Gevrey solvability near the characteristic set for a class of planar complex vector fields of infinite type

We study the Gevrey solvability of a class of complex vector fields, defined on Omega(epsilon) = (-epsilon, epsilon) x S(1), given by L = partial derivative/partial derivative t + (a(x) + ib(x))partial derivative/partial derivative x, b not equivalent to 0, near the characteristic set Sigma = {0} x S(1). We show that the interplay between the order of vanishing of the functions a and b at x = 0 plays a role in the Gevrey solvability. (C) 2008 Elsevier Inc. All rights reserved.

Solvability near the characteristic set for a special class of complex vector fields

This work deals with the solvability near the characteristic set Sigma = {0} x S-1 of operators of the form L = partial derivative/partial derivative t+(x(n) a(x)+ ix(m) b(x))partial derivative/partial derivative x, b not equivalent to 0 and a(0) not equal 0, defined on Omega(epsilon) = (-epsilon, epsilon) x S-1, epsilon > 0, where a and b are real-valued smooth functions in (-epsilon, epsilon) and m >= 2n. It is shown that given f belonging to a subspace of finite codimension of C-infinity (Omega(epsilon)) there is a solution u is an element of L-infinity of the equation Lu = f in a neighborhood of Sigma; moreover, the L-infinity regularity is sharp.

Kinetics of the combustion of olive oil. A semi-global model

Support for this work was provided by PROMETEO/2009/043/FEDER of Generalitat Valenciana (Spain) and CTQ2008-05520 (Spanish MCI/research).

Semi-global techniques in image matching and change detection with applications to civil and environmental engineering.

This work of thesis wants to present a dissertation of the wide range of modern dense matching algorithms, which are spreading in different application and research fields, with a particular attention to the innovative “Semi-Global” matching techniques. The choice of develop a semi-global numerical code was justified by the need of getting insight on the variables and strategies that affect the algorithm performances with the primary objective of maximizing the method accuracy and efficiency, and the results level of completeness. The dissertation will consist in the metrological characterization of the proprietary implementation of the semi-global matching algorithm, evaluating the influence of several matching variables and functions implemented in the process and comparing the accuracy and completeness of different results (digital surface models, disparity maps and 2D displacement fields) obtained using our code and other commercial and open-source matching programs in a wide variety of application fields.

C(k)-solvability near the characteristic set for a class of planar complex vector fields of infinite type

This paper deals with semi-global C(k)-solvability of complex vector fields of the form L = partial derivative/partial derivative t + x(r) (a(x) + ib(x))partial derivative/partial derivative x, r >= 1, defined on Omega(epsilon) = (-epsilon, epsilon) x S(1), epsilon > 0, where a and b are C(infinity) real-valued functions in (-epsilon, epsilon). It is shown that the interplay between the order of vanishing of the functions a and b at x = 0 influences the C(k)-solvability at Sigma = {0} x S(1). When r = 1, it is permitted that the functions a and b of L depend on the x and t variables, that is, L = partial derivative/partial derivative t + x(a(x, t) + ib(x, t))partial derivative/partial derivative x, where (x, t) is an element of Omega(epsilon).

Nonexistence of global solutions for a class of complex vector fields on two-torus

The goal of this paper is study the global solvability of a class of complex vector fields of the special form L = partial derivative/partial derivative t + (a + ib)(x)partial derivative/partial derivative x, a, b epsilon C(infinity) (S(1) ; R), defined on two-torus T(2) congruent to R(2)/2 pi Z(2). The kernel of transpose operator L is described and the solvability near the characteristic set is also studied. (c) 2008 Elsevier Inc. All rights reserved.

Solvability in the large for a class of complex vector fields on the cylinder

This work deals with global solvability of a class of complex vector fields of the form L = partial derivative/partial derivative t + (a(x, t)+ ib(x, t))partial derivative/partial derivative x, where a and b are real-valued C-infinity functions, defined on the cylinder Omega = R x S-1. Relatively compact (Sussmann) orbits are allowed. The connection with Malgrange's notion of L-convexity for supports is investigated. (C) 2011 Elsevier Masson SAS. All rights reserved.

A perturbation approach to the stabilization of nonlinear cascade systems with time-delay

The effect of bounded input perturbations on the stability of nonlinear globally asymptotically stable delay differential equations is analyzed. We investigate under which conditions global stability is preserved and if not, whether semi-global stabilization is possible by controlling the size or shape of the perturbation. These results are used to study the stabilization of partially linear cascade systems with partial state feedback.

