This dissertation is devoted to the development of new flow-based formulations for the asymmetric traveling salesman problem (ATSP) and to the demonstration of their applicability in effectively solving some scheduling problems. The ATSP is commonly encountered in the areas of manufacturing planning and scheduling, and transportation logistics. The integration of decisions pertaining to production and shipping, in the supply chain context, has given rise to an additional and practical relevance to this problem especially in situations involving sequence-dependent setups and routing of vehicles. Our objective is to develop new ATSP formulations so that algorithms can be built by taking advantage of their relaxations (of integer variables, thereby, resulting in linear programs) to effectively solve large-size problems. In view of our objective, it is essential to have a formulation that is amenable to the development of an effective solution procedure for the underlying problem. One characteristic of a formulation that is helpful in this regard is its tightness. The tightness of a formulation usually refers to the quality of its approximation to the convex hull of integer feasible solutions. Another characteristic is its compactness. The compactness of a formulation is measured by the number of variables and constraints that are used to formulate a given problem. Our formulations for the ATSP and the scheduling problems that we address are both tight and compact. We present a new class of polynomial length formulations for the asymmetric traveling salesman problem (ATSP) by lifting an ordered path-based model using logical restrictions in concert with the Reformulation-Linearization Technique (RLT). We show that a relaxed version of this formulation is equivalent to a flow-based ATSP model, which, in turn, is tighter than the formulation based on the exponential number of Dantzig-Fulkerson-Johnson (DFJ) subtour elimination constraints. The proposed lifting idea is applied to derive a variety of new formulations for the ATSP, and a detailed analysis of these formulations is carried out to show that some of these formulations are the tightest among those presented in the literature. Computational results are presented to exhibit the relative tightness of our formulations and the efficacy of the proposed lifting process.> While the computational results demonstrate the efficacy of employing the proposed theoretical RLT and logical lifting ideas, yet it remains of practical interest to take due advantage of the tightest formulations. The key requirement to accomplish this is the ability to solve the underlying LP relaxations more effectively. One approach, to that end, is to solve these LP relaxations to (near-) optimality by using deflected subgradient methods on Lagrangian dual formulations. We solve the LP relaxation of our tightest formulation, ATSP6, to (near-) optimality by using a deflected subgradient algorithm with average direction strategy (SA_ADS) (see Sherali and Ulular [69]). We also use two nondifferentiable optimization (NDO) methods, namely, the variable target value method (VTVM) presented by Sherali et al. [66] and the trust region target value method (TRTV) presented by Lim and Sherali [46], on the Lagrangian dual formulation of ATSP6. The preliminary results show that the near-optimal values obtained by the VTVM on solving the problem in the canonical format are the closest to the target optimal values. Another approach that we use is to derive a set of strong valid inequalities based on our tighter formulations through a suitable surrogation process for inclusion within the more compact manageable formulations. Our computational results show that, when the dual optimal solution is available, the associated strong valid inequalities generated from our procedure can successfully lift the LP relaxation of a less tight formulation, such as ATSP2R¯, to be as tight as the tightest formulation, such as ATSP6. We extend our new formulations to include precedence constraints in order to enforce a partial order on the sequence of cities to be visited in a tour. The presence of precedence constraints within the ATSP framework is encountered quite often in practice. Examples include: disassembly optimization (see Sarin et al. [62]), and scheduling of wafers/ ICs on automated testing equipments in a semiconductor manufacturing facility (see Chen and Hsia [17]); among others. Our flow-based ATSP formulation can very conveniently capture these precedence constraints. We also present computational results to depict the tightness of our precedence-constrained asymmetric traveling salesman problem (PCATSP) formulations. We, then, apply our formulations to the hot strip rolling scheduling problem, which involves the processing of hot steel slabs, in a pre-specified precedence order, on one or more rollers. The single-roller hot strip rolling scheduling problem can be directly formulated as a PCATSP. We also consider the multiple-roller hot strip rolling scheduling problem. This gives rise to the