<p>Alternate power sources in automotive class-8 trucking industry is a major focus of research in recent days. Green house gasses, oxides of Nitrogen(NOx), Oxides of Sulphur(SOx), hydrocarbons and particulate matter are major concerns contributing to the shift in alternate fuel strategies. Another direct relation to move to an alternate power strategy is the reduction in net fuel consumption which in turn implicitly improves the emission components.</p> <p>A holistic approach is needed while designing a modern class-8 vehicle. A variety of system architecture, control algorithms, diagnostic levers are needed to be manipulated to achieve the best of blends amongst Total Cost of Ownership (TCO), Drivability, Fuel</p> <p>Economy, Emissions Compliant, Hauling Capacity, etc. The control and system levers are not mutually exclusive and there is a strong correlation amongst all these control and system components. In order to achieve a consensus amongst all these levers to achieve a common objective, is a challenging and complex problem to solve. It is often required to shift the algorithm strategy to predictive information based rather than reactive logic. Predictively modulating and manipulating control logic can help with better fuel efficient solution along with emissions improvement. A further addition to the above challenge is when we add a fleet of vehicle to the problem. So, the problem now is to optimize a control action for a fleet</p> <p>of vehicles and design/select the correct component size. A lot of research has been done and is still underway to use a 48V hybrid system with a small battery using a simple charge sustaining SOC control strategy. This will make the system light enough not to compromise on the freight carrying capacity as well as give some extra boost during the high torque requirement sections in the route for a better fuel and emissions efficient solution. In this work a P2 type 48V hybrid system is used which is side mounted to the transmission via a gear system. The selection of the system and components enables the usage of different control strategies such as neutral coasting and Engine off coasting. This architecture with a traditional 12-15L Internal combustion engine along with a mild 48V hybrid system provides the most viable selection for a long haul class-8 application and is used in this work. It is also possible to identify other component sizes along with architectures for new configurations. The framework in this research work can help develop the study for different component sizing. While this research work is focused towards building a framework for achieving predictive control in a 3 truck platooning system using multi-agent based control, the other supporting work done also helps understand the optimal behavior of the interacting multiple controls when the corridor information such as road grade and route speed limit are known a-priori, in a single vehicle. The build up of this work analyzes an offline simulation of a 4 control optimal solution for a single hybrid truck and then extend the optimal controls to a 3 truck platoon. In the single truck, this research will help identify the interacting zones in the route where the various control actions will provide the best cost benefits which is fuel economy. These benefits are associated as a function of exogenous look ahead information such as grade and speed limit. Further it is also possible to identify the optimal behavior and the look ahead horizon required for achieving that. In other words the optimal behavior and benefits associated with the global solution can be accomplished by implementing rule based control system with a look ahead horizon of 2-5 km. If this would not have been the case then it is almost impossible to design a predictive controller based on the entire route information which can stretch up to hundreds of kilometers. Optimal algorithms of such prediction horizon are not feasible to be implemented in real time controllers. This research work will also help understand the interaction between different active control actions such as predictive speed modulation, gear shift, coasting and power split with passive control levers such as slow down due to hybrid regeneration, hybrid boost during coasting, etc. This will help in architecting a system involving component specifications, active optimal control, look ahead information, hybrid system strength, etc, working in close interaction with each other. Though we analyze these predictive behavior for a single vehicle as a supporting work the prime objective is to include these predictive levers in a platooning system using an agent based method. This multi-agent based technique will help analyze the behavior of multiple trucks in a platoon in terms of fuel efficient safe operation. The focus of this research work is to not directly come up with a controller or strategy but rather to understand the optimality of this control levers for a multi-vehicle platoon system given a look ahead information is available. The research shows that predictive information will help in gaining fuel economy for a platoon of class-8 mild hybrid trucks. It also highlights the challenges in doing so and what needs to be traded off in order to achieve the net fuel benefit.</p>

Autonomous ships are one way to increase safety at sea and to decrease environmental impact of marine traveling and shipping. For this application, a good representation of the environment and a physical model of the ship are vital components. By optimizing the trajectory of the ship, a good trade-off between the time duration and energy consumption can be found. In this thesis, a three degree of freedom model that describes the dynamics of a small-scale surface ship is estimated. By using optimal control theory and a grey-box model, the parameters are estimated by defining an optimal control problem (OCP). The optimal solution is found by transcribing the problem into a nonlinear program and solving it using an interior point algorithm. The identification method is tested and validated using simulated data as well as using data from real world experiments. The performance of the estimated models is validated using cross validation. In a second track of this thesis, a trajectory is created in two steps. The first is path planning to find a shortest geometric path between two points. In the second step, the path is converted to a trajectory and is optimized to become dynamically feasible. For this purpose, a roadmap is generated from a modified version of the generalized Voronoi diagram. To find an initial path in the roadmap, the A-star algorithm is utilized and to connect start and goal position to the map a few different methods are examined. An initial trajectory is created by mapping a straight-line trajectory to the initial path, thus connecting time, position and velocity. The final trajectory is found by solving a discrete OCP initialized with the initial trajectory. The OCP contains spatial constraints that ensures that the vessel does not collide with static obstacles. The suggested estimation method resulted in models that could be used for trajectory planning to generate a dynamically feasible trajectory for both simulated and real data. The trajectory generated by the trajectory planner resulted in a collision-free trajectory, satisfying the dynamics of the estimated model, such that the trade-off between time duration and energy consumption is well balanced. Future work consists of implementation of a controller to see if the planned trajectory can be followed by the small-scale ship.

