Mémoire numérisé par la Division de la gestion de documents et des archives de l'Université de Montréal.

En écologie comme dans bien d’autres domaines, les échantillons de données de comptage comprennent souvent de nombreux zéros et quelques abondances fortes. Leur distribution est particulièrement surdispersée et asymétrique. Les méthodes les plus classiques d’inférence sont souvent mal adaptées à ces distributions, à moins de disposer d’échantillons de très grande taille. Il est donc nécessaire de s’interroger sur la validité des méthodes d’inférence, et de quantifier les erreurs d’estimation pour de telles données. Ce travail de thèse a ainsi été motivé par un jeu de données d’abondance de poissons, correspondant à un échantillonnage ponctuel par pêche électrique. Ce jeu de données comprend plus de 2000 échantillons, dont chacun correspond aux abondances ponctuelles (considérées indépendantes et identiquement distribuées) d’une espèce pour une campagne de pêche donnée. Ces échantillons sont de petite taille (en général, 20 _ n _ 50) et comprennent de nombreux zéros (en tout, 80% de zéros). Les ajustements de plusieurs modèles de distribution classiques pour les données de comptage ont été comparés sur ces échantillons, et la distribution binomiale négative a été sélectionnée. Nous nous sommes donc intéressés à l’estimation des deux paramètres de cette distribution : le paramètre de moyenne m, et le paramètre de dispersion, q. Dans un premier temps, nous avons étudié les problèmes d’estimation de la dispersion. L’erreur d’estimation est d’autant plus importante que le nombre d’individus observés est faible, et l’on peut, pour une population donnée, quantifier le gain en précision résultant de l’exclusion d’échantillons comprenant très peu d’individus. Nous avons ensuite comparé plusieurs méthodes de calcul d’intervalles de confiance pour la moyenne. Les intervalles de confiance basés sur la vraisemblance du modèle binomial négatif sont, de loin, préférables à des méthodes plus classiques comme la méthode de Student. Par ailleurs, ces deux études ont révélé que certains problèmes d’estimation étaient prévisibles, à travers l’observation de statistiques simples des échantillons comme le nombre total d’individus, ou le nombre de comptages non-nuls. En conséquence, nous avons comparé la méthode d’échantillonnage à taille fixe, à une méthode séquentielle, où l’on échantillonne jusqu’à observer un nombre minimum d’individus ou un nombre minimum de comptages non-nuls. Nous avons ainsi montré que l’échantillonnage séquentiel améliore l’estimation du paramètre de dispersion mais induit un biais dans l’estimation de la moyenne ; néanmoins, il représente une amélioration des intervalles de confiance estimés pour la moyenne. Ainsi, ce travail quantifie les erreurs d’estimation de la moyenne et de la dispersion dans le cas de données de comptage surdispersées, compare certaines méthodes d’estimations, et aboutit à des recommandations pratiques en termes de méthodes d’échantillonnage et d’estimation. / In ecology as well as in other scientific areas, count samples often comprise many zeros, and few high abundances. Their distribution is particularly overdispersed, and skewed. The most classical methods of inference are often ill-adapted to these distributions, unless sample size is really large. It is thus necessary to question the validity of inference methods, and to quantify estimation errors for such data. This work has been motivated by a fish abundance dataset, corresponding to punctual sampling by electrofishing. This dataset comprises more than 2000 samples : each sample corresponds to punctual abundances (considered to be independent and identically distributed) for one species and one fishing campaign. These samples are small-sized (generally, 20 _ n _ 50) and comprise many zeros (overall, 80% of counts are zeros). The fits of various classical distribution models were compared on these samples, and the negative binomial distribution was selected. Consequently, we dealt with the estimation of the parameters of this distribution : the parameter of mean m and parameter of dispersion q. First, we studied estimation problems for the dispersion. The estimation error is higher when few individuals are observed, and the gain in precision for a population, resulting from the exclusion of samples comprising very few individuals, can be quantified. We then compared several methods of interval estimation for the mean. Confidence intervals based on negative binomial likelihood are, by far, preferable to more classical ones such as Student’s method. Besides, both studies showed that some estimation problems are predictable through simple statistics such as total number of individuals or number of non-null counts. Accordingly, we compared the fixed sample size sampling method, to a sequential method, where sampling goes on until a minimum number of individuals or positive counts have been observed. We showed that sequential sampling improves the estimation of dispersion but causes the estimation of mean to be biased ; still, it improves the estimation of confidence intervals for the mean. Hence, this work quantifies errors in the estimation of mean and dispersion in the case of overdispersed count data, compares various estimation methods, and leads to practical recommendations as for sampling and estimation methods.

