À travers une approche de contrôle optimal, cette thèse de doctorat propose une étude des modèles et des techniques de résolution dans un domaine d'application propre à la gestion du trafic aérien. Motivés par la croissance des flux aériens d'une part, et les développements en théorie du contrôle optimal d'autre part, ces travaux portent sur l'analyse du problème d'évitement de conflits aériens. Cette étude permet le développement de nouvelles approches et algorithmes en vue d'aider les contrôleurs aériens dans leur tâche. Ainsi, dans le cadre du trafic aérien, afin de préserver des distances minimales de sécurité entre avions, lors de phases tactiques et de configurations des vols en-route, notre recherche se focalise sur une stratégie de régulation subliminale en vitesse (variations très réduites), pour assurer la séparation entre avions, tout en conservant leur trajectoire prédéfinie. D'une part, une méthode de résolution numérique en contrôle optimal telle que la méthode directe de tir, impliquant une discrétisation totale ou partielle du problème, transforme le problème initial en un problème en programmation non linéaire de grande taille. Ce type de méthodes peut générer des problèmes d'optimisation de grande taille numériquement di_ciles à résoudre. Suivant le nombre de variables du problème, elles peuvent s'avérer trop coûteuse en termes de temps de calculs. D'autre part, les contraintes sur les variables d'états du problème posent des di_cultés de résolution, par exemple, pour l'usage d'une méthode numérique indirecte de tir. Développant les informations caractéristiques des conflits aériens, une détection et une détermination a priori des zones de conflits permettent alors la décomposition du problème présenté de contrôle optimal en sous-problèmes plus aisés à résoudre. La résolution des sous-problèmes hors-zones peut être abordée en utilisant les conditions du principe du maximum de Pontryagin, ce qui en permet une résolution e_cace. Une combinaison de méthodes numériques directes de tir et d'application des conditions du principe du maximum de Pontryagin est proposée, et des implémentations numériques valident ce type d'approche. / The purpose of this doctoral thesis is to study models and solution techniques based on optimal control approaches to address air tra_c management problems. Motivated by the growth of air tra_c volume, and by the advances in optimal control theory, this research works focus on analysing aircraft conflict avoidance problem. This study allows development of new approaches and algorithms to help air tra_c controllers. In the framework of air tra_c management, to ensure the minimum safety distances between aircraft, in tactical phases and en-route flight configurations, this thesis focusses on a subliminal velocity regulation strategy to perform the separation, while preserving the aircraft predefined trajectories. A numerical optimal control solution approach as the direct shooting method, wherein involves a total or partial discretization of the problem, transforms the initial problem into a large scale nonlinear programming problem. This kind of methods could generate large-size optimization problems which are numerically di_cult to solve. Depending on the number of variables which involved, this approaches could be too expensive in terms of computation time. Moreover, the state-variables constraints of the problem lead to numerical di_culties, e.g., considering the indirect numerical shooting method. Tailored on aircraft conflict avoidance problems, a detection and a determination of a priori conflict zones allow the decomposition of the optimal control problem into sub-problems, easier to solve than the original one. Solving the o_-zones sub-problems can be addressed using the Pontryagin maximum principle, which allows in this case directly the solution. A combination of direct numerical shooting method and application of conditions of Pontryagin's maximum principle is proposed, and numerical experiments validate this approach.

The study is conducted to determine practical modelling and simulation techniques to perform dynamic stability and performance analysis on a 3 Degrees of freedom aircraft model using a Modelica-based commercial tool called Modelon Impact. This study is based on a conceptual aircraft model where in-depth details about the aircraft configuration are unknown and the aim is to determine a suitable model that can capture the longitudinal dynamics and aerodynamic constraints of the aircraft during the conceptual design phase. Requirements include short execution time, easy model development, and minimal data requirements. Therefore, this thesis aims at developing plant and control architectures in  Modelon Impact which can be utilized for the rapid development of aircraft concepts with adequate fidelity in a longitudinal mission-based tracking environment. In a conceptual aircraft design environment, to identify a suitable methodology that mitigates the limitations of a traditional feedback controller, two methodologies are considered for comparison: Sequential DAE resolution (SDR) and Dynamic inversion (DI) control which is discussed from an object-oriented aircraft model. The advantages and shortcomings of each of the models discussed above are compared by conducting several experiments in increasing order of longitudinal mission complexity, and the most appropriate model among the two for a conceptual stage of aircraft design development is ascertained. The two methodologies discussed are compared for their level of complexity, code structure, readability, and ease of usability.

Thesis presents description of the air traffic safety, efficiency, capacity and preferences of navigation equipment. Those aspect are further used to suggestion of future advancement airspace, which occur during almost all phases of the flight.

