Bei der Kristallzüchtung insbesondere von Halbleitern hat die Form des freien Randes (dem Interface zwischen fester und flüssiger Phase) einen starken Einfluss auf die Qualität des Kristalls. Die Dissertation befasst sich mit der Optimalsteuerung der Form und des Verlaufs des freien Randes. Als Vorlage für die in der Arbeit betrachteten Modellkonfigurationen dient das VGF-Verfahren (Vertical Gradient Freeze). Der Erstarrungsprozess wird durch ein Zweiphasen-Stefan-Problem mit durch Konvektion und Lorentzkräfte getriebener Strömung beschrieben. Der freie Rand wird als Graph formuliert. Das Kontrollziel besteht in der Ansteuerung eines gewünschten Verlaufs des freien Randes. Als Kontrollgrößen dient die Temperatur auf der Wand des Schmelztiegels und/oder wandnahe oder verteilte Lorentzkräfte. Das Kontrollziel wird durch Minimierung eines geeigneten Kosten-Funktionals erreicht. Das daraus resultierende Minimierungsproblem wird mit einem Adjungierten-Ansatz gelöst. Anhand numerischer Experimente mit Aluminium und Gallium-Arsenid Schmelzen wird gezeigt, das das vorgestellte Verfahren gut funktioniert.

The operation of groups of heavy-duty vehicles at small inter-vehicular distances, known as platoons, lowers the overall aerodynamic drag and, therefore, reduces fuel consumption and greenhouse gas emissions. Experimental tests conducted on a flat road and without traffic have shown that platooning has the potential to reduce the fuel consumption up to 10%. However, platoons are expected to drive on public highways with varying topography and traffic. Due to the large mass and limited engine power of heavy-duty vehicles, road slopes can have a significant impact on feasible and optimal speed profiles. Therefore, maintaining a short inter-vehicular distance without coordination can result in inefficient or even infeasible speed trajectories. Furthermore, external traffic can interfere by affecting fuel-efficiency and threatening the safety of the platooning vehicles. This thesis addresses the problem of safe and fuel-efficient control for heavy-duty vehicle platooning. We propose a hierarchical control architecture that splits this complex control problem into two layers. The layers are responsible for the fuel-optimal control based on look-ahead information on road topography and the real-time vehicle control, respectively. The top layer, denoted the platoon coordinator, relies on a dynamic programming framework that computes the fuel-optimal speed profile for the entire platoon. The bottom layer, denoted the vehicle control layer, uses a distributed model predictive controller to track the optimal speed profile and the desired inter-vehicular spacing policy. Within this layer, constraints on the vehicles' states guarantee the safety of the platoon. The effectiveness of the proposed controller is analyzed by means of simulations of several realistic scenarios. They suggest a possible fuel saving of up to 12% for the follower vehicles compared to the use of existing platoon controllers. Analysis of the simulation results shows how the majority of the fuel saving comes from a reduced usage of vehicles brakes. A second problem addressed in the thesis is model predictive control for obstacle avoidance and lane keeping for a passenger car. We propose a control framework that allows to control the nonlinear vehicle dynamics with linear model predictive control. The controller decouples the longitudinal and lateral vehicle dynamics into two successive stages. First, plausible braking and throttle profiles are generated. Second, for each profile, linear time-varying models of the lateral dynamics are derived and used to formulate a collection of linear model predictive control problems. Their solution provides the optimal control input for the steering and braking actuators. The performance of the proposed controller has been evaluated by means of simulations and real experiments. / <p>QC 20150911</p>

The electric power industry and society are facing the challenges and opportunities of transforming the present power grid into a smart grid. To meet these challenges, new types of control systems are connected over IT infrastructures. While this is done to meet highly set economical and environmental goals, it also introduces new sources of uncertainty in the control loops. In this thesis, we consider control design taking some of these uncertainties into account. In Part I of the thesis, some economical and environmental concerns in smart grids are taken into account, and a scheduling framework for static loads (e.g., smart appliances in residential areas) and dynamic loads (e.g., energy storage systems) in the distribution level is investigated. A robust formulation is proposed taking the user behavior uncertainty into account, so that the optimal scheduling cost is less sensitive to unpredictable changes in user preferences. In addition, a novel distributed algorithm for the studied scheduling framework is proposed, which aims at minimizing the aggregated electricity cost of a network of apartments sharing an energy storage system. We point out that the proposed scheduling framework is applicable to various uncertainty sources, storage technologies, and programmable electrical loads. In Part II of the thesis, we study smart grid uncertainty resulting from possible security threats. Smart grids are one of the most complex cyber-physical systems considered, and are vulnerable to various cyber and physical attacks. The attack scenarios consider cyber adversaries that may corrupt a few measurements and reference signals, which may degrade the system’s reliability and even destabilize the voltage magnitudes. In addition, a practical attack-resilient framework for networked control systems is proposed. This framework includes security information analytics to detect attacks and a resiliency policy to improve the performance of the system running under the attack. Stability and optimal performance of the networked control system under attack and by applying the proposed framework, is proved here. The framework has been applied to an energy management system and its efficiency is demonstrated on a critical attack scenario. / <p>QC 20160830</p>

