<div>Previous studies have shown that implementing trajectory optimization can reduce state estimations errors. These navigation based path planning problems are often diffcult to solve being computationally burdensome and exhibiting other numerical issues, so former studies have often used lower-delity methods or lacked explanatory power.</div><div><br></div><div><div>This work utilizes indirect optimization methods, particularly optimal control theory, to obtain high-quality solutions minimizing state estimation errors approximated by a continuous-time extended Kalman lter. Indirect methods are well-suited to this because necessary conditions of optimality are found prior to discretization and numerical computation. They are also highly parallelizable enabling application to increasingly larger problems.</div></div><div><br></div><div><div>A simple one dimensional problem shows some potential obstacles to solving problems of this type including regions of the trajectory where the control is unimportant. Indirect trajectory optimization is applied to a more complex scenario to minimize location estimation errors of a single cart traveling in a 2-D plane to a goal location and measuring range from a xed beacon. This resulted in a 96% reduction of the location error variance when compared to the minimum time solution. The single cart problem also highlights the importance of the matrix that encodes the linearization of the vehicle's measurement with respect to state. It is shown in this case that the vehicle roughly attempts to maximize the magnitude of its elements. Additionally, the cart problem further illustrates problematic regions of a design space where the objective is not signicantly affected by the trajectory.</div></div><div><br></div><div><div>An aircraft descent problem demonstrates the applicability of these methods to aerospace problems. In this case, estimation error variance is reduced 28.6% relative to the maximum terminal energy trajectory. Results are shown from two formulations of this problem, one with control constraints and one with control energy cost, to show the benets and disadvantages of the two methods. Furthermore, the ability to perform trade studies on vehicle and trajectory parameters is shown with this problem by solving for dierent terminal velocities and different initial locations.</div></div>

La dispersion du pollen est une composante majeure des flux de gènes chez les plantes, contribuant à la diversité génétique et à sa structure spatiale. Son étude à l'échelle d'un épisode de reproduction permet de comprendre l'impact des changements actuels (fragmentation, anthropisation....) et de proposer des politiques de conservation. Deux types de méthodes basées sur les marqueurs microsatellites estiment la fonction de dispersion du pollen: (i) les méthodes directes (e.g. mating model) basées sur l'assignation de paternité et nécessitant un échantillonnage exhaustif (position et génotype des individus du site étudié, génotypes de graines échantillonnées sur des mères); (ii) les méthodes indirectes (e.g. TwoGener), nécessitant un échantillonnage réduit (génotypes des graines, génotypes et positions des mères) et résumant les données en indices génétiques. Nous proposons la formalisation statistique de ces deux types de méthodes et montrons qu'elles utilisent des fonctions de dispersion différentes: les méthodes directes estiment une fonction forward potentielle (déplacement du pollen depuis le père), les méthodes indirectes une fonction backward intégrative (de la fécondation jusqu'à l'existence du père). Nous explicitons le lien entre fonctions backward et forward, des hypothèses menant à leur équivalence, et des contraintes affectant les fonctions backward. Nous développons enfin une méthode de calcul bayésien approché qui permet (i) une estimation forward, (ii) avec des intervalles de crédibilité, (iii) à partir d'un jeu de données non exhaustif et d'informations partielles (e.g. positions sans génotype) et (iv) l'utilisation de différents modèles de dispersion. / Pollen dispersal is a major component of gene flow in plants. It determines to genetic diversity and spatial genetic structure.Studying it at the scale of a single reproduction event enables to understand the impact of current changes (fragmentation, anthropization ...) and to propose conservation practices.Two types of methods, based on microsatellite markers, estimate pollen dispersal functions : (i) direct methods (e.g. mating model) based on paternity assignment require exhaustif sampling (position and genotype of individuals in the study plot, genotypes of seeds harvested on mothers); (ii) indirect methods (e.g. TwoGener), require a weaker sampling (seeds genotypes, genotypes and positions of their mothers) and summarize data through genetic indices.We propose a statistical formalization of both types of methods and show that they rely on different dispersal functions : the direct methods estimate a potential forward function (pollen transfer from the father), whereas the indirect methods estimate an integrative backward one (from fecondation to father existence). We exhibit the link between forward and backward functions, assumptions leading to their equivalence and constrains affecting the backward functions.Finally, we develop an Approximate Bayesian Computation method, which enable (i) a forward estimation, (ii) with credibility intervals, (iii) from a non exhaustive dataset and partial information (e.g. positions without genotypes) and (iv) the use of different dispersal models.