Les problèmes d'optimisation continue sont nombreux, en économie, en traitement de signal, en réseaux de neurones, etc. L'une des solutions les plus connues et les plus employées est l'algorithme évolutionnaire, métaheuristique basée sur les théories de l'évolution qui emprunte des mécanismes stochastiques et qui a surtout montré de bonnes performances dans la résolution des problèmes d'optimisation continue. L’utilisation de cette famille d'algorithmes est très populaire, malgré les nombreuses difficultés qui peuvent être rencontrées lors de leur conception. En effet, ces algorithmes ont plusieurs paramètres à régler et plusieurs opérateurs à fixer en fonction des problèmes à résoudre. Dans la littérature, on trouve pléthore d'opérateurs décrits, et il devient compliqué pour l'utilisateur de savoir lesquels sélectionner afin d'avoir le meilleur résultat possible. Dans ce contexte, cette thèse avait pour objectif principal de proposer des méthodes permettant de remédier à ces problèmes sans pour autant détériorer les performances de ces algorithmes. Ainsi nous proposons deux algorithmes :- une méthode basée sur le maximum a posteriori qui utilise les probabilités de diversité afin de sélectionner les opérateurs à appliquer, et qui remet ce choix régulièrement en jeu,- une méthode basée sur un graphe dynamique d'opérateurs représentant les probabilités de passages entre les opérateurs, et en s'appuyant sur un modèle de la fonction objectif construit par un réseau de neurones pour mettre régulièrement à jour ces probabilités. Ces deux méthodes sont détaillées, ainsi qu'analysées via un benchmark d'optimisation continue / The problems of continuous optimization are numerous, in economics, in signal processing, in neural networks, and so on. One of the best-known and most widely used solutions is the evolutionary algorithm, a metaheuristic algorithm based on evolutionary theories that borrows stochastic mechanisms and has shown good performance in solving problems of continuous optimization. The use of this family of algorithms is very popular, despite the many difficulties that can be encountered in their design. Indeed, these algorithms have several parameters to adjust and a lot of operators to set according to the problems to solve. In the literature, we find a plethora of operators described, and it becomes complicated for the user to know which one to select in order to have the best possible result. In this context, this thesis has the main objective to propose methods to solve the problems raised without deteriorating the performance of these algorithms. Thus we propose two algorithms:- a method based on the maximum a posteriori that uses diversity probabilities for the operators to apply, and which puts this choice regularly in play,- a method based on a dynamic graph of operators representing the probabilities of transitions between operators, and relying on a model of the objective function built by a neural network to regularly update these probabilities. These two methods are detailed, as well as analyzed via a continuous optimization benchmark

O cádmio (Cd) é importante poluente ambiental, que prejudica a produtividade das plantas e traz consequências graves à saúde humana. Uma das possíveis estratégias para mitigar os danos provocados pelo Cd na planta é o suprimento adequado de potássio (K), uma vez que esse nutriente atua na modulação de processos fisiológicos e mecanismos antioxidantes dos vegetais. Objetivou-se avaliar a importância do K nos mecanismos envolvidos na tolerância do capim tanzânia (Panicum maximum cv. Tanzânia) ao estresse oxidativo induzido pelo Cd. As plantas foram cultivadas em casa de vegetação com delineamento de blocos completos ao acaso, em esquema fatorial 3x4, com três doses de K (0,4; 6,0 e 11,6 mmol L-1) combinadas com quatro doses de Cd (0,0; 0,5; 1,0 e 1,5 mmol L-1) fornecidas em solução nutritiva, com seis repetições, sendo três destinadas à avaliação dos parâmetros produtivos e nutricionais e outras três aos parâmetros fisiológicos e metabólicos. Foram avaliados dois períodos de crescimento das plantas, sendo o primeiro corte aos 35 dias após o transplantio das mudas e o segundo aos 27 dias após o primeiro. No segundo crescimento não foi adicionado Cd na solução nutritiva. O aumento do fornecimento de K resultou em incremento na produção de massa seca da parte aérea