Precise navigation of autonomous underwater vehicles (AUV) is one of the most important challenges in the realization of distributed and cooperative algorithms for marine applications. We investigate an underwater navigation technology that enables an AUV to compute its trajectory in the presence of unknown currents in real time and simultaneously estimate the currents, using range or distance measurements from a single known location. This approach is potentially useful for small AUVs which have severe volume and power constraints. The main contribution of this work is observability analysis of the proposed navigation system using novel approaches towards uniform observability of linear time-varying (LTV) systems. We utilize the notion of limiting systems in order to address uniform observability of LTV systems. Uniform observability of an LTV system can be studied by assessing finite time observability of its limiting systems. A new definition of uniform observability over a finite interval is introduced in order to address existence of an observer whose estimation error is bounded by an exponentially decaying function on the finite interval. We also show that for a class of LTV systems, uniform observability of a lower dimensional subsystem derived from an LTV system is sufficient for uniform observability of the LTV system. / Ph. D.

Ce manuscrit porte sur la synthèse d'observateurs grand gain pour des systèmes non linéaires à sorties échantillonnées et retardées. Trois contributions sont proposées à la lecture de ce manuscrit. La première contribution, pour une classe de systèmes Multi-entrées / Multi-sorties uniformément observables et dont les sorties sont regroupées en un seul bloc, met en jeu le problème du processus d'acquisition des mesures de sorties (continues, échantillonnées, retardées ou non) et propose un cadre commun pour l'ensemble des cas possibles. La deuxième contribution propose un observateur grand gain filtré sur cette même classe de systèmes dans l'optique de réduire la sensibilité au bruit de mesure, dans le cas où la sortie est continue puis dans le cas où cette dernière est échantillonnée. La dernière contribution vise à étendre la synthèse grand gain standard pour une large classe de systèmes Multi-entrées / Multi-sorties uniformément observables dont les mesures des sorties sont continues. Pour chacune de ces contributions, il a été montré que l'erreur d'observation de chacun des observateurs proposés converge exponentiellement vers zéro en l'absence d'incertitudes sur le système. Toutes ces contributions ont été illustrées par différents exemples issus de plusieurs domaines d'étude. / This manuscript deals with the synthesis of high gain observers for nonlinear systems with sampled and delayed outputs. Three contributions are proposed for consideration in this manuscript. The first contribution, for a class of Multi-input / Multi-output systems whose outputs are grouped into a single block, involves the problem of the acquisition process of output measurements (continuous, sampled, delayed or not) and proposes a common framework for all possible cases. The second contribution proposes a filtered high gain observer on this same class of systems in order to reduce the sensitivity to measurement noise, in the case where the output is continuous and then in the case where the latter is sampled. The last contribution aims to extend the standard high gain synthesis for a large class of uniformly observable Multi-input / Multi-output systems with continuous output measurements. For each of these contributions, it has been shown that the observation error of each of the proposed observers converges exponentially towards zero in the absence of uncertainties in the system. All these contributions have been illustrated through several examples from different fields of study.

This dissertation addresses attitude control and inertial navigation of autonomous underwater vehicles (AUVs). We present theoretical justification for using simplified models, derive system identification algorithms, and verify our results through extensive field trials. Although this research focuses on small AUVs with limited instrumentation, the results are useful for underwater vehicles of any size. For attitude control of aircraft systems, second-order equivalent pitch-axis models are common and extensively studied. However, similar analysis has not been performed for the pitch-axis motion of underwater vehicles. In this dissertation, we study the utility and the limitations of second-order approximate models for AUVs. We seek to improve the flight performance and shorten the time required to re-design a control algorithm when the shape, mass-distribution, and/or net buoyancy of an AUV/payload configuration changes. In comparison to commonly implemented AUV attitude controllers, which neglect roll motion and address pitch and yaw dynamics separately, we derive a novel linear time-varying model that explicitly displays the coupling between pitch and yaw motion due to nonzero roll angle and/or roll rate. The model facilitates an Hâ control design approach that explicitly addresses robustness against those coupling terms and significantly reduces the effect of pitch and yaw coupling. To improve AUV navigation, we investigate algorithms for calibrating a triaxial gyroscope using angular orientation measurements and formally define AUV trajectories that are persistently exciting and for which the calibration coefficients are uniformly observable. To improve AUV guidance, we propose a near real-time ocean current identification method that estimates a non-uniform flow-field using only sparse flow measurements. / Ph. D.

