L’objectif de cette thèse est d’appliquer la théorie du contrôle optimal à la dynamique d’ensembles inhomogènes de spins. La première partie est dévouée au contrôle d’un ensemble de spins couplé à une cavité. La théorie est introduite en détail, et une méthode générale pour contrôler efficacement les spins est présentée. Plusieurs pulses sont déterminés dans les régimes de bonne et de mauvaise cavité. De même, les fonctions non linéaires généralisées sont utilisées afin de déterminer des approximations simples. Dans un second temps, le problème de la maximisation du Signal-sur-Bruit d’un écho de spin est abordé, et des conditions d’optimisations sont établies. Il est montré que les nouveaux pulses sont supérieurs à ceux de l’état de l’art, en termes de fidélité et d’augmentation du Signal-sur-Bruit. Par ailleurs, ils permettent d’explorer de nouvelles situations (e.g. mesure de FID (Free Induction Decay) en CQED avec un taux de perte de cavité plus long que T2∗). La seconde partie est dévouée à des problèmes de RMN/IRM standard. Deux situations de "sélectivité" sont étudiées. La première consiste à déterminer le pulse le plus court qui produit la transformation la plus sélective par rapport aux offsets. Dans le cas ultra-sélectif, la solution optimale est un arc singulier d’amplitude constante. Cependant, si des contraintes de robustesse sont ajoutées, la solution optimale peut-être un arc régulier. La seconde est celle de l’optimisation de base de données pour des expériences de MR-fingerprinting. Dans ce cas, un champ de contrôle est conçu pour générer une base de données "d’empreinte digitale" qui maximise le processus de reconnaissance entre spins de paramètres différents. / The goal of this thesis is to apply optimal control theory to the dynamics ofinhomogeneous spin ensembles. The first part focuses on the control of a spin ensemble coupled to a cavity. The theory is introduced in detail, and a general method to efficiently control spins ispresented. Several pulses are derived in the bad/good cavity regimes using numerical optimal control techniques. Additionally, non-linear generalized functions are used in order to derivesimple approximated solutions. In a second step, the problem of spin echo Signal to Noise Ratio maximization is investigated, and maximization conditions are derived. It is shown that new pulses are superior to state-of-the-art square pulses in terms of fidelity and SNR maximization. Moreover, they allow us to explore new situations (e.g. Free Induction Decay measurementsin cavity-QED with a cavity damping longer than T2∗). The second part focuses on standard NMR/MRI problems. Two distinct situations of selectivity are investigated. The first one consists of determining the time minimum pulse which produces the most offset-selective transformation. In the ultra-selectivity case, the optimal solution is a singular arc of constant amplitude. However,if additional robustness constraints are taken into account, the optimal solution can be a regular arc. The second situation is the optimization of databases for MR-fingerprinting experiments. In this case, a control field is designed so that it generates a fingerprint database which maximizesthe recognition process between several spins with different parameters.

System Lupus Erythematosus (SLE) is a chronic inflammatory autoimmune disorder that affects many parts of the body including skin, joints, kidneys, brains and other organs. Lupus Nephritis (LN) is a disease caused by SLE. Given the complexity of LN, we establish an optimal treatment strategy based on a previously developed mathematical model.For our thesis work, the model variables are: Immune Complexes (I), Pro-inflammatory mediators (P), Damaged tissue (D), and Anti-inflammatory mediators (A). The analysis in this research project focuses on analyzing therapeutic strategies to control damage using both parameter estimation techniques (integration of data to quantify any uncertainties associated with parameters) and optimal control with the goal of minimizing time spent on therapy for treating damaged tissue by LN.

Cette thèse s'intéresse à une étude des EDSR ergodiques, avec pour principal objectif leur application à l'étude du comportement en temps long de certaines EDP. Dans un premier temps, nous démontrons des résultats (qui sont déjà connus dans le cadre où l'EDS sous-jacente est à bruit additif) dans un cadre de bruit sous-jacent multiplicatif. Par la suite, l'introduction d'un nouvel aléa via un processus de Poisson nous permet de nous intéresser non plus au comportement en temps long d'une seule EDP, mais au comportement en temps long d'un système d'EDP couplées. Enfin, lorsque l'EDS sous-jacente est bruitée par un processus de Lévy, le lien est fait avec des équations intégro-différentielles partielles. L'application de ces équations à la résolution de problèmes de contrôle optimal est également présentée. / In this thesis, we are interested in studying ergodic BSDEs, and our main goal is to apply our results to the large time behaviour of some PDEs. First, we prove some results (already known in the case where the underlying SDE has an additive noise) in the case of an underlying multiplicative noise. Then, we introduce a Poisson process and it leads us to the large time behaviour of a system of coupled PDEs. Finally, when the underlying SDE has a Lévy noise, we make a link with partial integro-differential equations. We also apply these equations to solve some optimal control problems.