Inthis degree project, a solution on a coarse grid is recovered by fitting apartial differential equation to a few known data points. The PDE to consideris the heat equation and the Dupire’s equation with their synthetic data,including synthetic data from the Black-Scholes formula. The approach to fit aPDE is by optimal control to derive discrete approximations to regularized Hamiltoncharacteristic equations to which discrete stepping schemes, and parameters forsmoothness, are examined. By non-parametric numerical implementation thedervied method is tested and then a few suggestions on possible improvementsare given / I detta examensarbete återskapas en lösning på ett glest rutnät genom att anpassa en partiell differentialekvation till några givna datapunkter. De partiella differentialekvationer med deras motsvarande syntetiska data som betraktas är värmeledningsekvationen och Dupires ekvation inklusive syntetiska data från Black-Scholes formel. Tillvägagångssättet att anpassa en PDE är att med hjälp av optimal styrning härleda diskreta approximationer på ett system av regulariserade Hamilton karakteristiska ekvationer till vilka olika diskreta stegmetoder och parametrar för släthet undersöks. Med en icke-parametrisk numerisk implementation prövas den härledda metoden och slutligen föreslås möjliga förbättringar till metoden.

L'objectif de ce manuscrit est de présenter mes travaux concernant la modélisation des ablations thermiques par ultrasons focalisés. La méthode de simulation du faisceau acoustique, fondée sur l'utilisation de la bibliothèque k-Wave, est appliquée à un cas concret de propagation des ultrasons à travers une couche de tissu superficiel. Des mesures à l'hydrophone réalisées dans différentes configurations sur des échantillons biologiques fournissent une validation en régime linéaire. A partir de ces résultats, l'influence des tissus superficiels sur la focalisation est évaluée en fonction de la géométrie du problème grâce à des simulations non linéaires.La modélisation thermique des traitements est ensuite discutée avec la volonté de réaliser des simulations thermiques réellement quantitatives. En particulier, un modèle équivalent de la déposition de chaleur en présence d'ébullition est proposé et validé grâce à l'utilisation de données expérimentales originales, diversifiées et peu coûteuses à acquérir.Finalement, un algorithme d'optimisation fondé sur le principe du maximum de Pontryagin est proposé afin d'optimiser la durée des traitements. L'approche étudiée consiste à optimiser la trajectoire du point focal pour maximiser l'efficacité de la déposition de chaleur. A travers une série d'exemples, les avantages et les limites de l'algorithme proposé sont discutés. / This manuscript aims at discussing the complex issue of modeling high-intensity focused ultrasound thermal ablations. An acoustical simulation method, based on the use of the k-Wave library, is described and applied to the description of the interaction between the acoustic beam and the superficial tissue layers. It is validated in the linear domain based on hydrophone measurements realized in different configurations with biological samples. Nonlinear simulations are subsequently used to evaluate the influence of the tissue geometry on the beam focusing.The thermal modeling of the treatment is then discussed with intent to design a truly quantitative model. An equivalent model of the modified heat deposition pattern in presence of boiling is presented and validated based on the use of original, diverse and unexpensive data.Finally, an algorithm is proposed to optimize the focal spot trajectory in order to maximize the heat deposition efficiency, thus reducing treatment time. The advantages and the limits of the approach are discussed based on different examples.