multiple-asymmetric traveling salesman problem (mATSP). Not many formulations have been presented in the literature for the mATSP, and there are none for the mATSP formulations involving a precedence order among the cities to be visited by the salesmen, which is the case for the multiple-roller hot strip rolling scheduling problem. To begin with, we develop new formulations for the mATSP and show the validity of our formulations, and present computational results to depict their tightness. Then, we extend these mATSP formulations to include a pre-specified, special type of precedence order in which to process the slabs, and designate the resulting formulations as the restricted precedence-constrained multiple-asymmetric traveling salesman problem (rPCmATSP) formulations. We directly formulate the multiple-roller hot strip rolling scheduling problem as a rPCmATSP. Furthermore, we consider the hot strip rolling scheduling problem with slab selection in which not all slabs need to be processed. We model the single-roller hot strip rolling scheduling problem with slab selection as a multiple-asymmetric traveling salesman problem with exactly two traveling salesmen. Similarly, the multiple-roller hot strip rolling scheduling problem with slab selection is modeled as a multiple-asymmetric traveling salesman problem with (m+1) traveling salesmen. A series of computational experiments are conducted to exhibit the effectiveness of our formulations for the solution of hot strip rolling scheduling problems. Furthermore, we develop two mixed-integer programming algorithms to solve our formulations. These are based on Benders΄ decomposition [13] and are designated Benders΄ decomposition and Modified Benders΄ methods. In concert with a special type of precedence order presented in the hot strip rolling scheduling problems, we further introduce an adjustable density ratio of the associated precedence network and we use randomly generated test problems to study the effect of various density ratios in solving these scheduling problems. Our experimentation shows the efficacy of our methods over CPLEX. Finally, we present a compact formulation for the job shop scheduling problem, designated as JSCD (job shop conjunctive-disjunctive) formulation, which is an extension of our ATSP formulations. We use two test problems given in Muth and Thompson [53] to demonstrate the optimal schedule and the lower bound values obtained by solving the LP relaxations of our formulations. However, we observe that the lower bound values obtained by solving the LP relaxations of all variations of our JSCD formulation equal to the maximum total processing time among the jobs in the problem. / Ph. D.

This dissertation develops efficient solution techniques for general and problem-specific applications within nonconvex optimization, exploiting the constructs of the Reformulation-Linearization Technique (RLT). We begin by developing a technique to enhance general problems in nonconvex optimization through the use of a new class of RLT cuts, called semidefinite cuts. While these cuts are valid for any general problem for which RLT is applicable, we demonstrate their effectiveness in optimizing a nonconvex quadratic objective function over a simplex. Computational results indicate that on average, the semidefinite cuts have reduced the number of nodes in the branch-and-bound tree by a factor of 37.6, while decreasing solution time by a factor of 3.4. The semidefinite cuts have also led to a significant reduction in the optimality gap at termination, in some cases producing optimal solutions for problems that could not be solved using RLT alone. We then narrow our focus to the class of mixed-integer programming (MIP) problems, and develop a modification of Benders' decomposition method using concepts from RLT and lift-and-project cuts. This method is particularly motivated by the class of two-stage stochastic programs with integer recourse. The key idea is to design an RLT or lift-and-project cutting plane scheme for solving the subproblems where the cuts generated have right-hand sides that are functions of the first-stage variables. An illustrative example is provided to elucidate the proposed approach. The focus is on developing a first comprehensive finitely convergent extension of Benders' methodology for problems having 0-1 mixed-integer subproblems. We next address a specific challenging MIP application known as the facility layout problem, and we significantly improve its formulation through outer-linearization techniques and concepts from disjunctive programming. The enhancements produce a substantial increase in the accuracy of the layout produced, while at the same time, providing a dramatic reduction in computational effort. Overall, the maximum error in department size was reduced from about 6% to nearly zero, while solution time decreased by a factor of 110. Previously unsolved test problems from the literature that had defied even approximate solution methods have been solved to exact optimality using our proposed approach. / Ph. D.

