Cette thèse comprend deux parties indépendantes.Dans la première partie nous contribuons une nouvelle méthode qui, étant donnée un volume de tolérance, génère un maillage triangulaire surfacique garanti d’être dans le volume de tolérance, sans auto-intersection et topologiquement correct. Un algorithme flexible est conçu pour capturer la topologie et découvrir l’anisotropie dans le volume de tolérance dans le but de générer un maillage de faible complexité.Dans la seconde partie nous contribuons une nouvelle approche pour calculer une fonction de correspondance entre deux surfaces. Tandis que la plupart des approches précédentes procède par composition de correspondance avec un domaine simple planaire, nous calculons une fonction de correspondance en optimisant directement une fonction de sorte à minimiser la variance d’un plan de transport entre les surfaces / This thesis is divided into two independent parts.In the first part, we introduce a method that, given an input tolerance volume, generates a surface triangle mesh guaranteed to be within the tolerance, intersection free and topologically correct. A pliant meshing algorithm is used to capture the topology and discover the anisotropy in the input tolerance volume in order to generate a concise output. We first refine a 3D Delaunay triangulation over the tolerance volume while maintaining a piecewise-linear function on this triangulation, until an isosurface of this function matches the topology sought after. We then embed the isosurface into the 3D triangulation via mutual tessellation, and simplify it while preserving the topology. Our approach extends toDépôt de thèseDonnées complémentairessurfaces with boundaries and to non-manifold surfaces. We demonstrate the versatility and efficacy of our approach on a variety of data sets and tolerance volumes.In the second part we introduce a new approach for creating a homeomorphic map between two discrete surfaces. While most previous approaches compose maps over intermediate domains which result in suboptimal inter-surface mapping, we directly optimize a map by computing a variance-minimizing mass transport plan between two surfaces. This non-linear problem, which amounts to minimizing the Dirichlet energy of both the map and its inverse, is solved using two alternating convex optimization problems in a coarse-to-fine fashion. Computational efficiency is further improved through the use of Sinkhorn iterations (modified to handle minimal regularization and unbalanced transport plans) and diffusion distances. The resulting inter-surface mapping algorithm applies to arbitrary shapes robustly and efficiently, with little to no user interaction.

The thesis is devoted to finding robust non-conflict paths in multi-agent path finding (MAPF). We propose several new techniques for the construction of these types of paths and describe their properties. We deal with the use of contingency planning and we create a tree plan for the agents where the specific path is chosen by the agents during the execution based on the current delay. Next we present an algorithm that increases robustness while maintaining the original length of the solution and we combine it with the previous approach. Then we will focus on the method of increasing robustness by changing the speed of agents. Finally we experimentally verify the applicability of these techniques on different types of graphs. We will show that all the proposed methods are significantly more robust than the classic solution and they also have certain advantages over previously known constructions of robust plans.

This thesis deals with the multi-stage stochastic programming problems. In the first part, there are introduced two-stage and multi-stage stochastic programming problems. Next, two methods how to generate scenarios are described in detail - the moment method and paths-based methods. The second chapter describes the flower-girl problem, its various formulations and other extensions using ro- bustness and endogenous randomness. The practical part follows, where several different formulations of the flower-girl problem are solved. First, the problem when the florist sells roses with an unlimited life for one week is solved. Then this problem is reformulated as a two-stage problem and the results are compared. Then a formulation with a limited rose life of 2 days is presented. The greatest attention is paid to the problem with a limited rose life of 4 days - the basic formulation of the problem and several extended formulations are solved. 1

Every manufactured product has an environmental impact, a social impact, and an economic impact. As engineers, we should do our best to understand how our design decisions influence these impacts (the three pillars of sustainability), and at the same time make decisions that collectively lead to maximum positive impacts, or minimum negative impacts on the economy, environment, and society. Many times, engineers show interest and want to design for all three pillars of sustainability but are often constrained to focus on the environmental and economic aspects, leaving out social sustainability due to lack of understanding and resources. In practice, this leaves the social dimension of sustainability out of sight and reach for many engineers. So to assist engineers to consider and improve the social impacts of their products, we have created two methods. The first method is focused on meeting customers' unmet needs through the use of collaborative products (a product created by temporarily combining physical components from two or more products to perform new tasks) and the second method is to be used throughout the product development process in order to increase the potential social impacts of the product being designed. It will assist engineers to become aware of social impact categories sometimes overlooked, especially when designing for global engineering. If engineers are able to focus on all three pillars of sustainability early in the design process, including social sustainability, they can add social impact indicators along with technical performance measurements during the product development process and design a product that better meets the requirements for environment, economic, and social sustainability. This is why it is important for engineers to know how to handle the complexity and uncertainty associated with design parameters when creating products for social impacts aimed at global development. In this dissertation, the two methods are outlined and explained. The demonstration of the first method showed that by using the method of collaborative product design to create a brick press, the task-per-cost ratio was improved by 30%. The demonstration of the second method showed that a redesign of the cup seal in the India Mark II/III hand pump system (a product used by approximately 10% of the world's population) could extend the service interval with 12% by replacing the cup seals. Lastly, conclusions related to improving social impacts when engineering for global development and suggestions for future research are outlined.