Traditionally, the design of complex aerospace systems requires iteration among segregated disciplines such as aerodynamic modeling and trajectory optimization. Multidisciplinary design optimization algorithms have been developed to efficiently orchestrate the interaction among these disciplines during the design process. For example, vehicle capability is generally obtained through sequential iteration among vehicle shape, aerodynamic performance, and trajectory optimization routines in which aerodynamic performance is obtained from large pre-computed tables that are a function of angle of attack, sideslip, and flight conditions. This numerical approach segregates advancements in vehicle shape design from advancements in trajectory optimization. This investigation advances the state-of-the-art in conceptual hypersonic aerodynamic analysis and trajectory optimization by removing the source of iteration between aerodynamic and trajectory analyses and capitalizing on fundamental linkages across hypersonic solutions. Analytic aerodynamic relations, like those derived in this investigation, are possible in any flow regime in which the flowfield can be accurately described analytically. These relations eliminate the large aerodynamic tables that contribute to the segregation of disciplinary advancements. Within the limits of Newtonian flow theory, many of the analytic expressions derived in this investigation provide exact solutions that eliminate the computational error of approximate methods widely used today while simultaneously improving computational performance. To address the mathematical limit of analytic solutions, additional relations are developed that fundamentally alter the manner in which Newtonian aerodynamics are calculated. The resulting aerodynamic expressions provide an analytic mapping of vehicle shape to trajectory performance. This analytic mapping collapses the traditional, segregated design environment into a single, unified, mathematical framework which enables fast, specialized trajectory optimization methods to be extended to also include vehicle shape. A rapid trajectory optimization methodology suitable for this new, mathematically integrated design environment is also developed by relying on the continuation of solutions found via indirect methods. Examples demonstrate that families of optimal hypersonic trajectories can be quickly constructed for varying trajectory parameters, vehicle shapes, atmospheric properties, and gravity models to support design space exploration, trade studies, and vehicle requirements definition. These results validate the hypothesis that many hypersonic trajectory solutions are connected through fast indirect optimization methods. The extension of this trajectory optimization methodology to include vehicle shape through the development of analytic hypersonic aerodynamic relations enables the construction of a unified mathematical framework to perform rapid, simultaneous hypersonic aerodynamic and trajectory optimization. Performance comparisons relative to state-of-the-art methodologies illustrate the computational advantages of this new, unified design environment.

Considered a biodiversity hotspot, the Brazilian Cerrado contains a rich mammalian fauna, despite the high level of degradation in this area. The loss of habitat is major in the Triângulo Mineiro region, where few studies evaluated mammal diversity. In this way, the aim of this study was threefold: 1) evaluate the species richness and composition of medium and large-sized mammals in the Fazenda Experimental do Glória, 2) investigate the patterns of spatial distribution of these animals and 3) determine seasonal variations in this distribution patterns. The Fazenda Experimental do Glória (685 ha), hereafter called FEG, is located in the municipality of Uberlândia, Triângulo Mineiro region. Data were collected from august 2008 to October 2009, in a total of 116 field trips. Four fragments were studied, by walking in pre-existent trails. Medium and large-sized mammals were recorded in those trails through direct (visualizations) and indirect (observation of tracks, faeces, bones, vocalizations and interviews with local population) methods. Distribution of species in the physiognomies was obtained using presence/absence data, and this result was evaluated in order to suggest possible associations between habitat characteristics and species habitat use. Twenty-one medium and large-sized mammals were recorded in the study site, including three species considered vulnerable, three endangered and one critically endangered. Procyon cancrivorus, Dasypus novemcinctus, Mazama sp., Myrmecophaga tridactyla e Chrysocyon brachyurus presented the higher relative frequency. Gallery forest contained a high number of species (n =14) than the other physiognomies. Although a few species seemed restricted to certain habitats, most species explored several physiognomies, indicating