Combination antiviral drug therapy improves the survival rates of patients chronically infected with hepatitis B virus by controlling viral replication and enhancing immune responses. Some of these drugs have side effects that make them unsuitable for long-term administration. To address the trade-off between the positive and negative effects of the combination therapy, we investigated an optimal control problem for a delay differential equation model of immune responses to hepatitis virus B infection. Our optimal control problem investigates the interplay between virological and immunomodulatory effects of therapy, the control of viremia and the administration of the minimal dosage over a short period of time. Our numerical results show that the high drug levels that induce immune modulation rather than suppression of virological factors are essential for the clearance of hepatitis B virus.

The urge to consume does not seem to stop, thus, the need for transportation of goods will most likely not decrease. At the same time jurisdictions and regulations around greenhouse gas emissions are sharpening and pushing the industry towards a more environmentally friendly state. The freight and transportation industry is facing a huge challenge in the upcoming years and solutions are needed to feed the demand of society. Two, of many, proposals of solving, at least, parts of the above mentioned problem is platooning and the look-ahead controller. Platooning denotes the concept of slipstream where maximum utilization of aerodynamic drag reduction is endeavoured. The lookahead controller exploits the surrounding topographical information in order to yield an optimal driving strategy, often resulting in that the vehicle initiates the phenomenon of pulse and glide, which denotes alternating between high load operation points and freewheeling, i.e. engaging neutral gear. This work has sought to investigate these concepts to determine whether or not additional fuel-efficiency can be added by manipulating and re-designing the control unit of the system. The proposed addition is built upon the look-ahead controller and supplements it by enabling communication between vehicles such that micro-transactions may occur in order to aid decision making regarding the choice of driving strategies. A vehicle model, a platoon model and the novel optimization based look-ahead-controller was synthesized and developed, where dynamic programming was used as the optimization solver of the controller. The look-ahead controller was verified such that one can conclude that it behaves according to the assumptions of such a system. The proposed micro-transaction system was also verified to conclude that it behaves as assumed, yielding a reduction in fuel consumption. For a platoon of two members, a 1.2% and 1.7% reduction in fuel consumption for the leading and following vehicle respectively was obtained, compared to an identical platooning setup, using a lookahead controller, but where no negotiations using micro-transactions are allowed between the vehicles.