A main thrust of this thesis is to develop and explore linearization-based numeric-analytic integration techniques in the context of stochastically driven nonlinear oscillators of relevance in structural dynamics. Unfortunately, unlike the case of deterministic oscillators, available numerical or numeric-analytic integration schemes for stochastically driven oscillators, often modelled through stochastic differential equations (SDE-s), have significantly poorer numerical accuracy. These schemes are generally derived through stochastic Taylor expansions and the limited accuracy results from difficulties in evaluating the multiple stochastic integrals. We propose a few higher-order methods based on the stochastic version of transversal linearization and another method of linearizing the nonlinear drift field based on a Girsanov change of measures. When these schemes are implemented within a Monte Carlo framework for computing the response statistics, one typically needs repeated simulations over a large ensemble. The statistical error due to the finiteness of the ensemble (of size N, say)is of order 1/√N, which implies a rather slow convergence as N→∞. Given the prohibitively large computational cost as N increases, a variance reduction strategy that enables computing accurate response statistics for small N is considered useful. This leads us to propose a weak variance reduction strategy. Finally, we use the explicit derivative-free linearization techniques for state and parameter estimations for structural systems using the extended Kalman filter (EKF). A two-stage version of the EKF (2-EKF) is also proposed so as to account for errors due to linearization and unmodelled dynamics. In Chapter 2, we develop higher order locally transversal linearization (LTL) techniques for strong and weak solutions of stochastically driven nonlinear oscillators. For developing the higher-order methods, we expand the non-linear drift and multiplicative diffusion fields based on backward Euler and Newmark expansions while simultaneously satisfying the original vector field at the forward time instant where we intend to find the discretized solution. Since the non-linear vector fields are conditioned on the solution we wish to determine, the methods are implicit. We also report explicit versions of such linearization schemes via simple modifications. Local error estimates are provided for weak solutions. Weak linearized solutions enable faster computation vis-à-vis their strong counterparts. In Chapter 3, we propose another weak linearization method for non-linear oscillators under stochastic excitations based on Girsanov transformation of measures. Here, the non-linear drift vector is appropriately linearized such that the resulting SDE is analytically solvable. In order to account for the error in replacing of non-linear drift terms, the linearized solutions are multiplied by scalar weighting function. The weighting function is the solution of a scalar SDE(i.e.,Radon-Nikodym derivative). Apart from numerically illustrating the method through applications to non-linear oscillators, we also use the Girsanov transformation of measures to correct the truncation errors in lower order discretizations. In order to achieve efficiency in the computation of response statistics via Monte Carlo simulation, we propose in Chapter 4 a weak variance reduction strategy such that the ensemble size is significantly reduced without seriously affecting the accuracy of the predicted expectations of any smooth function of the response vector. The basis of the variance reduction strategy is to appropriately augment the governing system equations and then weakly replace the associated stochastic forcing functions through variance-reduced functions. In the process, the additional computational cost due to system augmentation is generally far less besides the accrued advantages due to a drastically reduced ensemble size. The variance reduction scheme is illustrated through applications to several non-linear oscillators, including a 3-DOF system. Finally, in Chapter 5, we exploit the explicit forms of the LTL techniques for state and parameters estimations of non-linear oscillators of engineering interest using a novel derivative-free EKF and a 2-EKF. In the derivative-free EKF, we use one-term, Euler and Newmark replacements for linearizations of the non-linear drift terms. In the 2-EKF, we use bias terms to account for errors due to lower order linearization and unmodelled dynamics in the mathematical model. Numerical studies establish the relative advantages of EKF-DLL as well as 2-EKF over the conventional forms of EKF. The thesis is concluded in Chapter 6 with an overall summary of the contributions made and suggestions for future research.

