Thesis (M.S.)--Virginia Polytechnic Institute and State University, 1991. / Vita. Abstract. Includes bibliographical references (leaves 67-69). Also available via the Internet.

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In prophet problems, two players with different levels of information make decisions to optimize their return from an underlying optimal stopping problem. The player with more information is called the "prophet" while the player with less information is known as the "gambler." In this thesis, as in the majority of the literature on such problems, we assume that the prophet is omniscient, and the gambler does not know future outcomes when making his decisions. Certainly, the prophet will get a better return than the gambler. But how much better? The goal of a prophet problem is to find the least upper bound on the difference (or ratio) between the prophet's return, M, and the gambler's return, V. In this thesis, we present new prophet problems where we seek the least upper bound on M-V when there is a fixed cost per observations. Most prophet problems in the literature compare M and V when prophet and gambler buy (or sell) one asset. The new prophet problems presented in Chapters 3 and 4 treat a scenario where prophet and gambler optimize their return from selling two assets, when there is a fixed cost per observation. Sharp bounds for the problems on small time horizons are given; for the n-day problem, rough bounds and a description of the distributions for the random variables that maximize M-V are presented.

In this dissertation we present new results regarding optimality of block designs with limited resources. The dissertation is organized as follows. The first chapter outlines the theory of optimal block design. The second chapter shows new work in optimal minimally connected block designs with spatial correlation structure. The third chapter details the discovery of the optimal incomplete designs with two blocks. The fourth chapter does the same for the optimal binary incomplete designs with three blocks. The fifth chapter summarizes the techniques used and new results found and lists possible future research topics. / Ph. D.

This thesis consists of an introduction and five articles. A common theme in all the articles is optimal timing when acting on a financial market. The main topics are optimal selling of an asset, optimal exercising of an American option, optimal stopping games and optimal strategies in trend following trading. In all the articles, we consider a financial market different from the standard Black-Scholes market. In two of the articles this difference consists in allowing for jumps of the underlying process. In the other three, the difference is that we have incomplete information about the drift of the underlying process. This is a natural assumption in many situations, including the case of a true buyer of an American option, trading in a market which exhibits trends, and optimal liquidation of an asset in the presence of a bubble. These examples are all addressed in this thesis.

Ce travail s’inscrit dans le projet plus global SHARE dont l’objectif principal est de concevoir une station de contrôle sol universelle mono-opérateur de nouvelle génération pour le contrôle et la commande de drones à voilure fixe et voilure tournante.L’objectif de cette thèse est de développer un simulateur générique de la station de contrôle capable de simuler en temps réels les différents types de drones, les capteurs embarqués (caméra), l’environnement et les différentes missions militaires définies par le standard STANAG 4586. Après une modélisation des différentes parties de la station, nous présentons l’architecture adoptée pour le simulateur et le module de contrôle. Ce dernier est divisé en plusieurs niveaux hiérarchiques, dont le niveau supérieur contient les algorithmes de planification de trajectoire pour les drones à voilure fixe HALE (haute altitude, longue endurance). Ces algorithmes servent à calculer un chemin admissible entre un point de départ et un point d’arrivée en minimisant une fonction de coût.Enfin nous avons développé un système d’aide à la décision pour la gestion en ligne des missions, capable de réaliser une sélection d’objectifs, et une sélection du meilleur chemin proposé par les algorithmes de planification de trajectoire. Cet outil a pour objectif d’aider l’opérateur de la station à prendre la meilleure décision en maximisant les récompenses obtenues lors de la réalisation des objectifs et en minimisant certains critères tels que la consommation des ressources, le danger, les conditions météorologiques, etc. / The presented work is part of a larger project called SHARE, which consists in developing a universal new generation ground control station for the monitoring and the control of fixed and rotary wing UAVs (Unmanned Aerial Vehicle).The objective of this PhD thesis is to develop a generic ground control station simulator capable of simulating in real time different types of UAVs, onboard sensors, several flight environments, and various military missions which are defined according to the STANAG 4586 standard. First, we introduce the model of the different parts of the station, and then we present the architecture adopted for the simulator and the control module. The latter is divided into several hierarchical levels; the upper level contains the path planning algorithms for fixed wing HALE (High Altitude, Long Endurance) UAV. These algorithms are used to calculate an admissible path between initial and final position by minimizing a cost function.Finally, in order to manage missions online, we developed a decision support system that is capable of performing a variety of objectives. This system also supplies the operator the best paths proposed by planning algorithms. This tool aims to help the station operator to make the decision by maximizing the rewards obtained during the achieving the objectives and minimizing certain criteria (resource consumption, danger, weather,..).