do capim tanzânia exposto às doses de Cd até 1,0 mmol L-1, no segundo corte. O acúmulo de Cd na parte aérea do capim foi mais elevado em condições de alta disponibilidade de Cd (1,5 mmol L-1) e de K (11,6 mmol L-1). O aumento das doses de Cd resultou em mais baixas concentrações de cálcio, magnésio, enxofre e manganês e mais elevadas concentrações de K, cobre, ferro e zinco na parte aérea do capim, no segundo corte. O maior fornecimento de K proporcionou mais elevadas taxas de assimilação de CO2 e de transpiração, condutância estomática, eficiência quântica do fotossistema II e taxa de transporte de elétrons em plantas expostas a doses intermediárias de Cd (0,5 a 1,0 mmol L-1). As concentrações de malondialdeído (MDA), peróxido de hidrogênio (H2O2) e prolina na parte aérea das plantas foram mais altas em condições de altas disponibilidades de Cd. As mais altas doses de K para plantas submetidas ao estresse por Cd resultaram em mais baixas concentrações de MDA devido ao incremento proporcionado por esse nutriente na atividade das enzimas antioxidantes superóxido dismutase (SOD), catalase (CAT), guaiacol peroxidase (GPX), ascorbato peroxidase (APX) e glutationa redutase (GR), avaliadas no segundo corte. O K promoveu aumento das concentrações de espermidina e espermina em plantas sob toxidez por Cd. Portanto, o K ameniza os efeitos tóxicos induzidos pelo Cd no capim tanzânia, reduzindo o estresse oxidativo por meio do aumento da atividade das enzimas antioxidantes e da concentração de poliaminas, o que resulta em maior produção de massa seca da parte aérea e maior acúmulo de Cd, aumentando a capacidade de fitoextração de Cd pelo capim tanzânia. / Cadmium (Cd) is an important environmental pollutant, which damages plant productivity and has serious consequences for human health. One of the possible strategies to mitigate the damage caused by Cd in the plant is the supply of potassium (K), since this nutrient acts in the modulation of the physiological processes and antioxidant mechanisms of the plants. The aim of this study was to evaluate the importance of K in the mechanisms involved in the tolerance of tanzania guinea grass (Panicum maximum cv. Tanzania) to the oxidative stress induced by Cd. Plants were grown in a greenhouse, in randomized complete block design, using a 3x4 factorial, with three rates of K (0.4, 6.0 and 11.6 mmol L-1) combined with four rates of Cd (0.0, 0.5, 1.0 and 1.5 mmol L-1) provided in nutrient solution, with six replications, three for the evaluation of productive and nutritional parameters and three for physiological and metabolic parameters. Two plant growth periods were evaluated, with the first harvest done at 35 days after seedlings transplanting and the second at 27 days after the first. In the second growth, Cd was not added to the nutrient solution. High K supply increased dry matter yield of tanzania guinea grass receiving Cd rates up to 1.0 mmol L-1, at the second harvest. The accumulation of Cd in the shoots of the grass was high in the conditions of high availability of Cd (1.5 mmol L-1) and K (11.6 mmol L-1). The increase in Cd rates resulted in low concentrations of calcium, magnesium, sulfur and manganese and high concentrations of K, copper, iron and zinc in the shoots of the grass at the second harvest. High K supply provided high rates of CO2 assimilation, transpiration, stomatal conductance, quantum efficiency of photosystem II and rate of electron transport in plants grown in intermediate rates of Cd (0.5 to 1.0 mmol L-1). The concentrations of malondialdehyde (MDA), hydrogen peroxide (H2O2) and proline in the shoots were high in conditions of high availability of Cd. High rates of K in plants submitted to Cd stress resulted in low concentrations of MDA due to the activities superoxide dismutase (SOD), catalase (CAT), guaiacol peroxidase (GPX), ascorbate peroxidase (APX) and glutathione reductase (GR) determined in the second harvest. K resulted in high concentrations of spermidine and spermine in plants under the toxic effect of Cd. Therefore, K alleviates the toxic effects induced by Cd in tanzania guinea grass, reducing oxidative stress by increasing the activity of antioxidant enzymes and the concentration of polyamines, which results in high shoot dry mass production and high Cd accumulation, increasing the capacity of Cd phytoextraction by tanzania guinea grass.