Many control algorithms for ABS systems have been proposed in the literature since the introduction of this equipment by Bosch in 1978. In general, one can divide these control algorithms into two different types: those based on a regulation logic with wheel acceleration thresholds that are used by most commercial ABS systems; and those based on wheel slip control that are preferred in the large majority of academic algorithms. Each approach has its pros and cons [Shida 2010]. Oversimplifying, one can say that the strength of the first ones is their robustness; while that of the latter ones their short braking distances (on dry grounds) and their absence of limit cycles. At the midpoint of this industry/academy dichotomy, based on the concept of extended braking stiffness (XBS), a quite different class of ABS control strategies has been proposed by several researchers (see, e.g., [Sugai 1999] and [Ono 2003]). This concept combines the advantages from both the industrial and academic approaches. Nevertheless, since the slope of the tyre characteristic is not directly measurable, it introduces the question of real-time XBS estimation. The first part of this thesis is devoted to the study of this estimation problem and to a generalization of the proposed technique to a larger class of systems. From the technological point of view, the design of ABS control systems is highly dependent on the ABS system characteristics and actuator performance. Current ABS control algorithms on passenger cars, for instance the Bosch ABS algorithm, are based on heuristics that are deeply associated to the hydraulic nature of the actuator. An interesting observation is that they seem to work properly only in the presence of a specific delay coming from the hydraulic actuation [Gerard 2012]. For brake systems that have different delays compared to those of hydraulic actuators, like electric in-wheel motors (with a smaller delay) or pneumatic trailer brakes (with a bigger delay), they might be no longer suitable [Miller 2013]. Therefore, adapting standard ABS algorithms to other advanced actuators becomes an imperative goal in the automobile industry. This goal can be reached by the compensation of the delays induced by actuators. The second part of this thesis is focused on this issue, and to the generalization of the proposed technique to a particular class of nonlinear systems. Throughout this thesis, we employ two different linearization techniques: the linearization of the error dynamics in the construction of model-based observers [Krener 1983] and the linearization based on restricted state feedback [Brockett 1979]. The former is one of the simplest ways to build an observer for dynamical systems with output and to analyze its convergence. The main idea is to transform the original nonlinear system via a coordinate change to a special form that admits an observer with a linear error dynamics and thus the observer gains can be easily computed to ensure the observer convergence. The latter is a classical method to control nonlinear systems by converting them into a controllable linear state equation via the cancellation of their nonlinearities. It is worth mentioning that existing results for observer design by error linearization in the literature are only applied to the case of regular time scalings ([Guay 2002] and [Respondek 2004]). The thesis shows how to extend them to the case of singular time scalings. Besides, the thesis combines the classical state feedback linearization with a new method for the input delay compensation to resolve the output tracking problem for restricted feedback linearizable systems with input delays.

Depuis l'introduction du premier système ABS par Bosch, en 1978, de nombreux algorithmes de commande pour les systèmes ABS ont été proposés dans la littérature. En général, ces algorithmes peuvent être divisés en deux catégories : ceux basés sur une logique de régulation déterminée par des seuils sur l'accélération angulaire des roues et ceux basés sur la régulation du taux de glissement. Chaque approche a ses avantages et ses inconvénients. D'une manière simplifiée, on peut dire que le point fort du premier type est sa robustesse ; tandis que ceux du deuxième type sont leur courte distance de freinage (sur les terrains secs) et leur absence de cycles limite. Au milieu de cette dichotomie industrielle/académique, en se basant sur un concept appelé extended braking stiffness (XBS), une classe complètement différente de stratégies de commande pour l'ABS a été proposée par certains chercheurs. Ce concept combine les avantages des deux approches. Néanmoins, puisque l’XBS n'est pas directement mesurable, elle introduit la question de son estimation en temps réel. La première partie de cette thèse est consacrée à l'étude de ce problème d'estimation et à une généralisation de la technique proposée à une plus grande classe de systèmes. D'un point de vue technologique, la conception des systèmes de contrôle pour l'ABS est fortement dépendante des caractéristiques physiques du système et des performances de l'actionneur. Les algorithmes de commande actuels pour l'ABS sur les véhicules, par exemple l'algorithme ABS de Bosch, sont basés sur des approches heuristiques qui sont profondément liées à la nature hydraulique de l'actionneur. Ils ne fonctionnent correctement qu'en présence d'un retard spécifique associé à la nature hydraulique de l'actionneur. Pour les systèmes de freinage qui ont un retard différent de ceux des actionneurs hydrauliques, comme les moteurs-roues électriques par exemple (un retard plus court) ou les freins pneumatiques des semi-remorques (un retard