This thesis essentially deals with the development and numerical explorations of a few improved Monte Carlo filters for nonlinear dynamical systems with a view to estimating the associated states and parameters (i.e. the hidden states appearing in the system or process model) based on the available noisy partial observations. The hidden states are characterized, subject to modelling errors, by the weak solutions of the process model, which is typically in the form of a system of stochastic ordinary differential equations (SDEs). The unknown system parameters, when included as pseudo-states within the process model, are made to evolve as Wiener processes. The observations may also be modelled by a set of measurement SDEs or, when collected at discrete time instants, their temporally discretized maps. The proposed Monte Carlo filters aim at achieving robustness (i.e. insensitivity to variations in the noise parameters) and higher accuracy in the estimates whilst retaining the important feature of applicability to large dimensional nonlinear filtering problems. The thesis begins with a brief review of the literature in Chapter 1. The first development, reported in Chapter 2, is that of a nearly exact, semi-analytical, weak and explicit linearization scheme called Girsanov Corrected Linearization Method (GCLM) for nonlinear mechanical oscillators under additive stochastic excitations. At the heart of the linearization is a temporally localized rejection sampling strategy that, combined with a resampling scheme, enables selecting from and appropriately modifying an ensemble of locally linearized trajectories whilst weakly applying the Girsanov correction (the Radon- Nikodym derivative) for the linearization errors. Through their numeric implementations for a few workhorse nonlinear oscillators, the proposed variants of the scheme are shown to exhibit significantly higher numerical accuracy over a much larger range of the time step size than is possible with the local drift-linearization schemes on their own. The above scheme for linearization correction is exploited and extended in Chapter 3, wherein novel variations within a particle filtering algorithm are proposed to weakly correct for the linearization or integration errors that occur while numerically propagating the process dynamics. Specifically, the correction for linearization, provided by the likelihood or the Radon-Nikodym derivative, is incorporated in two steps. Once the likelihood, an exponential martingale, is split into a product of two factors, correction owing to the first factor is implemented via rejection sampling in the first step. The second factor, being directly computable, is accounted for via two schemes, one employing resampling and the other, a gain-weighted innovation term added to the drift field of the process SDE thereby overcoming excessive sample dispersion by resampling. The proposed strategies, employed as add-ons to existing particle filters, the bootstrap and auxiliary SIR filters in this work, are found to non-trivially improve the convergence and accuracy of the estimates and also yield reduced mean square errors of such estimates visà-vis those obtained through the parent filtering schemes. In Chapter 4, we explore the possibility of unscented transformation on Gaussian random variables, as employed within a scaled Gaussian sum stochastic filter, as a means of applying the nonlinear stochastic filtering theory to higher dimensional system identification problems. As an additional strategy to reconcile the evolving process dynamics with the observation history, the proposed filtering scheme also modifies the process model via the incorporation of gain-weighted innovation terms. The reported numerical work on the identification of dynamic models of dimension up to 100 is indicative of the potential of the proposed filter in realizing the stated aim of successfully treating relatively larger dimensional filtering problems. We propose in Chapter 5 an iterated gain-based particle filter that is consistent with the form of the nonlinear filtering (Kushner-Stratonovich) equation in our attempt to treat larger dimensional filtering problems with enhanced estimation accuracy. A crucial aspect of the proposed filtering set-up is that it retains the simplicity of implementation of the ensemble Kalman filter (EnKF). The numerical results obtained via EnKF-like simulations with or without a reduced-rank unscented transformation also indicate substantively improved filter convergence. The final contribution, reported in Chapter 6, is an iterative, gain-based filter bank incorporating an artificial diffusion parameter and may be viewed as an extension of the iterative filter in Chapter 5. While the filter bank helps in exploring the phase space of the state variables better, the iterative strategy based on the artificial diffusion parameter, which is lowered to zero over successive iterations, helps improve the mixing property of the associated iterative update kernels and these are aspects that gather importance for highly nonlinear filtering problems, including those involving significant initial mismatch of the process states and the measured ones. Numerical evidence of remarkably enhanced filter performance is exemplified by target tracking and structural health assessment applications. The thesis is finally wound up in Chapter 7 by summarizing these developments and briefly outlining the future research directions

The objective of this research work is to investigate, design and measurement of a digital predistortion linearizer that is able to compensate the dynamic nonlinear distortion of a High Power Amplifier (PA). The effectiveness of the proposed baseband predistorter (PD) on the performance of a WLAN OFDM transmitter utilizing a nonlinear PA with memory effect is observed and discussed. For this purpose, a 10W Class-A/B power amplifier with a gain of 22 dB, operated over the 3.5 GHz frequency band was designed and implemented. The proposed baseband PD is independent of the operating RF frequency and can be used in multiband applications. Its operation is based on the Hammerstein system, taking into account PA memory effect compensation, and demonstrates a noticeable improvement compared to memoryless predistorters. Different types of modelling procedures and linearizers were introduced and investigated, in which accurate behavioural models of Radio Frequency (RF) PAs exhibiting linear and nonlinear memory effects were presented and considered, based on the Wiener approach employing a linear parametric estimation technique. Three new linear methods of parameter estimation were investigated, with the aim of reducing the complexity of the required filtering process in linear memory compensation. Moreover, an improved wiener model is represented to include the nonlinear memory effect in the system. The validity of the PA modelling approaches and predistortion techniques for compensation of nonlinearities of a PA were verified by several tests and measurements. The approaches presented, based on the Wiener system, have the capacity to deal with the existing trade-off between accuracy and convergence speed compared to more computationally complex behavioural modelling algorithms considering memory effects, such as those based on Volterra series and Neural Networks. In addition, nonlinear and linear crosstalks introduced by the power amplifier nonlinear behaviour and antennas mutual coupling due to the compact size of a MIMO OFDM transmitter have been investigated.