A definição de valores máximos de variáveis hidrológicas na engenharia de recursos hídricos atua como ferramenta de extrema importância em vista de inúmeras aplicações práticas que se utilizam desses valores. Neste trabalho é apresentada uma revisão do estado da arte na definição de valores máximos de variáveis hidrológicas (metodologia estatística e determinística). Na metodologia estatística é mostrada uma avaliação conceitual e crítica, na qual é apresentado um exemplo numérico que demonstra as inconsistências ou falhas que caracterizam a necessidade de revisão nos conceitos. Na metodologia determinística é demonstrada as técnicas que definirão os valores da precipitação máxima provável e algumas considerações adicionais quanto à metodologia determinística, principalmente no que se refere às imprecisões dos valores determinados para a precipitação máxima provável/enchente máxima provável. A partir das conclusões sobre ambas as metodologias avaliadas é aplicado uma nova metodologia para determinação de valores máximos de projeto. Essa metodologia, denominada conjugada, resulta da combinação dos procedimentos atualmente usados: metodologia probabilística e determinística. Com o objetivo de caracterizar as importantes contribuições do método conjugado para engenharia, são apresentados alguns estudos de casos que procuram demonstrar a aplicabilidade prática do método e suas vantagens em detrimento aos métodos atuais. A conclusão é que o método conjugado representa um avanço em relação aos métodos atualmente utilizados, uma vez que é consistente com o fenômeno físico e permite atribuir probabilidades às variáveis hidrológicas, resultando em valores de projeto mais realista. / The description of extreme values of hydrological variables in water resources engineering is an extremely importance tool for innumerable practical applications. This work provides a review of statistical and deterministic methods that are used to estimate extreme values of hydrological variables. A critical and conceptual evaluation of statistical methods is presented along with a numerical example that demonstrates the inconsistencies or imperfections of such methods, characterizing the necessity of revisions of these concepts. Deterministic methods to estimate the maximum probable precipitation are also presented and some additional considerations regarding the methodology are discussed, especially those concerned to the imprecise estimates of the maximum probable precipitation/flood. A new methodology to estimate extreme values of hydrologic variables for engineering projects is developed based upon conclusions about the evaluated methodologies. This new methodology is called conjugated, and results from the combination of the currently used statistical and deterministic procedures. In order to characterize the important contributions provided by the conjugated method, some case studies are presented as an attempt to demonstrate its practical applicability as well as its advantages over current methods. The conclusion is that the conjugate method represents an advance with respect to current methods because it is consistent with the physical phenomenon and it allows assigning probabilities to the hydrological variable, resulting in more realistic values to be employed in engineering projects.