plus grand), ils ne sont plus appropriés et ont un fonctionnement déficient. Par conséquent, l'adaptation des algorithmes standards de l'ABS pour d'autres actionneurs avancés devient un objectif primordial dans l'industrie automobile. Cet objectif peut être atteint par la compensation des retards induits par les actionneurs. La deuxième partie de cette thèse se concentre sur cette question, et à la généralisation de la technique proposée à une classe particulière de systèmes non linéaires.Tout au long de cette thèse, nous utilisons deux techniques de linéarisation différentes : la linéarisation de la dynamique d'erreur dans la construction des observateurs basés sur des modèles et la linéarisation basée sur le retour d'état restreint. La première est l'une des façons les plus simples pour synthétiser un observateur pour des systèmes dynamiques avec sortie et pour analyser sa convergence. L'idée principale est de transformer le système non linéaire original via un changement de coordonnées en un système différemment formalisé, qui admette un observateur avec une dynamique d'erreur linéaire et les gains de l'observateur peuvent donc être facilement calculés pour en assurer la convergence. Cette dernière est une méthode classique pour commander des systèmes non linéaires en les convertissant en une équation d'état linéaire contrôlable via l'annulation de leurs non-linéarités. Il convient de mentionner que les résultats existants pour la synthèse des observateurs par la linéarisation de l'erreur dans la littérature ne sont appliqués que pour le cas des changements réguliers de l'échelle de temps. Cette thèse explique comment les étendre aux cas des changements singuliers de l'échelle de temps. Par ailleurs, la thèse combine la linéarisation classique par retour d'état avec une nouvelle méthode de compensation du retard de l'entrée pour résoudre le problème de suivi de la sortie pour des systèmes linéarisables par retour d'état restreint avec des retards de l'entrée. / Many control algorithms for ABS systems have been proposed in the literature since the introduction of this equipment by Bosch in 1978. In general, one can divide these control algorithms into two different types: those based on a regulation logic with wheel acceleration thresholds that are used by most commercial ABS systems; and those based on wheel slip control that are preferred in the large majority of academic algorithms. Each approach has its pros and cons [Shida 2010]. Oversimplifying, one can say that the strength of the first ones is their robustness; while that of the latter ones their short braking distances (on dry grounds) and their absence of limit cycles. At the midpoint of this industry/academy dichotomy, based on the concept of extended braking stiffness (XBS), a quite different class of ABS control strategies has been proposed by several researchers (see, e.g., [Sugai 1999] and [Ono 2003]). This concept combines the advantages from both the industrial and academic approaches. Nevertheless, since the slope of the tyre characteristic is not directly measurable, it introduces the question of real-time XBS estimation. The first part of this thesis is devoted to the study of this estimation problem and to a generalization of the proposed technique to a larger class of systems. From the technological point of view, the design of ABS control systems is highly dependent on the ABS system characteristics and actuator performance. Current ABS control algorithms on passenger cars, for instance the Bosch ABS algorithm, are based on heuristics that are deeply associated to the hydraulic nature of the actuator. An interesting observation is that they seem to work properly only in the presence of a specific delay coming from the hydraulic actuation [Gerard 2012]. For brake systems that have different delays compared to those of hydraulic actuators, like electric in-wheel motors (with a smaller delay) or pneumatic trailer brakes (with a bigger delay), they might be no longer suitable [Miller 2013]. Therefore, adapting standard ABS algorithms to other advanced actuators becomes an imperative goal in the automobile industry. This goal can be reached by the compensation of the delays induced by actuators. The second part of this thesis is focused on this issue, and to the generalization of the proposed technique to a particular class of nonlinear systems. Throughout this thesis, we employ two different linearization techniques: the linearization of the error dynamics in the construction of model-based observers [Krener 1983] and the linearization based on restricted state feedback [Brockett 1979]. The former is one of the simplest ways to build an observer for dynamical systems with output and to analyze its convergence. The main idea is to transform the original nonlinear system via a coordinate change to a special form that admits an observer with a linear error dynamics and thus the observer gains can be easily computed to ensure the observer convergence. The latter is a classical method to control nonlinear systems by converting them into a controllable linear state equation via the cancellation of their nonlinearities. It is worth mentioning that existing results for observer design by error linearization in the literature are only applied to the case of regular time scalings ([Guay 2002] and [Respondek 2004]). The thesis shows how to extend them to the case of singular time scalings. Besides, the thesis combines the classical state feedback linearization with a new method for the input delay compensation to resolve the output tracking problem for restricted feedback linearizable systems with input delays.