L’objectif de cette thèse vise à identifier les principes sous-tendant la planification des mouvements 3D du membre supérieur tout en tenant compte des différences inter-individuelles régulièrement observées dans ce domaine. Dans cette optique, l’approche choisie combine des expériences originales précisément des tâches de pointage laissant le choix du point final libre) avec des techniques de calcul avancées (ici des méthodes de contrôle optimal inverse numérique). Des mouvements de pointage du bras sans position finale précisément prescrite sont examinés dans différentes conditions de vitesse et/ou de masse afin de laisser émerger des stratégies motrices variées et d’évaluer les éventuels principes de planification motrice sous-jacents. L’idée centrale est de s’écarter du paradigme classique consistant à étudier des mouvements point-à-point (où la cible est généralement indiquée par un point dans l’espace, par exemple une cible lumineuse) et porte sur l’étude d’une tâche dans laquelle le choix du point final du mouvement est laissé libre aux participants afin de faire surgir les différences interindividuelles ainsi que le processus de sélection ou de décision motrice qui a conduit aux stratégies observées. Ce type de tâche permet de mieux décoder les caractéristiques du contrôleur moteur humain. Les résultats empiriques sont ensuite modélisés et interprétés grâce au contrôle optimal inverse dont l’hypothèse associée estque les trajectoires expérimentales découlent de la minimisation d’une certaine fonction de coût qui est éventuellement composite. Cette approche combinée vise à révéler les principes ou règles qui gouvernent le processus de planification de ce type de mouvement des membres supérieurs et d’établir un lien entre les paramètres pertinents du geste, les fonctions de coûts et les caractéristiques individuelles.Les résultats montrent que les sujets produisent des stratégies motrices différentes aux niveaux cinématique et dynamique en fonction de la façon dont ils s’adaptent aux changements de vitesse et/ou de masse. Dans l’ensemble, ces changements ont des effets significatifs sur les trajectoires de la main (par exemple l’emplacement des points finaux choisis par les sujets) et les commandes motrices (notamment sur l’utilisation des couples d’interaction). Pourtant, certains sujets présentaient des dépendances plus exacerbées que d’autres qui ne variaient que peu leur stratégie de pointage par rapport aux changements de vitesse ou de masse induits par la tâche. L’investigation par contrôle optimal inverse a montré que ces résultats pouvaient être expliqués par une optimisation d’un coût composite mélangeant essentiellement des variables cinématique et dynamique durant la phase de planification motrice. Un tel modèle composite surpassait les prédictions des modèles séparés soit cinématique soit dynamique dans la prédiction de l’évolution des caractéristiques importantes du mouvement et des différences interindividuelles. En outre, il a permis de réconcilier des résultats controversés débattus dans des études antérieures en montrant que des comportements adaptatifs divergents peuvent émerger en fonction du poids des fonctions de coût élémentaires qui composent la fonction de coût totale. Dans l’ensemble, nos résultats suggèrent que la planification motrice des mouvements 3D non-contraints du bras mêle nécessairement des variables cinématiques et cinétiques, et que ce compromis semble être idiosyncrasique et ainsi conduire à des différences interindividuelles subtiles. / The purpose of this thesis is to identify principles that could guide the planning of 3D upper-limb movements for different individuals. To this aim, the chosen approach combines novel experiments (namely, a “free reach-endpoint" motor task) with advanced computational techniques (here numerical inverse optimal control). Arm pointing movements without a prescribed final hand position are examined under different conditions of speed or load in order to let emerge various motor control strategies and assess the possible underlying motor planning principles. A core idea is to depart from classical point-to-point reaching paradigms (where the target is generally a dot, e.g. a spotlight target) to study a task in which the endpoint is left free to theparticipants in order to emphasize inter-individual differences as well as the selection process and motor decision that led to the observed strategies. This paradigm thus allows to better decipher the characteristics of the human motor controller. Empirical results are then modeled and interpreted in the inverse optimal control framework, hypothesizing that empirical arm trajectories derive from the minimization of a certain, possibly composite, cost function. This combined approach aims at revealing which principle or rule conceivably drives the planning process of these unrestrained upper-limb movements and to stablish a link between relevant motion parameters, cost functions and inter-individual peculiarities.The results show that subjects produced different motor strategies at both kinematic and dynamic levels depending on how they adapted to speed and/or load variations. Overall, significant motor adaptation of hand trajectories (e.g. location of reach endpoints) and motor commands (e.g. use of interaction torque) were found. Yet, some subjects exhibited stronger dependences than others who varied only little their reach strategies with respect to task-induced speed or load changes. When investigated from the optimal control viewpoint, these results could be accounted for by a composite cost essentially weighting kinematic and dynamic variables differentially at the motor planning stage. Such a composite model outperformed separate kinematic and dynamic ones in predicting the evolution of many important motion features and in explaining inter individual differences. Moreover, it allowed reconciling controversial findings of previous studies by showing that divergent adaptive behaviors can emerge depending on the weights of the elementary cost that may compose the total cost function. In sum, the present results suggest that motor planningof unrestrained3D arm movements necessarily mixes kinematic and kinetic variables and that this trade-off may be idiosyncratic and lead to subtle inter individual differences.