O cádmio (Cd) é importante poluente ambiental, que prejudica a produtividade das plantas e traz consequências graves à saúde humana. Uma das possíveis estratégias para mitigar os danos provocados pelo Cd na planta é o suprimento adequado de potássio (K), uma vez que esse nutriente atua na modulação de processos fisiológicos e mecanismos antioxidantes dos vegetais. Objetivou-se avaliar a importância do K nos mecanismos envolvidos na tolerância do capim tanzânia (Panicum maximum cv. Tanzânia) ao estresse oxidativo induzido pelo Cd. As plantas foram cultivadas em casa de vegetação com delineamento de blocos completos ao acaso, em esquema fatorial 3x4, com três doses de K (0,4; 6,0 e 11,6 mmol L-1) combinadas com quatro doses de Cd (0,0; 0,5; 1,0 e 1,5 mmol L-1) fornecidas em solução nutritiva, com seis repetições, sendo três destinadas à avaliação dos parâmetros produtivos e nutricionais e outras três aos parâmetros fisiológicos e metabólicos. Foram avaliados dois períodos de crescimento das plantas, sendo o primeiro corte aos 35 dias após o transplantio das mudas e o segundo aos 27 dias após o primeiro. No segundo crescimento não foi adicionado Cd na solução nutritiva. O aumento do fornecimento de K resultou em incremento na produção de massa seca da parte aérea do capim tanzânia exposto às doses de Cd até 1,0 mmol L-1, no segundo corte. O acúmulo de Cd na parte aérea do capim foi mais elevado em condições de alta disponibilidade de Cd (1,5 mmol L-1) e de K (11,6 mmol L-1). O aumento das doses de Cd resultou em mais baixas concentrações de cálcio, magnésio, enxofre e manganês e mais elevadas concentrações de K, cobre, ferro e zinco na parte aérea do capim, no segundo corte. O maior fornecimento de K proporcionou mais elevadas taxas de assimilação de CO2 e de transpiração, condutância estomática, eficiência quântica do fotossistema II e taxa de transporte de elétrons em plantas expostas a doses intermediárias de Cd (0,5 a 1,0 mmol L-1). As concentrações de malondialdeído (MDA), peróxido de hidrogênio (H2O2) e prolina na parte aérea das plantas foram mais altas em condições de altas disponibilidades de Cd. As mais altas doses de K para plantas submetidas ao estresse por Cd resultaram em mais baixas concentrações de MDA devido ao incremento proporcionado por esse nutriente na atividade das enzimas antioxidantes superóxido dismutase (SOD), catalase (CAT), guaiacol peroxidase (GPX), ascorbato peroxidase (APX) e glutationa redutase (GR), avaliadas no segundo corte. O K promoveu aumento das concentrações de espermidina e espermina em plantas sob toxidez por Cd. Portanto, o K ameniza os efeitos tóxicos induzidos pelo Cd no capim tanzânia, reduzindo o estresse oxidativo por meio do aumento da atividade das enzimas antioxidantes e da concentração de poliaminas, o que resulta em maior produção de massa seca da parte aérea e maior acúmulo de Cd, aumentando a capacidade de fitoextração de Cd pelo capim tanzânia. / Cadmium (Cd) is an important environmental pollutant, which damages plant productivity and has serious consequences for human health. One of the possible strategies to mitigate the damage caused by Cd in the plant is the supply of potassium (K), since this nutrient acts in the modulation of the physiological processes and antioxidant mechanisms of the plants. The aim of this study was to evaluate the importance of K in the mechanisms involved in the tolerance of tanzania guinea grass (Panicum maximum cv. Tanzania) to the oxidative stress induced by Cd. Plants were grown in a greenhouse, in randomized complete block design, using a 3x4 factorial, with three rates of K (0.4, 6.0 and 11.6 mmol L-1) combined with four rates of Cd (0.0, 0.5, 1.0 and 1.5 mmol L-1) provided in nutrient solution, with six replications, three for the evaluation of productive and nutritional parameters and three for physiological and metabolic parameters. Two plant growth periods were evaluated, with the first harvest done at 35 days after seedlings transplanting and the second at 27 days after the first. In the second growth, Cd was not added to the nutrient solution. High K supply increased dry matter yield of tanzania guinea grass receiving Cd rates up to 1.0 mmol L-1, at the second harvest. The accumulation of Cd in the shoots of the grass was high in the conditions of high availability of Cd (1.5 mmol L-1) and K (11.6 mmol L-1). The increase in Cd rates resulted in low concentrations of calcium, magnesium, sulfur and manganese and high concentrations