a generalist pattern of habitat use. Regarding the frequency of use of different physiognomies, our results suggest that species use in a higher frequency those areas that present food and other important resources. Spatial distribution of species was similar between seasons, except for Lontra longicaudis, which presented a higher frequency in the dry season. This study point out the importance of FEG for mammal conservation; however, in the long-term, the small size and isolation of fragments in this area will not be able to maintain viable populations of the studied mammals. In this way, management decisions, such as connecting FEG fragments with each other and with the surrounding areas, are crucial for conservation of these populations. / O Cerrado, um dos hotspots para conservação da biodiversidade mundial, abriga uma rica fauna de mamíferos, mesmo diante da degradação atual do bioma. De forma similar, o elevado grau de devastação do Cerrado é refletido para o estado de Minas Gerais incluindo o Triângulo, onde estudos da mastofauna são incipientes. Dessa forma, este estudo objetivou determinar a riqueza e composição de mamíferos de médio e grande porte na Fazenda Experimental do Glória; avaliar os padrões de distribuição espacial das espécies e o uso do mosaico de fitofisionomias, bem como identificar possíveis variações da distribuição entre estações climáticas. A Fazenda Experimental do Glória (FEG), área deste estudo, está situada no município de Uberlândia, na região do Triângulo Mineiro e possui uma área de 685 ha. Os dados foram coletados de agosto de 2008 a outubro de 2009, totalizando 116 visitas a campo. Foram selecionados quatro fragmentos naturais ou em regeneração que foram percorridos em trilhas pré-existentes. Os mamíferos de médio e grande porte foram registrados por meio de métodos indiretos (pegadas, fezes, crânios, tegumentos, vocalizações e entrevistas) e diretos (visualizações). A distribuição das espécies de mamíferos de médio e grande porte foi obtida a partir dos registros de presença nos fragmentos. O uso das fitofisionomias foi analisado buscando sugerir possíveis associações entre características do ambiente e a presença das espécies. Foram registradas 21 espécies de mamíferos silvestres de médio e grande porte, sendo três espécies vulneráveis, três em perigo e uma criticamente em perigo para Minas Gerais. As espécies com maior freqüência relativa foram Procyon cancrivorus, Dasypus novemcinctus, Mazama sp., Myrmecophaga tridactyla e Chrysocyon brachyurus. A fitofisionomia mais especiosa foi a mata de galeria (n =14) e embora alguns mamíferos pareçam restritos a um habitat, a maioria deles explorou mais de uma fitofisionomia analisada, mostrando-se generalistas. Em relação à freqüência de uso das diferentes fitofisionomias, as espécies parecem usar com maior freqüência ambientes que ofereçam os recursos alimentares que elas necessitam. A distribuição das espécies não diferiu entre as estações seca e chuvosa, exceto para Lontra longicaudis, que teve maior ocorrência na estação seca. Portanto, a FEG desempenha importante papel na conservação da mastofauna, porém essa área isolada não conseguirá manter populações viáveis de todas as espécies, a médio e longo prazo, sendo necessária a adoção de medidas conservacionistas, como por exemplo, conectar os fragmentos da FEG entre si e com as áreas de entorno. / Mestre em Ecologia e Conservação de Recursos Naturais

Currently we can do genetic manipulation by means of direct and indirect methods. Indirect methods use strategy of gram-negative soil bacteria Agrobacterium tumefaciens, which introduces part of its own genes carried by the section of plasmid Ti called T-DNA into the genome of infected plants. It is difficult to reach the transformation of monocotyledonous plants using this method. Application of direct methods of transformation offers the possibility for transformation of monocotyledonous plants. One of the most effective methods of direct transformation is biolistic transformation. This diploma thesis dealt with the comparison of efficacy of biolistic and A. tumefaciens mediated transformation of tomato (Solanum lycopersicum L.).

The aim of my diploma thesis is to describe indirect methods that are used in the compilation of quarterly national accounts. The diploma thesis is divided into three parts and three chapters. The first chapter presents the theoretical background and describes the development of national accounts in the Czech Republic and the basic macroeconomic aggregates. The second chapter is devoted to the quarterly national accounts and mathematical and statistical methods that are used in their compilation. The third chapter describes in detail selected indirect methods, which consists in linking the indicator and aggregate. Consequently, this method is applied to the data of the Czech Republic and then quarterly estimates are constructed which are compared to actual values.