Les travaux présentés dans ce mémoire de thèse portent sur la linéarisation large bande d'amplificateurs de puissance par prédistorsion analogique. Ce travail vise à réduire la pollution spectrale provoquée par leur comportement non-linéaire lors d'une transmission satellite. Ce travail de thèse débute par une présentation des amplificateurs de puissance utilisés dans les émetteurs, en exposant les conséquences de leur comportement non-linéaire sur la qualité du signal. Pour pallier à cela, les techniques de linéarisation couramment utilisées ont été recensées, en mettant l'accent sur leurs avantages et inconvénients. C'est sur la base de cet état de l'art qu'une structure de prédistorsion analogique a pu être identifiée. Il s'agit d'une structure en réflexion à base de diodes Schottky, dont une partie de ce mémoire est consacrée à l'analyse de leur comportement non-linéaire. Appuyée par des résultats de simulations et des mesures effectuées sur maquettes, cette analyse nous a conduit à la mise en œuvre de la structure en réflexion dans le cadre de la linéarisation d'un amplificateur à tube à onde progressive (ATOP) en bande Ku. Nos travaux se sont ensuite tournés vers une nouvelle structure plus innovante, basée sur la mise en cascade de deux circuits de prédistorsion. La structure proposée bénéficie d'une configuration plus flexible et plus précise que la précédente, ce qui nous a permis d'obtenir de meilleurs résultats en matière d'amélioration de la linéarité. La dernière partie de ce travail de thèse est dédiée à l'approche expérimentale de deux méthodes numériques de prédistorsion en bande de base. L'intérêt de cette approche repose sur l'évaluation expérimentale de l'amélioration possible de la linéarité de l'ATOP et la comparaison avec les résultats obtenus par prédistorsion analogique. / The research reported in this PhD Thesis is focused on power amplifier wideband linearization by analog predistortion. This work aims to reduce the spectral regrowth due to their nonlinear response over the satellite transmission. This dissertation starts with a presentation of power amplifiers used in transmitters. Through it, we expose their nonlinearity effects on the signal quality. To overcome those effects, the lattest linearization methods were reviewed, highlighting their strengths and weaknesses. Based on this state of art, an analog predistortion structure was identified. It relates to a reflective structure made up of Schottky diodes, of which a part of this thesis is devoted to the analysis of its nonlinear behavior. Drawn on simulations and measurements, this analysis led us to the implementation of the reflective structure for the purpose of a traveling wave tube amplifier linearization over the Ku band. Our work was then directed towards to a new more innovative structure built on two predistortion circuits wired in series. This new structure gets a more flexible and accurate configuration compared to the previous one and allowed us to obtain better results regarding linearity improvement. The last part of this thesis work is dedicated to an experimental approach of two base band digital predistortion methods. The aim of this approach rests on the achievable enhancement of TWTA linearity and the comparison between the results obtained with the analog predistortion.