of K, copper, iron and zinc in the shoots of the grass at the second harvest. High K supply provided high rates of CO2 assimilation, transpiration, stomatal conductance, quantum efficiency of photosystem II and rate of electron transport in plants grown in intermediate rates of Cd (0.5 to 1.0 mmol L-1). The concentrations of malondialdehyde (MDA), hydrogen peroxide (H2O2) and proline in the shoots were high in conditions of high availability of Cd. High rates of K in plants submitted to Cd stress resulted in low concentrations of MDA due to the activities superoxide dismutase (SOD), catalase (CAT), guaiacol peroxidase (GPX), ascorbate peroxidase (APX) and glutathione reductase (GR) determined in the second harvest. K resulted in high concentrations of spermidine and spermine in plants under the toxic effect of Cd. Therefore, K alleviates the toxic effects induced by Cd in tanzania guinea grass, reducing oxidative stress by increasing the activity of antioxidant enzymes and the concentration of polyamines, which results in high shoot dry mass production and high Cd accumulation, increasing the capacity of Cd phytoextraction by tanzania guinea grass.

A definição de valores máximos de variáveis hidrológicas na engenharia de recursos hídricos atua como ferramenta de extrema importância em vista de inúmeras aplicações práticas que se utilizam desses valores. Neste trabalho é apresentada uma revisão do estado da arte na definição de valores máximos de variáveis hidrológicas (metodologia estatística e determinística). Na metodologia estatística é mostrada uma avaliação conceitual e crítica, na qual é apresentado um exemplo numérico que demonstra as inconsistências ou falhas que caracterizam a necessidade de revisão nos conceitos. Na metodologia determinística é demonstrada as técnicas que definirão os valores da precipitação máxima provável e algumas considerações adicionais quanto à metodologia determinística, principalmente no que se refere às imprecisões dos valores determinados para a precipitação máxima provável/enchente máxima provável. A partir das conclusões sobre ambas as metodologias avaliadas é aplicado uma nova metodologia para determinação de valores máximos de projeto. Essa metodologia, denominada conjugada, resulta da combinação dos procedimentos atualmente usados: metodologia probabilística e determinística. Com o objetivo de caracterizar as importantes contribuições do método conjugado para engenharia, são apresentados alguns estudos de casos que procuram demonstrar a aplicabilidade prática do método e suas vantagens em detrimento aos métodos atuais. A conclusão é que o método conjugado representa um avanço em relação aos métodos atualmente utilizados, uma vez que é consistente com o fenômeno físico e permite atribuir probabilidades às variáveis hidrológicas, resultando em valores de projeto mais realista. / The description of extreme values of hydrological variables in water resources engineering is an extremely importance tool for innumerable practical applications. This work provides a review of statistical and deterministic methods that are used to estimate extreme values of hydrological variables. A critical and conceptual evaluation of statistical methods is presented along with a numerical example that demonstrates the inconsistencies or imperfections of such methods, characterizing the necessity of revisions of these concepts. Deterministic methods to estimate the maximum probable precipitation are also presented and some additional considerations regarding the methodology are discussed, especially those concerned to the imprecise estimates of the maximum probable precipitation/flood. A new methodology to estimate extreme values of hydrologic variables for engineering projects is developed based upon conclusions about the evaluated methodologies. This new methodology is called conjugated, and results from the combination of the currently used statistical and deterministic procedures. In order to characterize the important contributions provided by the conjugated method, some case studies are presented as an attempt to demonstrate its practical applicability as well as its advantages over current methods. The conclusion is that the conjugate method represents an advance with respect to current methods because it is consistent with the physical phenomenon and it allows assigning probabilities to the hydrological variable, resulting in more realistic values to be employed in engineering projects.