Luftverkehrsprognosen stellen ein wichtiges Instrument dar, die Luftverkehrsinfrastruktur zu beeinflussen. Hinter vielen der Projekte, die von Luftverkehrsprognosen begleitet werden, stehen Interessen. Dies gilt insbesondere für Ausbauvorhaben von Flughäfen, die von eindeutigen Zielen und Wünschen getragen werden. Die Gutachter, die im Rahmen solcher Ausbauvorhaben tätig werden, sind der Gefahr ausgesetzt, beeinflusste Prognosen zu erstellen. Die Art und Intensität dieser Beeinflussung sowie die Methodik dieser Analysen sind Gegenstand dieses Aufsatzes. Zunächst wurden neuere Ergebnisse der OECD und EU erarbeitet und denen der Flughafenstudien gegenübergestellt. Nachfolgend wurde die Intensität der Beeinflussung auf Grundlage einer eigenen Untersuchung analysiert. Dabei wurden politische Entscheidungsträger im Rhein-Main-Gebiet nach Ihrer Verwendung von Studien und deren Ergebnisse befragt. Die Impact Study, als häufigste Forschungsmethodik, wurde in ihre Bestandteile zerlegt und mit der Full Cost-Benefit-Analyse, welche die durch die FAA empfohlene Methode ist, verglichen. Grundsätzlich sind solche Gutachten meist externe Analysen aus privatwirtschaftlicher Hand, die einerseits im Auftrag von regionalen Entscheidungsträgern, aber andererseits auch im Auftrag von Flughafen- und Fluggesellschaften angefertigt wurden. Die Unabhängigkeit der Prognosen ist damit gefährdet. Auf Grundlage der (neutralen) OECD- und EU-Ergebnisse zeigte sich, dass etwaige regionale Wirtschaftsimpulse und damit einhergehendes Beschäftigungswachstum durch erhöhten Flugverkehr nicht zu finden sind. Die kritische Analyse von „bezahlten Studien“ ist demnach von Bedeutung. Die Mehrzahl der politischen Amts- und Entscheidungsträger in Deutschland trifft allerdings Entscheidungen auf Basis keiner oder ausschließlich nicht-neutraler, bezahlter Auftragsstudien. Historisch betrachtet ist dies kein Novum. Bereits in den 60er Jahren kann man solche Studien und Entscheidungen nachweisen. Bezüglich des Forschungsdesign zeigte sich, dass Impact-Studien kaum für zur Beurteilung des Luftverkehrs geeignet sind. Sie beziehen die relevanten Effekte nur teilweise in ihre Berechnungen ein. Es wurde eine Reihe von systematischen Fehlern identifiziert. Die FAA-Richtlinien in den USA für methodisch korrekte Studien greifen nur wenig. Für weitere Forschung sehen wir die wichtige Aufgabe, die Methodik der Full Cost-Benefit-Analyse für die Prognose möglicher Effekte zur Anwendung zu bringen. / Aviation traffic forecasts and airport analyses are important instruments which influence decisions on aviation related infrastructure. Behind many of such infrastructure projects, which are supported by forecast analyses, one finds political interests. This is especially the case for aviation projects, such as infrastructure enlargement projects of airports, which are motivated by distinct goals and desires. Referees who act within this framework are exposed to the risk of producing biased results. The form and degree of intensity of such influence and manipulation, as well as the methodology of such forecast analyses, are the subject of this working paper. To begin with, newer research results by the OECD and the EU have been formulated and further compared to results of studies commissioned by airport operators. Subsequently, the degree of intensity of such influence has been analysed on the basis of our own research. A survey was thereby produced, investigating the application of neutral and non-neutral studies in the decision-making processes of the public administration in the Rhein-Main-area. Impact studies, which are currently the most used method, have been segmented and compared with studies using full cost-benefit-analysis, the recommended method by the FAA. With regard to these results, it can be argued that most forecast analyses are produced by private consultancies, by order of public entities but also by order of airport operators. The independence of such research and its results is therefore endangered. Recent OECD and EU research results have shown that eventual effects, such as regional economic stimulus and employment growth, are absent. Thus, care in the application of study results in this field is necessary. However, the majority of policy makers (in Germany) unfortunately base their decisions mostly on non-neutral studies. Historically seen, this is not a novelty. Regarding the research design, impact studies are hardly suitable for airport studies. Further, it can be shown that impact studies incorporate mostly only non-negative items in their cash flow calculations, compared to full cost-benefit-analyses which incorporate all relevant items. A number of systematic flaws are further identified. The regulation-guidelines by the FAA, which demand to incorporate all items, have had little impact on the research design of airport studies in the US so far. The promotion and fostering of full cost-benefit-analyses is necessary to lift the quality of airport studies.

Introductory part of this thesis concludes the development of air traffic, division of airports in the Czech Republic according to the Ministry of Transport, according to the Law on Civil Aviation and according to the Coding of the airports (Requirement L 14). The aim was to realize theoretical definition and division of output and economic indicators. After that comes choice of appropriate airports from the European Union. The choice has been made on the basis of the number of check-in passengers at the airport in Prague-Ruzyně. Eight most suitable airports have been chosen from all twenty-seven member countries of the EU. The following step is comparative analysis of these chosen airports on the basis of specified output and economic indicators for the years 2005-2009. The year 2010 has not been included, because the chosen airports did not complete their annual reports, balances and statements of profit and loss. From these sources the values for calculation of individual indicators have been chosen. These indicators have been shown in charts, evaluated by means of graphs in Excel Programme and further they have been characterized in words. The aim of the thesis was also the evaluation and comparison of output and economic indicators of effectiveness and after evaluation, proposal of methods of evaluations has followed.