The first essay formulates a dynamic general equilibrium optimal control model of an energy crop as part of a country's planned resource use over a period of time. The model attempts to allocate consumption, production, and factors of production to achieve the country's sustainable development goal. A Cobb-Douglas specification is used for both utility and production functions in the model. We calibrate the model with Thailand data. The selected model is used to generate the stationary state solution and to simulate the optimal policy function and optimal time paths. Two methods are used: a linear approximation method and the Runke-Kutta reverse shooting method. The model provides numerical results that can be used as information for decision makers and stakeholders to devise an economic plan to achieve sustainable development goals. The second essay studies the effect of international trade and changes in labor supply, land supply, and the price of imported energy on energy crop production for bio fuel and food, as well as impacts on social welfare. We develop a dynamic general equilibrium model to describe two baseline scenarios, a closed economy and an open economy. We find that international trade increases welfare and decreases the energy price. Furthermore, resources are allocated to produce more food under the open economy scenario than the quantities produced under a closed economy assumption. An increase in labor supply and land supply result in an increase in social welfare. An increase in imported energy price leads to a welfare loss, higher energy production, and lower food production. The third essay develops a partial equilibrium econometric model to project the impacts of an increase in ethanol production on the Thai agriculture sector over the next ten years. The model is applied to three scenarios for analyzing the effect of government ethanol production targets. The results from the baseline model and scenario analysis indicate that an expansion in ethanol production will result in a significant increase in cassava production, price, and land use. The increase in cassava production will shift land use from maize and sugar cane, thus increasing in price of maize.

Dans le domaine de l'anatomie, à l'investissement massif dans la constitution de base de données collectant des données d'imagerie médicale, doit répondre le développement de techniques numériques modernes pour une quantification de la façon dont les pathologies affectent et modifie les structures biologiques. Le développement d'approches géométriques via les espaces homogènes et la géométrie riemannienne en dimension infinie, initialisé il y a une dizaine d'années par Christensen et Miller, et simultanément Trouvé et Younes, et mettant en œuvre des idées originales de d'Arcy Thompson, a permis de construire ces dernières années un cadre conceptuel extrêmement efficace pour attaquer le problème de la modélisation et de l'analyse de la variabilité de populations de formes. Néanmoins, à l'intégration de l'analyse longitudinale des données, ont émergé des phénomènes biologiques de croissance ou de dégénérescence se manifestant via des déformations spécifiques de nature non difféomorphique. On peut en effet observer lors de la croissance d'un composant organique, une apparition progressive de matière qui ne s'apparente pas à un simple étirement du tissu initial. Face à cette observation, nous proposons de garder l'esprit géométrique qui fait la puissance des approches difféomorphiques dans les espaces de formes mais en introduisant un concept assez général de déploiement où l'on modélise les phénomènes de croissance comme le déploiement optimal progressif d'un modèle préalablement replié dans une région de l'espace. Nous présentons donc une généralisation des méthodes difféomorphiques classiques pour modéliser plus fidèlement l'évolution de chaque individu d'une population et saisir l'ensemble de la dynamique de croissance. Nous nous appuyons sur l'exemple concret de la croissance des cornes animales. La considération d'un a priori sur la dynamique de croissance de la corne, nous permet de construire un chemin continu dans un espace de formes, modélisant l'évolution de la corne de sa naissance, d'un état réduit à un point (comme l'état d'embryon pour un humain ou de graine pour une plante) à un âge adulte quelconque de corne bien déployée. Au lieu d'étirer la corne, nous anticipons l'arrivée matière nouvelle en des endroits prédéfinis. Pour cela, nous définissons une forme mère indépendante du temps dans un espace virtuel, qui est progressivement plongée dans l'espace ambiant en fonction d'un marqueur temporel prédéfini sur la forme mère. Finalement, nous aboutissons à un nouveau problème de contrôle optimal pour l'assimilation de données de surfaces évoluant dans le temps, conduisant à un problème intéressant dans le domaine du calcul des variations où le choix pour la représentation des données, courant ou varifold, joue un rôle inattendu. / The Large Deformation Diffeomorphic Metric Mapping (LDDMM) framework has proved to be highly efficient for addressing the problem of modelling and analysis of the variability of populations of shapes, allowing for the direct comparison and quantization of diffeomorphic morphometric changes. However, the analysis of medical imaging data also requires the processing of more complex changes, which especially appear during growth or aging phenomena. The observed organisms are subject to transformations over the time which are no longer diffeomorphic, at least in a biological sense. One reason might be a gradual creation of new material uncorrelated to the preexisting one. For this purpose, we offer to extend the LDDMM framework to address the problem of non diffeomorphic structural variations in longitudinal scenarios during a growth or degenerative process. We keep the geometric central concept of a group of deformations acting on a shape space. However, the shapes will be encoded by a new enriched mathematical object allowing through partial mappings an intrinsic evolution dissociated from external deformations. We focus on the specific case of the growth of animal horns.Ultimately, we integrate these growth priors into a new optimal control problem for assimilation of time-varying surface data, leading to an interesting problem in the field of the calculus of variations where the choice of the attachment term on the data, current or varifold, plays an unexpected role.