La locomotion anthropomorphe est un processus complexe qui met en jeu un très grand nombre de degrés de liberté, le corps humain disposant de plus de trois cents articulations contre une trentaine chez les robots humanoïdes. Pris dans leur ensemble, ces degrés de liberté montrent une certaine cohérence rendant possible la mise en mouvement du système anthropomorphe et le maintien de son équilibre, dans le but d'éviter la chute. Cette thèse met en lumière les fondements calculatoires à l'origine de cette orchestration. Elle introduit un cadre mathématique unifié permettant à la fois l'étude de la locomotion humaine, et la génération de trajectoires locomotrices pour les robots humanoïdes. Ce cadre consiste en une réduction de la dynamique corps-complet du système pour ne considérer que sa projection autour du centre de gravité, aussi appelée dynamique centroïdale. Bien que réduite, nous montrons que cette dynamique centroïdale joue un rôle central dans la compréhension et la formation des mouvements locomoteurs. Pour ce faire, nous établissons dans un premier temps les conditions d'observabilité de cette dynamique, c'est-à-dire que nous montrons dans quelle mesure cette donnée peut être appréhendée à partir des capteurs couramment employés en biomécanique et en robotique. Forts de ces conditions d'observabilité, nous proposons un estimateur capable de reconstruire la position non-biaisée du centre de gravité. A partir de cet estimateur et de l'acquisition de mouvements de marche sur divers sujets, nous mettons en évidence la présence d'un motif cycloïdal du centre de gravité dans le plan sagittal lorsque l'humain marche de manière nominale, c'est-à-dire sans y penser. La présence de ce motif suggère l'existence d'une synergie motrice jusqu'alors ignorée, soutenant la théorie d'une coordination générale des mouvements pendant la locomotion. La dernière contribution de cette thèse porte sur la locomotion multi-contacts. Les humains ont une agilité remarquable pour effectuer des mouvements locomoteurs qui nécessitent l'utilisation conjointe des bras et des jambes, comme lors de l'ascension d'une paroi rocheuse. Comment doter les robots humanoïdes de telles capacités ? La difficulté n'est certainement pas technologique, puisque les robots actuels sont capables de développer des puissances mécaniques suffisantes. Leurs performances, évaluées tant en termes de qualité des mouvements que de temps de calcul, restent très limitées. Dans cette thèse, nous abordons le problème de génération de trajectoires multi-contacts sous la forme d'un problème de commande optimale. L'intérêt de cette formulation est de partir du modèle réduit de la dynamique centroïdale tout en répondant aux contraintes d'équilibre. L'idée originale consiste à maximiser la vraisemblance de cette dynamique réduite vis-à-vis de la dynamique corps-complet. Elle repose sur l'apprentissage d'une mesure d'occupation qui reflète les capacités cinématiques et dynamiques du robot. Elle est effective : l'algorithmique qui en découle est compatible avec des applications temps réel. L'approche a été évaluée avec succès sur le robot humanoïde HRP-2, sur plusieurs modes de locomotions, démontrant ainsi sa polyvalence. / Anthropomorphic locomotion is a complex process that involves a very large number of degrees of freedom, the human body having more than three hundred joints against thirty in humanoid robots. Taken as a whole, these degrees of freedom show a certain coherence making it possible to set the anthropomorphic system in motion and maintain its equilibrium, in order to avoid falling. This thesis highlights the computational foundations behind this orchestration. It introduces a unified mathematical framework allowing both the study of human locomotion and the generation of locomotive trajectories for humanoid robots. This framework consists of a reduction of the body-complete dynamics of the system to consider only its projection around the center of gravity, also called centroid dynamics. Although reduced, we show that this centroidal dynamics plays a central role in the understanding and formation of locomotive movements. To do this, we first establish the observability conditions of this dynamic, that is to say that we show to what extent this data can be apprehended from sensors commonly used in biomechanics and robotics. Based on these observability conditions, we propose an estimator able to reconstruct the unbiased position of the center of gravity. From this estimator and the acquisition of walking motions on various subjects, we highlight the presence of a cycloidal pattern of the center of gravity in the sagittal plane when the human is walking nominally, that is, to say without thinking. The presence of this motif suggests the existence of a motor synergy hitherto unknown, supporting the theory of a general coordination of movements during locomotion. The last contribution of this thesis is on multi-contact locomotion. Humans have remarkable agility to perform locomotive movements that require joint use of the arms and legs, such as when climbing a rock wall. How to equip humanoid robots with such capabilities? The difficulty is certainly not technological, since current robots are able to develop sufficient mechanical powers. Their performances, evaluated both in terms of quality of movement and computing time, remain very limited. In this thesis, we address the problem of generating multi-contact trajectories in the form of an optimal control problem. The interest of this formulation is to start from the reduced model of centroid dynamics while responding to equilibrium constraints. The original idea is to maximize the likelihood of this reduced dynamic with respect to body-complete dynamics. It is based on learning a measurement of occupation that reflects the kinematic and dynamic capabilities of the robot. It is effective: the resulting algorithmic is compatible with real-time applications. The approach has been successfully evaluated on the humanoid robot HRP-2, on several modes of locomotion, thus demonstrating its versatility.

No description available.

This paper will investigate the development of a landing footprint for a re-entry vehicle. Vehicles can re-enter the atmosphere with a range of orientations, velocities and flight path angles. The central question is whether a vehicle with any combination of these states can be brought to an acceptable landing condition at a particular landing site and with a particular landing speed. To aide in this investigation several models must be implemented, including that of the atmosphere, the vehicles, the Earth, and the aerodynamics. A detailed analysis of the aerodynamic model will be treated, and the equations of motion subject to these aerodynamic laws will then be compared to results from existing atmospheric reentry software. The principles of optimization will then be employed to generate the footprint of landable states, based on maximum and minimum possible downrange distances, for two vehicle concepts.

Optimal control problems can in many cases become complicated and difficult to solve. One particular class of difficult control problems to solve are singular control problems. Standard methods for solving optimal control are discussed showing why those methods are difficult to apply to singular control problems. Then standard methods for solving singular control problems are discussed including why the standard methods can be difficult and often impossible to apply without having to resort to numerical techniques. Finally, an alternative method to solving a class of singular optimal control problems is given for a specific class of problems.

No description available.