Le contexte général de cette thèse est l’étude de problèmes inverses et directs en théorie du contrôle. Plus précisément, les trois problèmes étudiés sont les suivants.Le premier est un problème de contrôle optimal (approche directe). Il s’agit de fournir la synthèse temps minimum du modèle cinématique d'un drone volant à altitude constante, de vitesse linéaire non nécessairement constante voulant rejoindre une trajectoire circulaire de rayon de courbure minimum.Le deuxième problème concerne une approche inverse du contrôle optimal. Il s’agit d’élaborer des méthodes théoriques de reconstruction du critère optimisé dans un problème de contrôle optimal à partir d’un ensemble de solutions à ce problème, ainsi que caractériser les "bons" ensembles de trajectoires permettant la reconstruction du critère. Le contrôle optimal inverse connait un regain d’intérêt depuis une quinzaine d’années, en particulier dans l’étude des comportements moteurs humains. En effet, selon un paradigme largement accepté en neurophysiologie, parmi tous les mouvements possibles ceux effectivement réalisés sont solutions d’un processus d’optimisation.Le troisième problème traite de stabilisation par retour de sortie. Nous analysons, à travers un exemple académique tiré du contrôle quantique, le problème de stabilisation par retour de sortie (à l’aide d’un observateur) lorsque le point où l'on souhaite stabiliser le système correspond à un contrôle qui rend le système inobservable. L’idée générale est de perturber le retour d’état stabilisant afin de garantir l’observabilité du système tout en stabilisant le système sur la cible. L’analyse de cet exemple académique nous permet dans un second temps de dégager une méthode générale pouvant s’appliquer à une classe de système beaucoup plus large. / The overall context of this thesis is the study of inverse and direct problems in control theory. More specifically, the following three problems are studied.The first one is an optimal control problem (direct approach). The aim is to give a time minimum systhesis fora kinematic model of a UAV flying at constant altitude with positive (non-necessarily constant) linear velocityin order to steer it to a fixed circle of minimum turning radius.The second problem deals with an inverse approach of optimal control. The aim is to develop theoretical methods in order to reconstruct the minimized criterion in an optimal control problem from a set of solution to this problem. The aim is also to characterize the « good » sets of trajectories leading to the reconstruction of the criterion. In the last fifteen years, there has been a renewed interest in inverse optimal control, especially inhuman motor behavior. Indeed, according to a well accepted paradigm in neurophysiology, among all possible movements, those actually accomplished are solutions of an optimization process.The third problem tackles output feedback stabilization. We analyze, via a simple academic example from quantum control, the problem of dynamic output feedback stabilization, when the point where we want to stabilize corresponds to a control value that makes the system unobservable. The general idea is to perturb the stabilizing state feedback in order to ensure the observability of the system while stabilizing it to the target.The analysis of this example allows, secondly, to identify a general procedure that can be applied to a widerclass of systems.

Mémoire numérisé par la Division de la gestion de documents et des archives de l'Université de Montréal

We investigate the effect of a 120 meter sea level drop on transport through the Caribbean Sea and the Florida Straits during the Last Glacial Maximum (LGM) relative to the present, using the Regional Ocean Modeling System (ROMS). A geostrophic transport estimate for the Florida Straits suggests the LGM Florida Current was weaker than today by one third, inferring a likely decrease in the North Atlantic overturning circulation by 12-15 Sv. A possible impact of a shallower LGM Florida Straits sill depth on the Florida Current has been suggested. Our model results show that the volume transport through the Florida Straits is slightly reduced in a lower sea level model simulation when compared to a control sea level simulation (34.8 ± 2.0 Sv vs. 39.8 ± 2.3 Sv). The difference in transport is of the order of 5 Sv, representing a maximum limit to the LGM flow reduction due to sea level change. Therefore the change in sill depth between the LGM and the present is unlikely to have been a cause of the entire observed flow reduction.