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In this thesis, we formalize and study operatorial transformations of general dy- namic problems (nonlinear and/or nonlocal), to simplify or improve signi¯cantly problems like analysis, simulation, identication, control, estimation, etc. First, a generic formalism of dynamic problems, based on the notion of trajectorial formulations, is stated, and some operatorial transformations (a priori nonlocal and/or nonlinear) are studied, like time-scale transforamtions and operatorial parametrization of dynamic models. Then, the advantages of such transformations are highlighted on many concrete examples : desingularization of a nonlocal implicit ame front model, analysis and numerical scheme for a class of integrodierential wave equations, and control of a nonlinear model of fed-batch bioreactor.; L'objet de cette thèse est de formaliser et étudier la problématique de transformations opératorielles pour des problèmes dynamiques généraux (nonlinéaires et/ou nonlocaux), dans l'objectif d'apporter des simplifications ou améliorations significatives aux problèmes d'analyse, de simulation, d'identification, de commande, d'estimation, etc. Dans une première partie, un formalisme générique des problèmes dynamiques, centré autour de la notion de formulation trajectorielle, est posé, et plusieurs transformations opératorielles (\emph{a priori} elles aussi nonlinéaires et/ou nonlocales) sont étudiées, telles par exemple les transformations de type changement de temps ou la paramétrisation opératorielle de modèles dynamiques. L'intérêt de ces transformations est ensuite mis en lumière sur plusieurs exemples concrets, traités par voie analytique et mis en Suvre numériquement: désingularisation d'un modèle nonlocal implicite de front de flamme, analyse et schémas numériques pour une classe d'équations de propagation integro-differentielles, et contrôle d'un modèle nonlinéaire de bioréacteur fed-batch.

With the increasing concerns in the impact of automotive emissions of CO2 and NOx on the environment combined with today's speculation on oil crude supply, the need to find solutions reducing the fuel consumption and emission of tomorrow's cars is more than ever present. Although the first continuously variable transmissions (CVT) appeared over a hundred years ago, it is only with the recent technological improvements in material durability, lubrication oil as well as control related hardware and software, that these transmissions have proved their capabilities. Because of their ability to decouple the engine from the wheel speed, CVTs enable significant fuel gains by shifting the engine operating point for a certain power demand toward higher torque and lower speed. A CVT can be regarded as a system dedicated to converting the torque delivered by the engine to the wheels. Conversely, for the engine speed control, it can be seen as an actuator applying a load to the engine. Two control concepts of CVTs are recognized. First is the concept of ratio control, which is a natural extension to fixed gear ratio transmissions, enabling an actuation of the transmission ratio. Second and less conventional, is the torque control concept, which sets the torque to be transmitted. It is the particular mechanism of these variators that allows the transmission to automatically shift to the appropriate ratio. Torque control CVTs extend the benefits obtained with conventional ratio control CVTs as they provide a direct control of the load applied on the engine, resulting in a straightforward control of the powertrain. Moreover, when such CVTs are combined with an epicyclic gear train in a split torque arrangement to form an infinitely variable transmission (IVT), virtually no control is required for the operation at the geared neutral point (infinite or zero speed ratio depending on the definition). However, the extended ability of torque control CVTs to decouple the engine and the vehicle speeds causes strong internal interactions, which must be fully understood for their development. The objective of this thesis is to provide a comprehensive and coherent set of analytical tools for the development and operation of torque control CVT powertrains. The classical method of modeling, performance analysis and control is applied to the Torotrak IVT Series 3 and its torque control full toroidal variator. Each of these steps gives a different perspective of the dynamics involved within the variator, of the interactions of the variator with the surrounding subsystems (hydraulics and driveline) and of the powertrain control. The contribution of this work is threefold. Firstly, the most relevant dynamics involved in TC/CVT-based powertrains are described with an application to the Torotrak torque control IVT. The main technical achievements are the development and validation of a model for simulation of the full toroidal variator, an open-loop performance analysis of the powertrain and the development of a control strategy for the engine operating point based on the nonlinear input-output feedback linearization technique. Secondly, this work broadens the general theoretical knowledge base of the operation of CVT powertrains. The two control concepts are compared and formally defined resulting in a new and original classification of transmissions. Also, the problem of powertrain control is formalized with the development of high-level, low bandwidth models of the engine, the transmission and the vehicle featuring properties similar to those of the ratio control CVT powertrain model. Thirdly, the formal and progressive analysis made throughout this work shows how the classical method of modeling, performance analysis and control can be applied to complex systems. This relies most of all on the development of models of varying complexity adapted to the requirements of the system analysis, design and control.