The Diploma thesis deals with the problem of energy-efficient train control. It presents the basic survey of mathematical models used in the problem of energy-efficient train control, analysis of optimal driving regimes, determining optimal switching times between optimal driving regimes and timetabling of the train. The mathematical formulation of the problem is done using Newton's second law of motion and other known physical laws. To analyse optimal driving regimes and determine the switching times between optimal driving regimes, we apply tools of optimal control theory, particularly Pontryagin's Maximum Principle. The timetabling of the train is discussed from the numerical solution of the settled non-linear programming problem.

Tato diplomová práce se zabývá problematikou spojitého optimálního řízení, což je jedna z nejvýznamnějších aplikací teorie diferenciálních rovnic. Cílem této práce bylo jak nastudování matematické teorie optimálního řízení, tak především ukázat užití Pontrjaginova principu maxima a Bellmanova principu optimality při řešení vybraných úloh optimálního řízení. Důraz byl kladen především na problematiku časově a energeticky optimálního řízení elektrického vlaku, při zahrnutí kvadratické odporové funkce.

Approximately 2 to 3 million people in the United States suffer from chronic wounds, which are defined as wounds that do not heal in 30 days time; an estimated $25 billion per year is spent on their treatment in the United States. In our work, we focused on treating chronic wounds with bacterial infections using hyperbaric and topical oxygen therapies. We used a mathematical model describing the interaction between bacteria, neutrophils and oxygen. Optimal control theory was then employed to study oxygen treatment strategies with the mathematical model. Existence of a solution was shown for both therapies. Uniqueness was also shown for hyperbaric therapy. We then used a forward-backward sweep method to find numerical solutions for the therapies. We concluded by putting forth ideas for how this problem could progress toward finding applicable treatment strategies.

Applications such as urban surveillance, search and rescue, agricultural applications, military applications, etc., require miniature air vehicles (MAVs) to fly for a long time. But they have restricted flight duration due to their dependence on battery life, which necessitates optimal path planning. The generated optimal path should obey the curvature limits prescribed by the minimum turn radius/ maximum turn rate of the MAV. Further, in a dynamically changing environment, the final configuration that the MAV has to achieve may change en route, which demands the path to be replanned by an airborne processor in real-time. As MAVs are small in size and light in weight, wind has a very significant effect on the flight of MAVs and the computation of the minimum-time path in the presence of wind plays an important role. The thesis develops feasible trajectory generation algorithms which are fast, efficient, optimal and implementable in an onboard computer for rectilinear and circular path convergence problems and waypoint following problems both in the absence and in the presence of wind. The first part of the thesis addresses the problem of computation of optimal trajectories when MAVs fly on a two-dimensional (2D) plane maintaining a constant altitude. The shortest path is computed for MAVs from a given initial position and orientation to a given final path with a specified direction as required for a given mission. Unlike the classical Dubins problem where the shortest path was computed between two given configurations (position and orientation), the final point in this case is not specified. However, the final path, which can either be a rectilinear path or a circular path, and the direction to which the MAV should converge, is specified. The time-optimal path of MAVs is developed in the presence of wind mainly using the geometric approach although a few important properties are also obtained using optimal control theory, specifically, Pontryagin’s minimum principle (which provides only the necessary condition for optimality) for control-constrained systems. The complete optima l solution to this problem in all its generality is a major contribution of this thesis as existing methods in the literature that address this problem are either not optimal or do not give a complete solution. Further, the time-optimal path for specified initial and final configurations is generated in reasonably short time without computing all the path lengths of possible candidate paths, which is the method that exists in the literature for similar problems. Simulation results illustrate path generation for various cases, including the presence of steady and time-varying wind. Another problem in MAV path planning in 2D addressed in this thesis computes an extremal path that transitions between two consecutive waypoint segments (obtained by joining two way points in sequence) in a time-optimal fashion. This designed trajectory, named as γ-trajectory, is also used to track the maximum portion of waypoint segments in minimum time and the shortest distance between this trajectory and the associated waypoint can be set to a desired value. Another optimal path, called the loop trajectory, that goes through the way points as well as through the entire waypoint segments, is also proposed. Subsequently, the thesis proposes algorithms to generate trajectories in the presence of steady wind and compares these with the optimal trajectory generated using nonlinear programming based multiple shooting method to show that the generated paths are optimal in most cases. In three-dimensional (3D) space, if the initial and final configurations – in terms of (X,Y,Z) position, heading angle and flight path angle- of the vehicle are specified then shortest path computation is an interesting problem in literature. The proposed method in this thesis is based on 3D geometry and, unlike the existing iterative methods which yield suboptimal paths and are computationally more intensive, this method generates the shortest path in much less time. Due to its simplicity and low computational requirements, this approach can be implemented on a MAV in real-time. But, If the path demands very high pitch angle (as in the case of steep climbs), the generated path may not be flyable for an aerial vehicle with limited range of flight path angles. In such cases numerical methods, such as multiple shooting, coupled with nonlinear programming, are used to obtain the optimal solution. The time-optimal 3D path is also developed in the presence of wind which has a magnitude comparable to the speed of MAVs. The simulation results show path generation for a few sample cases to show the efficacy of the proposed approach as compared to the available approach in the literature. Next, the path convergence problem is studied in 3D for MAVs. The shortest path is generated to converge to a rectilinear path and a circular path starting from a known initial position and orientation. The method is also extended to compute the time-optimal path in the presence of wind. In simulation, optimal paths are generated for a variety of cases to show the efficacy of the algorithm. The other problem discussed in this thesis considers curvature-constrained trajectory generation technique for following a series of way points in 3D space. Extending the idea used in 2D, a γ-trajectory in 3D is generated to track the maximum portion of waypoint segments with a desired shortest distance between the trajectory and the associated waypoint. Considering the flyability issue of the plane a loop-trajectory is generated which is flyable by a MAV with constrained flight path angle. Simulation results are given for illustrative purposes. The path generation algorithms are all based on a kinematic model, considering the vehicle as a point in space. Implementing these results in a real MAV will require the dynamics of the MAV to be considered. So, a 6-DOF SIMULINK model of a MAV is used to demonstrate the tracking of the computed paths both in 2D plane and in 3D space using autopilots consisting of proportional-integral-derivative (PID )controllers .Achieving terminal condition accurately in real-time, if there is noisy measurement of wind data, is also addressed.