L’objectif principal de ce travail est l’étude de la planification de trajectoires pour des drones de type HALE ou MALE. Les modèles cinématiques de ces drones sont étudiés. Les drones HALE sont modélisés par le système de Dubins. Pour les drones MALE, le modèle est construit en étudiant le repère cinématique du drone. Nous considérons les problèmes de planification de trajectoires point-point et point-pattern. Il s’agit, à partir de la position courante du drone, de rejoindre un point ou une figure prédéfinie dans l’espace. La planification point-point est abordée sous forme d’un problème de contrôle optimal. Deux méthodes sont proposées pour résoudre le problème point-pattern. D’abord nous présentons la synthèse en temps minimal pour le système de Dubins. Ensuite, nous développons une méthode basée sur le principe de LaSalle. La première méthode est utilisée au sein d’un algorithme de planification pour des drones HALE. La deuxième permet de stabiliser les deux types de drones considérés vers un pattern. Nous proposons une extension des algorithmes de planification développés, basée sur une discrétisation del’espace grâce aux graphes de Voronoï et une méthode de planification discrète, pour construire des trajectoiresdans des milieux encombrés. Nous étudions également le problème de couplage drone/capteur. Il s’agit de calculer une trajectoire permettant de satisfaire les objectifs du drone et de son capteur (une caméra). L’algorithme proposé est construit à partir de la résolution d’un problème quadratique sous contraintes.Dans une seconde partie, nous analysons un problème de contrôle optimal inverse. Celui-ci permet d’améliorer les résultats des méthodes de planification en s’inspirant du comportement des pilotes. Après avoir posé le problème, les résultats théoriques sont exposés et le cas particulier du système de Dubins est étudié en pratique. / This thesis is about path planning for HALE or MALE UAVs (Unmanned Aircraft Vehicles), possibly under mission constraints. As such, the study is performed at the kinematic level : HALE UAVs are represented as Dubins systems, and a model for MALE UAVs is constructed by studying their kinematic frame. In the first part, we tackle the path planning problem for a UAV that must join a target (a point or a pattern), starting from any position. The point to point path planning problem is addressed as an optimal control problem. Regarding the point to pattern path planning problem, two different methods are proposed. The former consists in solving the minimum time synthesis for the Dubins system, in order to obtain a basis for a HALE UAVs planning algorithm. The latter method relies on the LaSalle principle ; it permits to stabilize a HALE or MALE UAV to a pattern.In addition, extensions of the previously developed algorithms to cluttered environnement are provided. This extension is achieved thanks to a space discretization using Voronoi diagrams and a discrete planning method. Finally, the mission constraints are dealt with as a coupling problem between the UAV and its sensors. The proposed algorithm is presented in the form of a constrained quadratic problem.In the second part of this thesis, we want to refine the planning algorithm to get a result closer to trajectories of pilots. In order to do that, we solve an inverse optimal control problem where the cost to find is computed from the experience of pilots. Theoretical results are presented and applied to the particular case of the Dubins system.

在行列設計(row-column design)的架構下，當行總和與列總和皆為總試驗處理數的倍數時，我們考慮行效果與列效果的相互比較之最適性。延續Shah和Sinha(1993)的結果，在給定行總和及列總和的情況下，我們導出達成齊一最適設計(uniformly optimal design)的充分條件。此外，當總實驗單位固定時，達成全域最適設計(universally optimal design)的充分條件亦被求出。我們同時列舉許多相關的設計排列法。 / We consider the problem of comparing row effects and column effects in the row-column design setup when the row sizes and column sizes are all multiples of the number of treatments. Following the work of Shah and Sinha (1993), we derive a sufficient condition for uniformly optimal designs for given values of the row sizes and column sizes. We also derive a sufficient condition for universally optimal designs when the total number of experimental units is fixed. Several examples of designs with high efficiencies are provided.