Die vorliegende Arbeit beschäftigt sich mit der Anwendung der indirekten Methoden zur automatisierten Lösung von einer bestimmten Klasse von Optimalen Steuerungsproblemen im Rahmen einer modellprädiktiven Regelung für Windenergieanlagen. In einem zweiten Teil wird der Einfluss dieser Regelungsmethode auf die Festigkeit des Triebstranges untersucht. Diese führt zu einer überproportionalen Beanspruchung und damit zu einer Reduktion der Betriebsfestigkeit. Es gilt entsprechende Randbedingungen für die der Regelung zugrunde liegenden Optimalen Steuerungsprobleme zu finden, so dass weiterhin die Energieausbeute maximiert werden kann, gleichzeitig jedoch die Beanspruchung durch die Regelung begrenzt wird.

<p>Numerical trajectory optimization is helpful not only for mission planning but also design</p> <p>space exploration and quantifying vehicle performance. Direct methods for solving the opti-</p> <p>mal control problems, which first discretize the problem before applying necessary conditions</p> <p>of optimality, dominate the field of trajectory optimization because they are easier for the</p> <p>user to set up and are less reliant on a forming a good initial guess. On the other hand,</p> <p>many consider indirect methods, which apply the necessary conditions of optimality prior to</p> <p>discretization, too difficult to use for practical applications. Indirect methods though provide</p> <p>very high quality solutions, easily accessible sensitivity information, and faster convergence</p> <p>given a sufficiently good guess. Those strengths make indirect methods especially well-suited</p> <p>for generating large data sets for system analysis and worth revisiting.</p> <p>Recent advancements in the application of indirect methods have already mitigated many</p> <p>of the often cited issues. Automatic derivation of the necessary conditions with computer</p> <p>algebra systems have eliminated the manual step which was time-intensive and error-prone.</p> <p>Furthermore, regularization techniques have reduced problems which traditionally needed</p> <p>many phases and complex staging, like those with inequality path constraints, to a signifi-</p> <p>cantly easier to handle single arc. Finally, continuation methods can circumvent the small</p> <p>radius of convergence of indirect methods by gradually changing the problem and use previ-</p> <p>ously found solutions for guesses.</p> <p>The new optimal control problem solver Giuseppe incorporates and builds upon these</p> <p>advancements to make indirect methods more accessible and easily used. It seeks to enable</p> <p>greater research and creative approaches to problem solving by being more flexible and</p> <p>extensible than previous solvers. The solver accomplishes this by implementing a modular</p> <p>design with well-defined internal interfaces. Moreover, it allows the user easy access to and</p> <p>manipulation of component objects and functions to be use in the way best suited to solve</p> <p>a problem.</p> <p>A new technique simplifies and automates what was the predominate roadblock to using</p> <p>continuation, the generation of an initial guess for the seed solution. Reliable generation of</p> <p>a guess sufficient for convergence still usually required advanced knowledge optimal contrtheory or sometimes incorporation of an entirely separate optimization method. With the</p> <p>new method, a user only needs to supply initial states, a control profile, and a time-span</p> <p>over which to integrate. The guess generator then produces a guess for the “primal” problem</p> <p>through propagation of the initial value problem. It then estimates the “dual” (adjoint)</p> <p>variables by the Gauss-Newton method for solving the nonlinear least-squares problem. The</p> <p>decoupled approach prevents poorly guessed dual variables from altering the relatively easily</p> <p>guess primal variables. As a result, this method is simpler to use, faster to iterate, and much</p> <p>more reliable than previous guess generation techniques.</p> <p>Leveraging the continuation process also allows for greater insight into the solution space</p> <p>as there is only a small marginal cost to producing an additional nearby solutions. As a</p> <p>result, a user can quickly generate large families of solutions by sweeping parameters and</p> <p>modifying constraints. These families provide much greater insight in the general problem</p> <p>and underlying system than is obtainable with singular point solutions. One can extend</p> <p>these analyses to high-dimensional spaces through construction of compound continuation</p> <p>strategies expressible by directed trees.