abstract: The main part of this work establishes existence, uniqueness and regularity properties of measure-valued solutions of a nonlinear hyperbolic conservation law with non-local velocities. Major challenges stem from in- and out-fluxes containing nonzero pure-point parts which cause discontinuities of the velocities. This part is preceded, and motivated, by an extended study which proves that an associated optimal control problem has no optimal $L^1$-solutions that are supported on short time intervals. The hyperbolic conservation law considered here is a well-established model for a highly re-entrant semiconductor manufacturing system. Prior work established well-posedness for $L^1$-controls and states, and existence of optimal solutions for $L^2$-controls, states, and control objectives. The results on measure-valued solutions presented here reduce to the existing literature in the case of initial state and in-flux being absolutely continuous measures. The surprising well-posedness (in the face of measures containing nonzero pure-point part and discontinuous velocities) is directly related to characteristic features of the model that capture the highly re-entrant nature of the semiconductor manufacturing system. More specifically, the optimal control problem is to minimize an $L^1$-functional that measures the mismatch between actual and desired accumulated out-flux. The focus is on the transition between equilibria with eventually zero backlog. In the case of a step up to a larger equilibrium, the in-flux not only needs to increase to match the higher desired out-flux, but also needs to increase the mass in the factory and to make up for the backlog caused by an inverse response of the system. The optimality results obtained confirm the heuristic inference that the optimal solution should be an impulsive in-flux, but this is no longer in the space of $L^1$-controls. The need for impulsive controls motivates the change of the setting from $L^1$-controls and states to controls and states that are Borel measures. The key strategy is to temporarily abandon the Eulerian point of view and first construct Lagrangian solutions. The final section proposes a notion of weak measure-valued solutions and proves existence and uniqueness of such. In the case of the in-flux containing nonzero pure-point part, the weak solution cannot depend continuously on the time with respect to any norm. However, using semi-norms that are related to the flat norm, a weaker form of continuity of solutions with respect to time is proven. It is conjectured that also a similar weak continuous dependence on initial data holds with respect to a variant of the flat norm. / Dissertation/Thesis / Doctoral Dissertation Applied Mathematics 2019

Le problème de la planification du mouvement a été largement étudié dans le cas de corps rigides articulés mais peu de travaux considèrent les corps déformables. En particulier, les tiges élastiques telles que cables électriques, flexibles hydrauliques et pneumatiques, apparaissent dans de nombreux contextes industriels. Du fait d'une modélisation complexe et d'un grand nombre de degrés de liberté, l'extension des méthodes de planification de mouvement à de tels corps est un problème particulièrement difficile. En se basant sur les propriétés des configurations à l'équilibre statique, cette thèse propose plusieurs approches au problème de planification de mouvement pour des tiges élastiques. / The motion planning problem has been broadly studied in the case of articulated rigid body systems but so far few work have considered deformable bodies. In particular, elastic rods such as electric cables, hydraulic or pneumatic hoses, appear in many industrial contexts. Due to complex models and high number of degrees of freedom, the extension of motion planning methods to such bodies is a difficult problem. By taking advantage of the properties of static equilibrium configurations, this thesis presents several approaches to the motion planning problem for elastic rods.

