Expressing an observer in preferred coordinates by transforming an injective immersion into a surjective diffeomorphism

When designing observers for nonlinear systems, the dynamics of the given system and of the designed observer are usually not expressed in the same coordinates or even have states evolving in different spaces. In general, the function, denoted $\tau$ (or its inverse, denoted $\tau^*$) giving one state in terms of the other is not explicitly known and this creates implementation issues. We propose to round this problem by expressing the observer dynamics in the the same coordinates as the given system. But this may impose to add extra coordinates, problem that we call augmentation. This may also impose to modify the domain or the range of the augmented" $\tau$ or $\tau^*$, problem that we call extension. We show that the augmentation problem can be solved partly by a continuous completion of a free family of vectors and that the extension problem can be solved by a function extension making the image of the extended function the whole space. We also show how augmentation and extension can be done without modifying the observer dynamics and therefore with maintaining convergence.Several examples illustrate our results.Comment: Submitted for publication in SIAM Journal of Control and Optimizatio

Spectral balancing techniques application to CDMA and UWB signaling

International audienceThis paper presents techniques for generating orthogonal bases of signals with jointly optimized spectra, in the sense that they are made as close as possible. To this end, we propose new criteria, the minimization of which leads to signals with close energy inside a set of prescribed subbands. We present a first algorithm that performs this spectrum balancing and that we apply to Walsh-Hadamard codes. As an example, we build balanced Walsh codes in CDMA comunications. Alternatively, we propose another way to perform spectrum balancing in two steps and that makes use of joint diagonalization techniques. As an example application, we show how balancing of Prolate Spheroidal Wave Functions (PSWFs) can be used to build orthogonal families of brief impulses with flat spectra that are of potential interest for Ultra Wide Band (UWB) communications

Growing syntax: The development of a DP in North Germanic

Grammaticalization as standardly conceived is a change whereby an item develops from a lexical to a grammatical or functional meaning, or from being less to more grammatical. In this article we show that this can only be part of the story; for a full account we need to understand the syntactic structures into which grammaticalizing elements fit and how they too develop. To achieve this end we consider in detail the history of definiteness marking within the noun phrase in North Germanic, and in particular in Faroese. We show how this change requires us to distinguish between projecting and nonprojecting categories, and how a category can emerge over time and only subsequently develop into a head with its own associated functional projection. The necessary structure, rather than being intrinsic to an aprioristic universal grammar, grows over time as part of the grammaticalization process. We suggest that this in turn argues for a parallel correspondence theory of grammar such as the one adopted here, lexical-functional grammar, in which dif-ferent dimensions of linguistic structure can change at different rates

On diffeomorphism extension

We state and prove a result concerning the fact that a diffeomorphism can be " extended " in such a way that its image is R^

Assessment of physical exposure to musculoskeletal risks in collaborative robotics using dynamic simulation

Many industrial tasks cannot be executed by a robot alone. A way to help workers in order to decrease the risk of musculoskeletal disorders is to assist them with a collaborative robot. Yet assessing its usefulness to the worker remains costly because it usually requires a prototype. We propose a dynamic simulation framework to model the performing of a task jointly by a virtual manikin and a robot. It allows to measure physical quantities in order to perform an ergonomic assessment of the robot. Experiments are carried out on two different robots. The results show that the proposed simulation framework is helpful for designing collaborative robots. Further work includes enhancing the simulation realism and validation on a real robot

Interaction eau-roche-CO2 en contexte de fuite contrôlée de CO2: apport du monitoring géochimique et isotopique lors d'un cas réel d'injection de CO2

Cette étude montre, dans un cas réel d'injection de CO2, comment une approche multi- isotopique (B, Li, S, O, Sr) combinée aux données chimiques permet (i) de tracer indirectement la réactivité et présence du CO2, (ii) de contraindre et comprendre précisément les interactions eau-roche-CO2 et les réponses isotopiques. L'originalité de ce travail consiste à utiliser des outils isotopiques développés dans les géosciences pour les appliquer à ce contexte particulier. L'idée majeure est d'utiliser ces outils comme traceurs des interactions eau-roche-CO2 afin de détecter toute anomalie de fuites de CO2 non décelables par les autres moyens de monitoring existant

De l'intérêt de la texture pour la segmentation du visage

National audienceDans cet article, nous évaluons l'intérêt d'utiliser la texture pour segmenter une image de visage en zones Peau, Fond et Cheveux. Tout d'abord, nous présentons des techniques existantes de détection de peau, nous justifions le choix a priori de la texture, ensuite nous construisons des indices caractéristiques locaux à partir de données apprises sur l'image. Nous définissons un modèle de classification s'appuyant conjointement sur les données couleur et texture. Nous montrons l'apport de cette approche en présentant quelques résultats prometteurs obtenus sur des images naturelles complexes