The major contributions of this thesis are categorized into three areas: (i) magnetic modeling, (ii) optimal performance assessment and (iii) multi-objective design methodology of the linear permanent-magnet (LPM) and linear variable reluctance (LVR) motors for manufacturing automation applications. The target application is to perform repetitive point-to-point positioning tasks on a continuous basis under temperature constraints. Through simplification, the constraint on temperature rise may be replaced by a constraint on average power dissipation, provided that the thermal resistance is constant and known. The basic framework of analysis is first introduced for a class of idealized linear synchronous (LS) motors, where magnetic saturation and spatial harmonics are neglected, to provide clarity and insight. The physics-based force models for the LPM and LVR motors, including spatial harmonics and magnetic saturation as appropriate, are then developed. Due to magnetic linearity, the force model of the LPM motor is derived from the analytical solution of the Poisson Equation. A nonlinear magnetic circuit analysis model is developed for the LVR motor that includes both spatial harmonics and magnetic saturation. The accuracy of both force models are verified by finite element analysis. Applying those force models, the optimal performance assessment of the LPM and LVR motors is explored using the mathematical framework discussed for the idealized LS motors. In particular, the relationship between travel time and travel distance is characterized in terms of average power dissipation. The performance assessment methodologies developed here may be applied to any motor technology used in manufacturing automation applications. The multi-objective design optimization problem is then defined and software for its solution is developed using Monte-Carlo synthesis, the performance assessment tools and dominance-based sorting. Design results for the LPM and LVR motors are then presented. Future research is discussed as the conclusion of the thesis.

The thesis studies determinants and adjustment paths of the people's weight from the view point of rational behavior.It followes the research approach of Becker and Murphy (1988), makes use of the utility function from Levy (2002), and corporates a budget constraint so as to establish an optimal control model for food consumption and weight, and to find out the relationship between them. Negative correlations are found between the steady-state weight and food prices, basal metabolic rate, and time discount rate.Positive correlations are found between the steady-state weight and income, marginal utility of food, and desirable weight. There is a tendancy to guide the actual steady-state weight to a much higher fluctuation margin than that of the desirable weight.In the dynamic analysis, it is also found that, regardless of an increase or decrease of the steady-state weight, both directions of adjustment show that the process of food consumption is always ``overshooting."In other words, when the steady-state weight becomes heavier (lighter), consumers first increase (decrease) their food consumption substantially. And, as the time goes by, there is a gradual decrease (increase) in food consumption owing to the fact that the food consumption is still higher (lower) than what is required for metabolism of the body that makes the weight getting to increase (decrease) till the new equilibrium is arrived.

Interest in space-borne, distributed multi-aperture interferometric systems is driven by a need for continuously sustained imaging with high resolution. Amplitude interferometry systems measure the Fourier components of the image corresponding to the wave vectors (locations in the so-called u-v plane) that are proportional to the relative positions of the apertures. Imaging to specified resolution demands measurement of the Fourier components with adequate signal-to-noise ratio over the interior of a disk in the u-v plane (the resolution disk). In this paper we concentrate on the case in which interferometric measurements are made while the apertures are changing their relative positions. This work discusses heuristic maneuvers and strategies for a system of two space-borne telescopes to cover the frequency plane while optimizing a cost function that includes both a measure of image quality and propulsive effort. The current study is motivated by previous research in which the optimization problem was formulated and the first-order necessary conditions (FONC) derived. The earlier work obtained short time horizon solutions to the FONC for various simple situations, but the complexity of the integro-differential equations for optimal maneuvering have heretofore prevented solution for an optimal maneuver for the entirety of the imaging process. In place of a direct attack on the FONC, the present work investigates various heuristic approaches to minimizing the cost function in the discretized state and discretized time domains in a hexagonal coordinate system. Using three classes of coverage rules, experimentation with a variety of maneuver strategies involving two apertures has led to a number of time-optimal or fuel-optimal solutions based on the initial conditions of the spacecraft. This thesis shows that an optimal maneuver can be determined from the starting positions of the spacecraft and that a self-spiral class of motion seems to be the most beneficial for long term strategies. Future work may focus on strategies for interferometric systems with more than two apertures and with a finer mesh of the hexagonal coordinate system.