Pour mener à bien leur mission, les satellites de télécommunications doivent rester à la verticale d'un même point de la Terre, sur une orbite dite géostationnaire, pour laquelle la période de révolution des satellites sur leur orbite est identique à la période de rotation de la Terre sur elle-même. Cependant, à cause des perturbations orbitales, les satellites tendent à s'en éloigner, et il est alors nécessaire de concevoir des stratégies de commande pour les maintenir dans un voisinage de cette position de référence. Du fait de leur grande valeur de poussée, les systèmes à propulsion chimique ont largement été utilisés, mais aujourd'hui les systèmes à propulsion électrique avec leur grande impulsion spécifique sont des alternatives viables pour réduire la masse d'ergols du satellite, et ainsi le coût au lancement, ou allonger la durée de vie du satellite, ce qui permettrait de limiter l'encombrement dans l'espace. Cependant, l'utilisation d'un tel système propulsif induit des contraintes opérationnelles issues en partie du caractère limité de la puissance électrique disponible à bord. Ces contraintes sont difficiles à prendre en compte dans la transcription du problème de maintien à poste en un problème de contrôle optimal à consommation minimale avec contraintes sur l'état et le contrôle. Ce manuscrit propose deux approches pour résoudre ce problème de commande optimale. La première, basée sur le développement et l'exploitation de conditions nécessaires d'optimalité, consiste à découper le problème initial en trois sous-problèmes pour former une méthode de résolution à trois étapes. La première étape permet de résoudre un problème de maintien à poste expurgé des contraintes opérationnelles, tandis que la deuxième, initialisée par le résultat de la première, produit une solution assurant le respect de ces dernières contraintes. La troisième étape permet d'optimiser la valeur des instants d'allumage et d'extinction des propulseurs dans le cadre du formalisme des systèmes à commutation. La seconde approche, dite " directe ", consiste à paramétrer le profil de commande par une fonction binaire et à le discrétiser sur l'horizon temporel de résolution. Les contraintes opérationnelles sont ainsi facilement transcrites en contraintes linéaires en nombres entiers. Après l'intégration numérique de la dynamique, le problème de contrôle optimal se résume à un problème linéaire en nombres entiers. Après la résolution du problème de maintien à poste sur un horizon court d'une semaine, le problème est résolu sur un horizon long d'un an par résolutions successives sur des horizons courts d'une durée de l'ordre de la semaine. Des contraintes de fin d'horizon court doivent alors être ajoutées afin d'assurer la faisabilité de l'enchaînement des problèmes sur l'horizon court constituant le problème sur l'horizon long. / Geostationary spacecraft have to stay above a fixed point of the Earth, on a so-called geostationary Earth orbit. For this orbit, the orbital period of the spacecraft is equal to the rotation period of the Earth. Because of orbital disturbances, spacecraft drift away their station keeping position. It is therefore mandatory to create control strategies in order to make the spacecraft stay in the vicinity of the station keeping position. Due to their high thrust capabilities, chemical thrusters have been widely used. However nowadays electric propulsion based thrusters with their high specific impulse are viable alternative in order to decrease the spacecraft mass or increase its longevity. The use of such a system induce the necessity to handle operational constraints because of the limited on-board power. These operational constraints are difficult to take into account in the mathematical transcription of the station keeping problem in an optimal control problem with control and state constraints. This thesis proposed two techniques in order to solve this optimal control problem. The first one is based on the computation of first order necessary conditions and consists in decomposing the overall problem in three sub-problems, leading to a three-step decomposition method. The first step solves an optimal control problem without the operational constraints. The second steps enforces these operational constraints thanks to dedicated equivalence schemes and the third one optimises the switching times of the control profile thanks to a method borrowed from the switched systems theory. The second proposed method consists in parametrising the on-off control profile with binary functions. After a time discretisation of the station keeping horizons, the operational constraints are easily recast as linear constraints on integer variables, the dynamics is numerically integrated and the station keeping problem is recast as a mixed integer linear programming problem. After the resolution of the problem over a short time horizon of one week, the station keeping problem is solved over a long time horizon of one year. To this end, the long time horizon is split in shorter horizons over which the problem is successively solved. End-of-cycle constraints have been set up in order to ensure the feasibility of the solution one short horizon after another.