Online auctions are arguably one of the most important and distinctly new applications of the internet. The predominant player in online auctions, eBay, has over 18.9 milllion users, and it was the host of over $5 billion worth of goods sold in the year 2000. Using methods from approximate dynamic programming and integer programming, we design algorithms for optimally bidding for a single item online auction, and simultaneous or overlapping multiple online auctions. We report computational evidence using data from eBay's web site from 1772 completed auctions for personal digital assistants and from 4208 completed auctions for stamp collections that show that (a) the optimal dynamic strategy outperforms simple but widely used static heuristic rules for a single auction, and (b) a new approach combining the value functions of single auctions found by dynamic programming using an integer programming framework produces high quality solutions fast and reliably. / Singapore-MIT Alliance (SMA)

Time-optimal solutions provide us with the fastest means to regulate a system in presence of input constraints. This advantage of time-optimal control solutions is offset by the fact that their real-time implementation involves computationally intensive iterative techniques. Moreover, time-optimal controls depend on the initial state and have to be recalculated for even the slightest perturbation. Clearly time-optimal controls are not good candidates for online regulation. Consequently, the search for alternatives to time-optimal solutions is a very active area of research. The work described here is inspired by the simplicity of optimal-aim concept. The "optimal-aim strategies" provide online regulation in presence of bounded inputs with minimal computational effort. These are based purely on state-space geometry of the plant and are inherently adaptive in nature. Optimal-aim techniques involve aiming of trajectory derivative (or the state velocity vector) so as to approach the equilibrium state in the best possible manner. This thesis documents the efforts to develop an online regulation algorithm for systems with input constraints. Through a number of hypotheses focussed on trying to reproduce the exact time-optimal solution, the diffculty associated with this task is demonstrated. A modification of optimal-aim concept is employed to develop a novel regulation algorithm. In this algorithm, aim directions are chosen in a special manner to generate the time-optimal control approximately. The control scheme thus developed is shown to be globally stabilizing for systems having eigenvalues in the CLHP (closed left half-plane). It is expected that this method or its modifications can be extended to higher dimensional systems as a part of future research. An alternative control algorithm involving a simple state-space aiming concept is also developed and discussed.

A central bank is usually assigned two functions: the control of inflation and the maintenance of a safetybanking sector. What are the precise conditions under which trigger strategies from the private sector can solve the time inconsistency problem and induce the central bank to choose zero inflation under a nonstationary natural rate? Can an optimal contract be used together with reputation forces to implement a desired socially optimal monetary policy rule? How to design a truthtelling contract to control the risk taking behaviors of the bank? My dissertation attempts to deal with these issues using three primary methodologies: monetary economics, game theory and optimal stochastic control theory.

For current status data, the failure time of interest may not be observed exactly. The type of this data consists only of a monitoring time and knowledge of whether the failure time occurred before or after the monitoring time. In order to be able to obtain more information from this data, so the monitoring time is very important. In this work, the optimal designs for determining the monitoring times such that maximum information may be obtained in bivariate copula model (Clayton) are investigated. Here, the D- optimal criterion is used to decide the best monitoring time Ci (i = 1; ¢ ¢ ¢ ; n), then use these monitoring times Ci to estimate the unknown parameters simultaneously by maximizing the corresponding likelihood function. Ds-optimal designs for estimation of association parameter in the copula model are also discussed. Simulation studies are presented to compare the performance of using monitoring time C¤D and C¤Ds to do the estimation.

This volume consists of four papers, which in principle could be read in any order. The common denominator is that they deal with contingent claims models of a firm's securities or related derivatives. A Framework for Valuing Corporate Securities Early applications of contingent claims analysis to the pricing of corporate liabilities tend to restrict themselves to situations where debt is perpetual or where financial distress can only occur at debt maturity. This paper relaxes these restrictions and provides an exposition of how most corporate liabilities can be valued as packages of two fundamental barrier contingent claims: a down-and-out call and a binary option. Furthermore, it is shown how the comparative statics of the resulting pricing formulae can be derived.A New Compound Option Pricing ModelThis paper extends the Geske (1979) compound option pricing model to the case where the security on which the option is written is a down-and-out call as opposed to a standard Black and Scholes call. Furthermore, we develop a general and flexible framework for valuing options on more complex packages of contingent claims - any claim that can be valued using the ideas in chapter 1. This allows us to study the interaction between the detailed characteristics of a firm's capital structure and the prices of for example stock options.Implementing Firm Value Based ModelsThis paper evaluates an implementation procedure for contingent claims models suggested by Duan (1994). Duan's idea is to use time series data of traded securities such as shares of common stock in order to estimate the dynamics of the firm's asset value. Furthermore, we provide an argument which allows us to relax the (common) assumption that the firm's assets may be continuously traded. It is sufficient to assume that the firm's assets are traded at one particular point in time.Asset Substitution, Debt Pricing, Optimal Leverage and MaturityChapters 1-3 have focused on the problem of pricing corporate securities.They have thus abstracted strategic aspects of corporate finance theory. This paper is an attempt to combine the contingent claims literature with the non-dynamic corporate finance literature. I allow the management of the firm to alter its investment policy strategically. This yields a model which allows us to examine the relationship between bond prices, agency costs, optimal leverage and maturity. / Diss. Stockholm : Handelshögsk.