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Cette thèse s’intéresse à la faisabilité des implémentations en boîte blanche de permutations pseudo-aléatoires sûres. Concrètement nous montrons comment un schéma de chiffrement fonctionnel à plusieurs entrées, qui satisfait une notion naturelle d’être à sens unique, est fondamental à la construction d’implémentations protégées contre les attaques d’extraction de clés. Comme contribution indépendante possédant son intérêt propre, nous étendons la notion de robustesse cryptographique. Sommairement, le chiffrement robuste garantit qu’un chiffré ne peut être lu au moyen de plusieurs clés. Décrite tout d’abord dans le contexte de la cryptographie à clé publique, nous étendons les définitions aux contextes du chiffrement fonctionnel et à l’authentification. / This thesis investigates the realizability of white-box implementations for secure pseudorandom permutations. Concretely, we show that multi-input functional encryption achieving a natural definition of one-wayness is instrumental in building implementations that are secure against key-extraction attacks. As a contribution of independent interest, we extend the notion of robustness to a larger set of primitives. Roughly speaking, robust encryption guarantees that a ciphertext cannot be decrypted under different keys. Initially formalized in a public-key context, we introduce compelling definitions for authentication and functional encryption schemes.

Cette thèse est consacrée à la planification robuste du matériel roulant ferroviaire dans un contexte de transport de voyageurs régional. Il s'agit de déterminer pour chaque engin une suite de trajets à réaliser sur une période donnée de façon à résister au mieux aux aléas pouvant apparaître en opérationnel. Dans ce but, nous proposons une définition et une caractérisation de la robustesse par des indicateurs propres au contexte d'étude. Nous abordons le problème par une approche structurelle différente des approches robustes classiques qui permet d'agir sur la structure d'une solution en fonction des indicateurs définis. Trois méthodes sont alors mises en œuvre dans le cadre de ce travail. Une résolution approchée par une heuristique gloutonne et une recherche locale permet d'obtenir des solutions rapidement. Une méthode de résolution approchée par génération de colonnes a été développée afin de prendre en compte plus de contraintes de façon intégrée. Une méthode basée sur un programme linéaire en nombres entiers résolu exactement traite un problème plus général. Afin de limiter le coût de la robustesse, ces méthodes sont basées sur un existant à SNCF répondant au problème de planification des ressources matérielles à coûts de production minimaux. Un outil de simulation du comportement des solutions en situation perturbée permet de comparer les solutions entre elles par évaluation des indicateurs de robustesse. Des expérimentations sur des instances réelles ont prouvé la pertinence des approches et ont mené à l'industrialisation d'un prototype. / This thesis deals with robust rolling-stock planning problems for passenger regional trains. It consists in building robust rolling-stock schedules to operate trains under technical constraints while anticipating operational disturbances that can occur. First of all, we define indicators to characterize robustness in context. We use these indicators to have an effect on solutions that we build. This structural approach is unusual compared to classical robust optimization approaches. We have implemented three methods to solve the problem. A sequential heuristic method enhanced by a local search gives solutions quickly. A column-generation method calculates approximate solutions.An integer linear program is solved exactly to obtain solutions to a global problem. These methods are based on an existing tool at SNCF that optimizes the rolling-stock planning problem to assure optimal production costs. A simulation tool evaluates robustness indicators to compare solutions. Tests on real instances have proved the relevance of the approaches and have lead to the use of a prototype in production

This dissertation explores the role of information frictions in the design of financial securities, the pricing of securities, and their business cycle implications. The first essay studies the risk- shifting problem between bondholders and shareholders, and the moral hazard problem between shareholders and the manager. Although, these two problems have been studied separately, my model is the first tractable frame-work to study these two frictions jointly. Using my model, I explore: i) How the presence of managerial moral hazard affects the risk-shifting problem, and ii) How optimal policies of the firm change in terms of leverage, managerial compensation, and investment decisions when the two problems are considered jointly. I show that the optimal amount of risk-shifting is amplified in the presence of managerial moral hazard. Moreover, my model delivers a non-monotonic relation between risk-shifting and leverage. This non-monotonicity has the potential to reconcile seemingly contradictory empirical evidence on the sign of this relation. The second essay (coauthored with Jianjun Miao) studies the design of an optimal contract for the manager when the shareholders are concerned about model misspecification. The model delivers counter-cyclical firm level equity premium, and has interesting implications for security design. The third essay incorporates accounting practices into models that generate business cycles through borrowing constraints. I show that the interaction of accounting frictions with the borrowing constraint has implications for the persistence and amplification of macroeconomic shocks.