Les Energies Marines Renouvelables (EMR) se développent aujourd’hui très vite tant au niveau de la recherche amont que de la R&D, et même des premiers démonstrateurs à la mer. Parmi ces EMR, l'énergie des vagues présente un potentiel particulièrement intéressant. Avec une ressource annuelle brute moyenne estimée à 40 kW/m au large de la côte atlantique, le littoral français est plutôt bien exposé. Mais l’exploitation à grande échelle de cette énergie renouvelable ne sera réalisable et pertinente qu'à condition d'une bonne intégration au réseau électrique (qualité) ainsi que d'une gestion et d'un dimensionnement optimisé au sens du coût sur cycle de vie. Une première solution de génération tout électrique pour un houlogénérateur a d’abord été évaluée dans le cadre de la thèse de Marie RUELLAN menée sur le site de Bretagne du laboratoire SATIE (ENS de Cachan). Ces travaux ont mis en évidence le potentiel de viabilité économique de cette chaîne de conversion et ont permis de poser la question du dimensionnement de l’ensemble convertisseur-machine et de soulever les problèmes associés à la qualité de l’énergie produite. Puis une seconde thèse a été menée par Judicaël AUBRY dans la même équipe de recherche. Elle a consisté, entre autres, en l’étude d’une première solution de traitement des fluctuations de la puissance basée sur un système de stockage par supercondensateurs. Une méthodologie de dimensionnement de l’ensemble convertisseur-machine et de gestion de l’énergie stockée fut également élaborée, mais en découplant le dimensionnement et la gestion de la production d’énergie et de ceux de son système de stockage. Le doctorant devra donc : 1. S’approprier les travaux antérieurs réalisés dans le domaine de la récupération de l’énergie des vagues ainsi que les modèles hydrodynamiques et mécaniques réalisés par notre partenaire : le LHEEA de l’Ecole Centrale de Nantes - 2. Résoudre le problème du couplage entre dimensionnement/gestion de la chaîne de conversion et dimensionnement/gestion du système de stockage. 3. Participer à la réalisation d’un banc test à échelle réduite de la chaine électrique et valider expérimentalement les modèles énergétiques du stockage et des convertisseurs statiques associés - 4. Proposer une méthodologie de dimensionnement de la chaine électrique intégrant le stockage et les lois de contrôle préalablement élaborées 5. Déterminer les gains en termes de capacités de stockage obtenus grâce à la mutualisation de la production (parc de machines) et évaluer l’intérêt d’un stockage centralisé - 6. Analyser l’impact sur le réseau d’une production houlogénérée selon divers scenarii, modèles et outils développés par tous les partenaires dans le cadre du projet QUALIPHE. L’exemple traité sera celui de l’Ile d’Yeu (en collaboration avec le SyDEV. / The work of this PhD thesis deals with the minimization of the per-kWh cost of direct-drive wave energy converter, crucial to the economic feasibility of this technology. Despite the simplicity of such a chain (that should provide a better reliability compared to indirect chain), the conversion principle uses an oscillating system (a heaving buoy for example) that induces significant power fluctuations on the production. Without precautions, such fluctuations can lead to: a low global efficiency, an accelerated aging of the fragile electrical components and a failure to respect power quality constraints. To solve these issues, we firstly study the optimization of the direct drive wave energy converter control in order to increase the global energy efficiency (from wave to grid), considering conversion losses and the limit s from the sizing of an electrical chain (maximum force and power). The results point out the effect of the prediction horizon or the mechanical energy into the objective function. Production profiles allow the study of the flicker constraint (due to grid voltage fluctuations) linked notably to the grid characteristics at the connection point. Other models have also been developed to quantify the aging of the most fragile and highly stressed components, namely the energy storage system used for power smoothing (with super capacitors or electrochemical batteries Li-ion) and power semiconductors.Finally, these aging models are used to optimize key design parameters using life-cycle analysis. Moreover, the sizing of the storage system is co-optimized with the smoothing management.