Multi-view 3D reconstruction using virtual cameras

Ce mémoire s'intéresse à la reconstruction d'un modèle 3D à partir de plusieurs images. Le modèle 3D est élaboré avec une représentation hiérarchique de voxels sous la forme d'un octree. Un cube englobant le modèle 3D est calculé à partir de la position des caméras. Ce cube contient les voxels et il définit la position de caméras virtuelles. Le modèle 3D est initialisé par une enveloppe convexe basée sur la couleur uniforme du fond des images. Cette enveloppe permet de creuser la périphérie du modèle 3D. Ensuite un coût pondéré est calculé pour évaluer la qualité de chaque voxel à faire partie de la surface de l'objet. Ce coût tient compte de la similarité des pixels provenant de chaque image associée à la caméra virtuelle. Finalement et pour chacune des caméras virtuelles, une surface est calculée basée sur le coût en utilisant la méthode de SGM. La méthode SGM tient compte du voisinage lors du calcul de profondeur et ce mémoire présente une variation de la méthode pour tenir compte des voxels précédemment exclus du modèle par l'étape d'initialisation ou de creusage par une autre surface. Par la suite, les surfaces calculées sont utilisées pour creuser et finaliser le modèle 3D. Ce mémoire présente une combinaison innovante d'étapes permettant de créer un modèle 3D basé sur un ensemble d'images existant ou encore sur une suite d'images capturées en série pouvant mener à la création d'un modèle 3D en temps réel.

Globally solvable systems of complex vector fields

We consider a class of involutive systems of n smooth vector fields on the n + 1 dimensional torus. We obtain a complete characterization for the global solvability of this class in terms of Liouville forms and of the connectedness of all sublevel and superlevel sets of the primitive of a certain 1-form in the minimal covering space.

Nonlinear Observers for Sensorless Control of Permanent Magnet Synchronous Motors

In this thesis, the industrial application of control a Permanent Magnet Synchronous Motor in a sensorless configuration has been faced, and in particular the task of estimating the unknown “parameters” necessary for the application of standard motor control algorithms. In literature several techniques have been proposed to cope with this task, among them the technique based on model-based nonlinear observer has been followed. The hypothesis of neglecting the mechanical dynamics from the motor model has been applied due to practical and physical considerations, therefore only the electromagnetic dynamics has been used for the observers design. First observer proposed is based on stator currents and Stator Flux dynamics described in a generic rotating reference frame. Stator flux dynamics are known apart their initial conditions which are estimated, with speed that is also unknown, through the use of the Adaptive Theory. The second observer proposed is based on stator currents and Rotor Flux dynamics described in a self-aligning reference frame. Rotor flux dynamics are described in the stationary reference frame exploiting polar coordinates instead of classical Cartesian coordinates, by means the estimation of amplitude and speed of the rotor flux. The stability proof is derived in a Singular Perturbation Framework, which allows for the use the current estimation errors as a measure of rotor flux estimation errors. The stability properties has been derived using a specific theory for systems with time scale separation, which guarantees a semi-global practical stability. For the two observer ideal simulations and real simulations have been performed to prove the effectiveness of the observers proposed, real simulations on which the effects of the Inverter nonlinearities have been introduced, showing the already known problems of the model-based observers for low speed applications.

Metodologie di apprendimento automatico applicate alla generazione di dati 3D

Il framework in oggetto, è un ambiente ideato con lo scopo di applicare tecniche di Machine Learning (in particolare le Random Forest) alle funzionalità dell'algoritmo di stereo matching SGM (Semi Global Matching), al fine di incrementarne l'accuratezza in versione standard. Scopo della presente tesi è quello di modificare alcune impostazioni di tale framework rendendolo un ambiente che meglio si adatti alla direzionalità delle scanline (introducendo finestre di supporto rettangolari e ortogonali e il training di foreste separate in base alla singola scanline) e ampliarne le funzionalità tramite l'aggiunta di alcune nuove feature, quali la distanza dal più vicino edge direzionale e la distintività calcolate sulle immagini Left della stereo pair e gli edge direzionali sulle mappe di disparità. Il fine ultimo sarà quello di eseguire svariati test sui dataset Middlebury 2014 e KITTI e raccogliere dati che descrivano l'andamento in positivo o negativo delle modifiche effettuate.