Les dernières années ont permis des développements très rapides, tant au niveau de l’élaboration que de l’application, d’algorithmes de commande prédictive non linéaire (CPNL), avec une gamme relativement large de réalisations industrielles. Un des obstacles les plus significatifs rencontré lors du développement de cette commande est lié aux incertitudes sur le modèle du système. Dans ce contexte, l’objectif principal de cette thèse est la conception de lois de commande prédictives non linéaires robustes vis-à-vis des incertitudes sur le modèle. Classiquement, cette synthèse peut s’obtenir via la résolution d’un problème d’optimisation min-max. L’idée est alors de minimiser l’erreur de suivi de la trajectoire optimale pour la pire réalisation d'incertitudes possible. Cependant, cette formulation de la commande prédictive robuste induit une complexité qui peut être élevée ainsi qu’une charge de calcul importante, notamment dans le cas de systèmes multivariables, avec un nombre de paramètres incertains élevé. Pour y remédier, une approche proposée dans ces travaux consiste à simplifier le problème d’optimisation min-max, via l’analyse de sensibilité du modèle vis-à-vis de ses paramètres afin d’en réduire le temps de calcul. Dans un premier temps, le critère est linéarisé autour des valeurs nominales des paramètres du modèle. Les variables d’optimisation sont soit les commandes du système soit l’incrément de commande sur l’horizon temporel. Le problème d’optimisation initial est alors transformé soit en un problème convexe, soit en un problème de minimisation unidimensionnel, en fonction des contraintes imposées sur les états et les commandes. Une analyse de la stabilité du système en boucle fermée est également proposée. En dernier lieu, une structure de commande hiérarchisée combinant la commande prédictive robuste linéarisée et une commande par mode glissant intégral est développée afin d’éliminer toute erreur statique en suivi de trajectoire de référence. L'ensemble des stratégies proposées est appliqué à deux cas d'études de commande de bioréacteurs de culture de microorganismes. / The last few years have led to very rapid developments, both in the formulation and the application of Nonlinear Model Predictive Control (NMPC) algorithms, with a relatively wide range of industrial achievements. One of the most significant challenges encountered during the development of this control law is due to uncertainties in the model of the system. In this context, the thesis addresses the design of NMPC control laws robust towards model uncertainties. Usually, the above design can be achieved through solving a min-max optimization problem. In this case, the idea is to minimize the tracking error for the worst possible uncertainty realization. However, this robust approach tends to become too complex to be solved numerically online, especially in the case of multivariable systems with a large number of uncertain parameters. To address this shortfall, the proposed approach consists in simplifying the min-max optimization problem through a sensitivity analysis of the model with respect to its parameters, in order to reduce the calculation time. First, the criterion is linearized around the model parameters nominal values. The optimization variables are either the system control inputs or the control increments over the prediction horizon. The initial optimization problem is then converted either into a convex optimization problem, or a one-dimensional minimization problem, depending on the nature of the constraints on the states and commands. The stability analysis of the closed-loop system is also addressed. Finally, a hierarchical control strategy is developed, that combines a robust model predictive control law with an integral sliding mode controller, in order to cancel any tracking error. The proposed approaches are applied through two case studies to the control of microorganisms culture in bioreactors.

L’introduction des systèmes électriques notamment des dispositifs d’électronique de puissance « embarqués » dans le domaine de transport aérien, requiert une forte compacité et une forte intégration des systèmes de conversions électriques ainsi des fonctionnalités électroniques a des hautes t ambiantes dépassant les 200°C.Mais pour répondre à ces besoins, le silicium a atteint ses limites d'où le recours à des nouveaux matériaux semi-conducteurs comme ceux à grand gap.Dans le cadre de ses recherches, Thales, en collaboration avec le laboratoire SATIE , mènent des investigations sur les performances des semi-conducteurs en technologie sic pour développer des convertisseurs aéronautiques de nouvelle génération.Ces travaux de thèse s'inscrivent dans le cadre d'une étude des potentialités des premiers composants SiC disponibles sur le marché. Cette étude permet de comparer les principales performances de ces dispositifs ainsi que les contraintes spécifiques induites lors de leur intégration dans les convertisseurs aéronautiques. / The potential of wide band gap transistors based on silicon carbide are remarkable and open new prospects for improvement (high efficiency, high breakdown voltage, high switching frequency and high operating temperature ...). This leads to volume and weight reduction for future converters. In order to improve new generation of power converters for future needs, Thales, in cooperation with SATIE and LTN IFSTTAR laboratories, performs investigations on the performances, advantages and disadvantages of SiC technology semiconductors. This comparative study will assess the strengths and weaknesses as well as the stresses induced during integration into aircraft converters of commercially available devices.