</p> <p>Lastly, a study into common convergence explicates their causes and recommends mitiga-</p> <p>tion strategies. In this area, the continuation process also serves an important role. Adaptive</p> <p>step-size routines usually suffice to handle common sensitivity issues and scaling constraints</p> <p>is simpler and out-performs scaling parameters directly. Issues arise when a cost functional</p> <p>becomes insensitive to the control, which a small control cost mitigates. The best perfor-</p> <p>mance of the solver requires proper sizing of the smoothing parameters used in regularization</p> <p>methods. An asymptotic increase in the magnitude of adjoint variables indicate approaching</p> <p>a feasibility boundary of the solution space.</p> <p>These techniques for indirect methods greatly facilitate their use and enable the gen-</p> <p>eration of large libraries of high-quality optimal trajectories for complex problems. In the</p> <p>future, these libraries can give a detailed account of vehicle performance throughout its flight</p> <p>envelope, feed higher-level system analyses, or inform real-time control applications.</p>

Consider a time-dependent optimal control problem, where the state evolution is described by an initial value problem. There are a variety of numerical methods to solve these problems. The so-called indirect approach is considered detailed in this thesis. The indirect methods solve decoupled boundary value problems resulting from the necessary conditions for the optimal control problem. The so-called Pantoja method describes a computationally efficient stage-wise construction of the Newton direction for the discrete-time optimal control problem. There are many relationships between multiple shooting techniques and Pantoja method, which are investigated in this thesis. In this context, the equivalence of Pantoja method and multiple shooting method of Riccati type is shown. Moreover, Pantoja method is extended to the case where the state equations are discretised using one of implicit numerical methods. Furthermore, the concept of symplecticness and Hamiltonian systems is introduced. In this regard, a suitable numerical method is presented, which can be applied to unconstrained optimal control problems. It is proved that this method is a symplectic one. The iterative solution of optimal control problems in ordinary differential equations by Pantoja or Riccati equivalent methods leads to a succession of triple sweeps through the discretised time interval. The second (adjoint) sweep relies on information from the first (original) sweep, and the third (final) sweep depends on both of them. Typically, the steps on the adjoint sweep involve more operations and require more storage than the other two. The key difficulty is given by the enormous amount of memory required for the implementation of these methods if all states throughout forward and adjoint sweeps are stored. One of goals of this thesis is to present checkpointing techniques for memory reduced implementation of these methods. For this purpose, the well known aspect of checkpointing has to be extended to a `nested checkpointing` for multiple transversals. The proposed nested reversal schedules drastically reduce the required spatial complexity. The schedules are designed to minimise the overall execution time given a certain total amount of storage for the checkpoints. The proposed scheduling schemes are applied to the memory reduced implementation of the optimal control problem of laser surface hardening and other optimal control problems. / Es wird ein Problem der optimalen Steuerung betrachtet. Die dazugehoerigen Zustandsgleichungen sind mit einer Anfangswertaufgabe definiert. Es existieren zahlreiche numerische Methoden, um Probleme der optimalen Steuerung zu loesen. Der so genannte indirekte Ansatz wird in diesen Thesen detailliert betrachtet. Die indirekten Methoden loesen das aus den Notwendigkeitsbedingungen resultierende Randwertproblem. Das so genannte Pantoja Verfahren beschreibt eine zeiteffiziente schrittweise Berechnung der Newton Richtung fuer diskrete Probleme der optimalen Steuerung. Es gibt mehrere Beziehungen zwischen den unterschiedlichen Mehrzielmethoden und dem Pantoja Verfahren, die in diesen Thesen detailliert zu untersuchen sind. In diesem Zusammenhang wird die aequivalence zwischen dem Pantoja Verfahren und der Mehrzielmethode vom Riccati Typ gezeigt. Ausserdem wird das herkoemlige Pantoja Verfahren dahingehend erweitert, dass die Zustandsgleichungen mit Hilfe einer impliziten numerischen Methode diskretisiert sind. Weiterhin wird das Symplektische Konzept eingefuehrt. In diesem Zusammenhang wird eine geeignete numerische Methode praesentiert, die fuer ein unrestringiertes Problem der optimalen Steuerung angewendet werden kann. In diesen Thesen wird bewiesen, dass diese Methode symplectisch ist. Das iterative Loesen