Vision-Based Tracking, Odometry and Control for UAV Autonomy

El principal objetivo de este trabajo es proporcionar una solución en tiempo real basada en visión estéreo o monocular precisa y robusta para que un vehículo aéreo no tripulado (UAV) sea autónomo en varios tipos de aplicaciones UAV, especialmente en entornos abarrotados sin señal GPS. Este trabajo principalmente consiste en tres temas de investigación de UAV basados en técnicas de visión por computador: (I) visual tracking, proporciona soluciones efectivas para localizar visualmente objetos de interés estáticos o en movimiento durante el tiempo que dura el vuelo del UAV mediante una aproximación adaptativa online y una estrategia de múltiple resolución, de este modo superamos los problemas generados por las diferentes situaciones desafiantes, tales como cambios significativos de aspecto, iluminación del entorno variante, fondo del tracking embarullado, oclusión parcial o total de objetos, variaciones rápidas de posición y vibraciones mecánicas a bordo. La solución ha sido utilizada en aterrizajes autónomos, inspección de plataformas mar adentro o tracking de aviones en pleno vuelo para su detección y evasión; (II) odometría visual: proporciona una solución eficiente al UAV para estimar la posición con 6 grados de libertad (6D) usando únicamente la entrada de una cámara estéreo a bordo del UAV. Un método Semi-Global Blocking Matching (SGBM) eficiente basado en una estrategia grueso-a-fino ha sido implementada para una rápida y profunda estimación del plano. Además, la solución toma provecho eficazmente de la información 2D y 3D para estimar la posición 6D, resolviendo de esta manera la limitación de un punto de referencia fijo en la cámara estéreo. Una robusta aproximación volumétrica de mapping basada en el framework Octomap ha sido utilizada para reconstruir entornos cerrados y al aire libre bastante abarrotados en 3D con memoria y errores correlacionados espacialmente o temporalmente; (III) visual control, ofrece soluciones de control prácticas para la navegación de un UAV usando Fuzzy Logic Controller (FLC) con la estimación visual. Y el framework de Cross-Entropy Optimization (CEO) ha sido usado para optimizar el factor de escala y la función de pertenencia en FLC. Todas las soluciones basadas en visión en este trabajo han sido probadas en test reales. Y los conjuntos de datos de imágenes reales grabados en estos test o disponibles para la comunidad pública han sido utilizados para evaluar el rendimiento de estas soluciones basadas en visión con ground truth. Además, las soluciones de visión presentadas han sido comparadas con algoritmos de visión del estado del arte. Los test reales y los resultados de evaluación muestran que las soluciones basadas en visión proporcionadas han obtenido rendimientos en tiempo real precisos y robustos, o han alcanzado un mejor rendimiento que aquellos algoritmos del estado del arte. La estimación basada en visión ha ganado un rol muy importante en controlar un UAV típico para alcanzar autonomía en aplicaciones UAV. ABSTRACT The main objective of this dissertation is providing real-time accurate robust monocular or stereo vision-based solution for Unmanned Aerial Vehicle (UAV) to achieve the autonomy in various types of UAV applications, especially in GPS-denied dynamic cluttered environments. This dissertation mainly consists of three UAV research topics based on computer vision technique: (I) visual tracking, it supplys effective solutions to visually locate interesting static or moving object over time during UAV flight with on-line adaptivity approach and multiple-resolution strategy, thereby overcoming the problems generated by the different challenging situations, such as significant appearance change, variant surrounding illumination, cluttered tracking background, partial or full object occlusion, rapid pose variation and onboard mechanical vibration. The solutions have been utilized in autonomous landing, offshore floating platform inspection and midair aircraft tracking for sense-and-avoid; (II) visual odometry: it provides the efficient solution for UAV to estimate the 6 Degree-of-freedom (6D) pose using only the input of stereo camera onboard UAV. An efficient Semi-Global Blocking Matching (SGBM) method based on a coarse-to-fine strategy has been implemented for fast depth map estimation. In addition, the solution effectively takes advantage of both 2D and 3D information to estimate the 6D pose, thereby solving the limitation of a fixed small baseline in the stereo camera. A robust volumetric occupancy mapping approach based on the Octomap framework has been utilized to reconstruct indoor and outdoor large-scale cluttered environments in 3D with less temporally or spatially correlated measurement errors and memory; (III) visual control, it offers practical control solutions to navigate UAV using Fuzzy Logic Controller (FLC) with the visual estimation. And the Cross-Entropy Optimization (CEO) framework has been used to optimize the scaling factor and the membership function in FLC. All the vision-based solutions in this dissertation have been tested in real tests. And the real image datasets recorded from these tests or available from public community have been utilized to evaluate the performance of these vision-based solutions with ground truth. Additionally, the presented vision solutions have compared with the state-of-art visual algorithms. Real tests and evaluation results show that the provided vision-based solutions have obtained real-time accurate robust performances, or gained better performance than those state-of-art visual algorithms. The vision-based estimation has played a critically important role for controlling a typical UAV to achieve autonomy in the UAV application.