, indicando que a seleção dos animais nesse período deverá fornecer melhor resposta a seleção. Valores altos e positivos de correlações genéticas foram estimados entre as diferentes medidas de PE, sendo maiores para as medidas em idades mais próximas. Devido as correlações genéticas estimadas entre os PEs medidos nas diferentes idades serem positivas e de altas magnitudes, pode se utilizar a medida tomada em apenas uma idade para a seleção. A melhor idade para a mensuração do PE indicada pelo modelo menos parametrizado é após os 360 dias, sendo que quanto mais próximo aos 495 dias, maiores são as estimativas. No terceiro artigo os dados foram analisados através de um modelo de RA sob análise bi-característica para estimar os parâmetros genéticos para PE e P. A curva média populacional, foi modelada utilizando regressão fixa de terceira ordem com o uso de polinômios de Legendre. O modelo de análise considerou o efeito residual como constante durante todo período de idade avaliado. A maior estimativa de herdabilidade para PE ocorreu próximo aos 495 dias de idade (0,52), enquanto que para P o valor máximo (0,35) foi observado aos 290 e aos 495 dias de idade. Estes valores sugerem que a seleção para ambas as características deve promover ganho genético. As correlações genéticas entre PE e P apresentaram valores variando de -0,22 a 0,59 ao longo do período avaliado. Estes valores sugerem resposta correlacionada de diferentes magnitudes, dependendo da característica selecionada e, também, da idade em que a seleção foi procedida. A medida do perímetro escrotal aos 450 dias pode ser utilizada como critério de seleção na população estudada.

L'objet de cette thèse est d'étudier la théorie du transport optimal sur un espace de Wiener abstrait. Les résultats qui se trouvent dans quatre principales parties, portent :Sur la convexité de l'entropie relative. On prolongera des résultats connus en dimension finie, sur l'espace de Wiener muni d'une norme uniforme, à savoir que l'entropie relative est (au moins faiblement) 1-convexe le long des géodésiques induites par un transport optimal sur l'espace de Wiener.Sur les mesures à densité logarithmiquement concaves. Le premier des résultats importants consiste à montrer qu'une inégalité de type Harnack est vraie pour le semi-groupe induit par une telle mesure sur l'espace de Wiener. Le second des résultats obtenus nous fournit une inégalité en dimension finie (mais indépendante de la dimension), contrôlant la différence de deux applications de transport optimal.Sur le problème de Monge. On s'intéressera au problème de Monge sur l'espace de Wiener, muni de plusieurs normes : des normes à valeurs finies, ou encore la pseudo-norme de Cameron-Martin.Sur l'équation de Monge-Ampère. Grâce aux inégalités obtenues précédemment, nous serons en mesure de construire des solutions fortes de l'équation de Monge-Ampère (induite par le coût quadratique) sur l'espace de Wiener, sous de faibles hypothèses sur les densités des mesures considérées / The aim of this PhD is to study the optimal transportation theory in some abstract Wiener space. You can find the results in four main parts and they are aboutThe convexity of the relative entropy. We will extend the well known results in finite dimension to the Wiener space, endowed with the uniform norm. To be precise the relative entropy is (at least weakly) geodesically 1-convex in the sense of the optimal transportation in the Wiener space.The measures with logarithmic concave density. The first important result consists in showing that the Harnack inequality holds for the semi-group induced by such a measure in the Wiener space. The second one provides us a finite dimensional and dimension-free inequality which gives estimate on the difference between two optimal maps.The Monge Problem. We will be interested in the Monge Problem on the Wiener endowed with different norms: either some finite valued norms or the pseudo-norm of Cameron-Martin.The Monge-Ampère equation. Thanks to the inequalities obtained above, we will be able to build strong solutions of the Monge-Ampère (those which are induced by the quadratic cost) equation on the Wiener space, provided the considered measures satisfy weak conditions

Cette thèse porte sur la modélisation, pour le contrôle, des profils de compositions dans les colonnes de distillation cryogénique. Nous obtenons un modèle non-linéaire de convection-diffusion par réduction d'un modèle d'équations-bilans singulièrement perturbé. Du point de vue de l'automatique, nous nous intéressons à la stabilité des profils de compositions résultants, ainsi qu'à leur observabilité. Du point de vue du procédé, la nouvauté de notre modèle réside dans la prise en compte d'une efficacité de garnissage dépendant des conditions d'opération de la colonne. Le modèle est validé par des comparaisons avec des données de fonctionnement dynamique issues d'une unité de séparation réelle, pour la séparation d'un mélange binaire. Sur le cas plus complexe d'une cascade de colonnes séparant un mélange ternaire, le modèle montre une grande sensibilité aux erreurs d'estimation des taux de reflux. Des résultats adaptés du champ de la chromatographie nous permettent de relier cette sensibilité à des erreurs d'estimation des vitesses d'ondes de compositions cohérentes. En parallèle, nous proposons et testons également un modèle de fonctions de transfert simple (fondé sur des gains statiques et des retards purs uniquement) pour les petites dynamiques de compositions, qui dépend explicitement de valeurs mesurables ou observables sur le procédé / This thesis addresses the problem of modeling the composition profiles dynamics inside cryogenic distillation columns, for control applications. We obtain a non-linear convection-diffusion model from the reduction of a singularly perturbed mass-balances model. In the control theory framework, we consider the stability of the resulting composition profiles and their observability. From the process viewpoint, we express the novelty of our model in terms of operating-conditions dependent packing efficiency. The model is validated against real dynamic plant data for a binary separation case. On a more complex, ternary separation columns cascade, the model shows highly sensitive to reflux rate estimation errors. Result adapted from the field of chromatography allows us to interpret this sensitivity in terms of erroneous coherent composition waves speeds. In parallel, we also propose and test a simple transfer functions model (based on static gains and pure delays only) for small composition dynamics, which explicitly depends on measurable or observable process data.