eines Problems der optimalen Steuerung in gewoenlichen Differentialgleichungen mit Hilfe von Pantoja oder Riccati aequivalenten Verfahren fuehrt auf eine Aufeinanderfolge der Durchlaeufetripeln in einem diskretisierten Zeitintervall. Der zweite (adjungierte) Lauf haengt von der Information des ersten (primalen) Laufes, und der dritte (finale) Lauf haeng von den beiden vorherigen ab. Ueblicherweise beinhalten Schritte und Zustaende des adjungierten Laufes wesentlich mehr Operationen und benoetigen auch wesentlich mehr Speicherplatzkapazitaet als Schritte und Zustaende der anderen zwei Durchlaeufe. Das Grundproblem besteht in einer enormen Speicherplatzkapazitaet, die fuer die Implementierung dieser Methoden benutzt wird, falls alle Zustaende des primalen und des adjungierten Durchlaufes zu speichern sind. Ein Ziel dieser Thesen besteht darin, Checkpointing Strategien zu praesentieren, um diese Methoden speichereffizient zu implementieren. Diese geschachtelten Umkehrschemata sind so konstruiert, dass fuer einen gegebenen Speicherplatz die gesamte Laufzeit zur Abarbeitung des Umkehrschemas minimiert wird. Die aufgestellten Umkehrschemata wurden fuer eine speichereffiziente Implementierung von Problemen der optimalen Steuerung angewendet. Insbesondere betrifft dies das Problem einer Oberflaechenabhaertung mit Laserbehandlung.

L'objectif premier de cette thèse est d'étudier certains aspects du contrôle d'attitude d'un corps rigide, afin d'optimiser la trajectoire d'un lanceur au cours de sa phase balistique. Nous y développons un cadre mathématique permettant de formuler ce problème comme un problème de contrôle optimal avec des contraintes intermédiaires sur l'état. En parallèle de l'étude théorique de ce problème, nous avons mené l'implémentation d'un logiciel d'optimisation basé sur la combinaison d'une méthode directe et d'un algorithme de point intérieur, permettant à l'utilisateur de traiter une phase balistique quelconque. Nous entendons par là qu'il est possible de spécifier un nombre quelconque de contraintes intermédiaires, correspondant à un nombre quelconque de largages de charges utiles. En outre, nous avons appliqué les méthodes dites indirectes, exploitant le principe du maximum de Pontryagin, à la résolution de ce problème de contrôle optimal. On cherche dans ce travail à trouver des trajectoires optimales du point de vue de la consommation en ergols, ce qui correspond à un coût L 1 . Réputé difficile numériquement, ce critère peut être atteint grâce à une méthode de continuation, en se servant d'un coût L 2 comme intermédiaire de calcul et en déformant progressivement ce problème L 2 . Nous verrons également d'autres exemples d'application des méthodes de continuation. Enfin, nous présenterons également un algorithme de contrôle robuste, permettant de rejoindre un état cible à partir d'un état perturbé, en suivant une trajectoire de référence tout en conservant la structure bang-bang des contrôles. La robustesse d'un contrôle peut également être améliorée par l'ajout de variations aiguilles, et un critère qualifiant la robustesse d'une trajectoire à partir des valeurs singulières d'une certaine application entrée-sortie est déduit. / The first objective of this work is to study some aspects of the attitude control problem of a rigid body, in order to optimize the trajectory of a launcher during a ballistic flight. We state this problem in a general mathematical setting, as an optimal control problem with intermediate constraints on the state. Meanwhile, we also implement an optimization software that relies on the combination of a direct method and of an interior-point algorithm to optimize any given ballistic flight, with any number of intermediate constraints, corresponding to any number of satellite separations. Besides, we applied the so-called indirect methods, exploiting Pontryagin maximum principle, to the resolution of this optimal control problem. In this work, optimal trajectories with respect to the consumption are looked after, which corresponds to a L 1 cost. Known to be numerically challenging, this criterion can be reached by performing a continuation procedure, starting from a L 2 cost, for which it is easier to provide a good initialization of the underlying optimization algorithm. We shall also study other examples of applications for continuation procedures. Eventually, we will present a robust control algorithm, allowing to reach a target point from a perturbed initial point, following a nominal trajectory while preserving its bang-bang structure. The robustness of a control can be improved introducing needle-like variations, and a criterion to measure the robustness of a trajectory is designed, involving the singular value decomposition of some end-point mapping.