Les véhicules aériens sans pilote (UAV), souvent appelés drones, trouvent de nombreuses applications dans la vie. Les applications de drones nécessitent plusieurs indicateurs de performance essentiels tels que la couverture, la force du signal, la latence et la mobilité dans des scénarios. Par conséquent, l'utilisation des communications sans fil dans les drones est essentielle pour répondre à toutes les exigences. En raison des connexions au haut débit entre les drones et les utilisateurs pour transférer des données de haut volume à haute résolution, les dernières générations sans fil, comme la norme LTE, sont privilégiées. Il est évident que l'intégration de blocs de radiofréquence (RF) est essentielle pour construire un système sur puce et réduire la taille des drones. Dans ce contexte, cette thèse vise à développer un amplificateur de puissance (PA) innovant avec haute performance reconfigurable entièrement intégré qui adresse les différents besoins imposés par le standard LTE à utiliser dans les applications des UAV. Le PA entièrement intégré en CMOS 65 nm a pour objectif de fournir une puissance de sortie élevée et résoudre le compromis entre la linéarité et l’efficacité. Un transformateur à quatre enroulements est implémenté pour configurer le fonctionnement en multi modes du PA. La technique « segmented bias » permet au PA d’améliorer la linéarité. Le PA obtient non seulement des performances élevées en RF, mais démontre également un potentiel pour l'adopter dans la bande 5G inférieure. / Unmanned aerial vehicles (UAVs), often known as drones, have been finding numerous applications in life. Drones applications need several essential performance indicators such as coverage, signal strength, latency, and mobility under scenarios. Therefore, the use of wireless communications in drones is critical to address all requirements. Because of high-speed connections between drones and users to transfer high-resolution high-volume data, latest wireless generations, namely the LTE standard, are privileged. It is straightforward that the integration of RF blocks is essential to build a system-on-chip and shrink the size of drones. To answer the above question, this thesis aims to develop a fully integrated reconfigurable high-performance innovated PA that supports 4G LTE standard to be used in UAVs’ applications. The fully integrated 65-nm CMOS power amplifier (PA) provides a watt-level output power, addresses the linearity/efficiency trade-off. A four-winding transformer is implemented to configure the multi-mode operation of the PA. The “segmented bias” technique allows the PA to increase the linearity. The PA not only obtains high radiofrequency performances but also demonstrates a potential to adopt it design in the lower 5G band.

Nesta dissertação, um tipo diferente de pêndulo invertido controlado por rodas de reação é apresentado. Sua principal diferença está em seu ponto de articulação, que é constituído por uma junta esférica que permite com que o pêndulo gire em torno de seus três eixos. Além disso, três rodas de reação são utilizadas para seu controle e estabilização. Primeiramente, um modelo do sistema é obtido a partir das equação de Euler-Lagrange, das leis de Newton e das leis de Kirchhoff. Em seguida, uma lei de controle que assegura a estabilização assintótica do sistema em um grande domínio é proposta. Por fim, simulações são realizadas para validar o controlador projetado. Esse sistema possui diversas características interessantes, tanto do ponto de vista teórico como do ponto de vista de pesquisa. Do ponto de vista teórico, o sistema é nãolinear e suas entradas são fortemente acopladas, o que torna particularmente adequado para o processo de projeto e implementação de diversas técnicas de estabilização. Do ponto de vista de pesquisa, são consideradas duas técnicas de controle não linear: linearização padrão e linearização exata. Para que o sistema seja robusto e não desperdice energia, essas duas leis de controle diferentes são comutadas para a obtencão de um número suficiente de domínio de estabilidade. / In this dissertation, a different kind of the reaction wheel pendulum is presented. The main difference is that its articulation point consists of a ball joint that allows the pendulum to rotate around its three axes. Furthermore, three reaction wheels are used for its control and stabilization. First, a model of the system is obtained from Euler-Lagrange equations, Newton laws and Kirchhoff laws. After that, a control law that assure asymptotic stabilization of the system in a large domain is proposed. Finally, simulations are performed to validate the designed controller. This system has several interesting features, both from a theoretical standpoint as from a research standpoint. From a theoretical standpoint, the system is nonlinear and its inputs are tightly coupled, making it particularly suitable for the design and implementation process of various stabilization techniques. From a research standpoint, two non-linear control techniques are considered: standard linearization and exact linearization. For the system to be robust and do not waste energy, these two different control laws are switched for obtaining a sufficiently large domain of stability.

Cette thèse porte sur la commande non linéaire des systèmes mécaniques sous-actionnés, ces systèmes possédant moins d'actionneur que de degrés de liberté. La dynamique interne de ces systèmes est souvent instable ce qui les rend difficiles à commander et requiert des méthodes de commande spécifiques. La contribution de cette thèse est la proposition de deux approches de commandes originales dont le but est la génération de cycle limites stables sur toutes les coordonnées du système mécanique sous-actionné. La première approche de commande est basée sur la linéarisation partielle par retour d'état et l'optimisation de trajectoires de référence. La seconde approche est basée sur les travaux récents sur la commande sans modèle, une technique de commande qui permet de contrôler un système sans avoir besoin de modèle mathématique préalable de sa dynamique. Ces deux approches de commande sont appliquées à un système mécanique sous-actionné particulier: le pendule inversé stabilisé par roue d'inertie. Plusieurs scénarios sont proposés, à la fois en simulation numérique et en temps-réel sur une plate-forme expérimentale. Les résultats obtenus attestent de la capacité des contrôleurs proposés à stabiliser le système autour de cycles limites stables en dépit de la présence de perturbations externes. / This thesis is focused on non linear control of underactuated mechanical systems, thoses systems with less actuators than degrees of freedom. The internal dynamics of such system is often unstable making them particulary difficult to control. Thus specific care must be taken when designing controlers for such systems. The main contribution of this thesis is the design of two new control schemes for stable limit cycles generation on all coordinates of underactuated mechanical systems. First control approach is based on partial feedback linearization and reference trajectories optimization. Second approach is based on recent work on model free control,a control scheme which doesn't require prior mathematicalmodel of the controlled system dynamics. The proposed approaches are applied to an inertiawheel inverted pendulumtestbed. Several experimental scenarios are proposed, both in numerical simulation and in realtime implementation. Obtained results demonstrate the ability of both controllers to stabilize the system around stable limit cycles and to reject external disturbances.

Für zufällige dynamische Systeme mit stetiger Zeit existieren zwei wichtige Klassen von Generatoren: Zum einen stationäre zufällige ifferentialgleichungen, i.e. gewöhnliche Differentialgleichungen, die von einem stationärer zufälligen Vektorfeld getrieben werden, und zum anderen stochastische Stratonovichdifferentialgleichungen mit weißem Rauschen. Während die erste Klasse sich gut in den ergodentheoretischen Rahmen der Theorie der zufälligen dynamischen Systeme einfügt, widersetzte sich die zweite Klasse lange Zeit der dynamischen Untersuchung aufgrund des "Konflikts zwischen Ergodentheorie und stochastischer Analysis". In dieser Arbeit wird gezeigt, daß beide Klassen von zufälligen dynamischen Systemen nicht wesentlich verschieden sind, genauer: Zu jeder stochastischen Stratonovichdifferentialgleichung mit weißem Rauschen (unter den üblichen Regularitätsforderungen an die Vektorfelder, die die Existenz von Flüssen garantieren) existiert eine stationäre zufällige Differentialgleichung derart, daß die erzeugten zufälligen dynamischen Systeme konjugiert sind. Als Anwendung wird eine Version des lokalen Linearisierungssatzes von Hartman/Grobman für stochastische Stratonovichdifferentialgleichungen bewiesen. / For continuous time random dynamical systems there exist two important classes of generators: on the one hand stationary random differential quations, i.e. ordinary differential equations driven by a stationary random vector field, and on the other hand stochastic Stratonovich differential equations with white noise. While the first class fits well into the framework of the theory of random dynamical systems, the second class resisted for a long time the dynamical investigation due to the "conflict between ergodic theory and stochastic analysis". The main result of this thesis is that both classes of random dynamical systems are not essentially distinct, more precisely: For each stochastic Stratonovich differential equation with white noise (under usual regularity assumptions) there exists a stationary random differential equation such that the corresponding random dynamical systems are conjugate. As an application a version of the local Hartman/Grobman theorem for stochastic differential equations is proved.