WorldCat Identities

Trélat, Emmanuel

Overview
Works: 61 works in 82 publications in 2 languages and 311 library holdings
Roles: Author, Other, Opponent, Thesis advisor, htt, Interviewee, Editor
Publication Timeline
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Most widely held works by Emmanuel Trélat
Contrôle optimal : théorie & applications by Emmanuel Trélat( Book )

5 editions published between 2005 and 2008 in French and held by 146 WorldCat member libraries worldwide

Mécanique céleste et contrôle des véhicules spatiaux by Bernard Bonnard( Book )

12 editions published between 2005 and 2006 in 3 languages and held by 78 WorldCat member libraries worldwide

Le but de ce livre est de présenter les développements récents du contrôle géométrique orienté vers la commande (notamment optimale) des véhicules spatiaux. Il est principalement destiné aux étudiants de 3e cycle et aux chercheurs, et son contenu a servi de base à une série de cours de contrôle et d'automatique enseignés à des étudiants de 3e cycle. Il s'appuie sur des projets de recherche avec l'ESTEC et le CNES, sur le contrôle d'attitude d'un satellite, le problème de transfert orbital en temps minimal, et le problème de rentrée atmosphérique d'une navette spatiale. Une première partie est consacrée à une introduction à la mécanique céleste, et la seconde au contrôle des véhicules spatiaux. Un dernier chapitre concerne les méthodes numériques dites indirectes, développées à partir des études des auteurs : méthode de tir et algorithmes de calcul des points conjugués
Mécanique céleste et contrôle des véhicules spatiaux by Bernard Bonnard( Book )

2 editions published between 2005 and 2006 in French and held by 8 WorldCat member libraries worldwide

Active particles by N Bellomo( Book )

1 edition published in 2017 in English and held by 5 WorldCat member libraries worldwide

"This volume collects ten surveys on the modeling, simulation, and applications of active particles using methods ranging from mathematical kinetic theory to nonequilibrium statistical mechanics. The contributing authors are leading experts working in this challenging field, and each of their chapters provides a review of the most recent results in their areas and looks ahead to future research directions. The approaches to studying active matter are presented here from many different perspectives, such as individual-based models, evolutionary games, Brownian motion, and continuum theories, as well as various combinations of these. Applications covered include biological network formation and network theory; opinion formation and social systems; control theory of sparse systems; theory and applications of mean field games; population learning; dynamics of flocking systems; vehicular traffic flow; and stochastic particles and mean field approximation. Mathematicians and other members of the scientific community interested in active matter and its many applications will find this volume to be a timely, authoritative, and valuable resource."--Publisher's website
Etude asymptotique et transcendance de la fonction valeur en contrôle optimal. Catégorie log-exp en géométrie sous-riemannienne dans le cas Martinet by Emmanuel Trélat( )

2 editions published in 2000 in French and held by 4 WorldCat member libraries worldwide

Le thème central de cette thèse est l'étude et le rôle des trajectoires anormales en théorie du contrôle optimal. On étudie l'optimalité des anormales pour des systèmes affines mono-entrée avec contrainte sur le contrôle, d'abord pour le problème du temps optimal, puis pour un cout quelconque a temps final fixe ou non. On étend cette théorie aux systèmes sous-riemanniens de rang 2. Ces résultats montrent que, sous des conditions générales, une trajectoire anormale est isolée parmi toutes les solutions du système ayant les mêmes conditions aux limites, et donc localement optimale, jusqu'à un premier point dit conjugue que l'on peut caractériser. On s'intéresse ensuite au comportement asymptotique et a la régularité de la fonction valeur associée a un système affine analytique avec un cout quadratique. On montre que, en l'absence de trajectoire anormale minimisante, la fonction valeur est sous-analytique et continue. S'il existe une anormale minimisante, on sort de la catégorie sous-analytique en général. La présence d'une anormale minimisante est responsable de la non-propreté de l'application exponentielle, ce qui provoque un phénomène de tangence des ensembles de niveaux de la fonction valeur par rapport à la direction anormale. Dans le cas affine mono-entrée ou sous-riemannien de rang 2, on décrit précisément ce contact, et on en déduit une partition de la sphère sous-riemannienne au voisinage de l'anormale en deux secteurs appelés secteur l et secteur l 2. La question de transcendance est étudiée dans le cas sous-riemannien de martinet ou la distribution est = Ker (dz y 2/2dx). On montre que pour une métrique générale graduée d'ordre 0 les sphères de petit rayon ne sont pas sous-analytiques. Dans le cas général intégrable les sphères de martinet appartiennent à la catégorie log-exp
Etude de la dynamique autour des points de Lagrange by Grégory Archambeau( Book )

2 editions published in 2008 in French and held by 3 WorldCat member libraries worldwide

The circular restricted three-body problem and its equilibrium, Lagrange points, are really interesting study issues for the scientific community with a view for space applications. Lagrange points offer a fix configuration relatively to two celestial bodies very interesting for observation mission, and trajectories of this problem offer a diminution of energetic constraints. After a recall of the mathematical definitions and a presentation of the main results of a qualitative study of this model, properties of the trajectories around Lagrange points are exploited to compute several missions in the Sun-Earth and Earth-Moon systems. A study of particular periodic orbits, Eight Lissajous orbits, is provided. A third-order approximation of these periodic orbits is obtained by a Lindstedt Poincaré's method. A Lyapunov exponents computation reveals a stability property of these orbits and their invariant manifolds around L1(Earth-Moon) which could be used to visit a large lunar strip at low cost
Commande optimale des systèmes de complémentarité linéaires by Alexandre Vieira( )

1 edition published in 2018 in English and held by 2 WorldCat member libraries worldwide

This thesis focuses on the optimal control of Linear Complementarity Systems (LCS). LCS are dynamical systems defined through Differential Algebraic Equations (DAE), where one of the variable is defined by a Linear Complementarity Problem.These systems can be found in the modeling of various phenomena, as Nash equilibria, hybrid dynamical systems or modeling of electrical circuits. Properties of the solution to these DAE essentially depend on properties that the matrix D in the complementarity must meet. These complementarity constraints induce two different challenges. First, the analysis of these dynamical systems often use state of the art tools, and their study still has some unansweredquestions. Second, the optimal control of these systems causes troubles due to on one hand the presence of the state in the constraints, on the other hand the violation of Constraint Qualifications, that are a recurring hypothesis for optimisation problems.The research presented in this manuscript focuses on the optimal control of these systems. We mainly focus on the quadratic optimal control problem (minimisation of a quadratic functional involving the state and the control), and the minimal time control. The results present two different aspects: first, we start with an analytical approach in order to find necessary conditions of optimality (if possible, these conditions are proved to be sufficient); secondly, a numerical approach is tackled, with the aim of getting precise results with a reduced computational time
Variational Methods for Tomographic Reconstruction with Few Views by Maïtine Bergounioux( )

1 edition published in 2018 in English and held by 2 WorldCat member libraries worldwide

Two-Sided Space-Time $$L^1$$ L1 Polynomial Approximation of Hypographs Within Polynomial Optimal Control by Bruno Després( )

1 edition published in 2018 in English and held by 2 WorldCat member libraries worldwide

Optimal Observation of the One-dimensional Wave Equation by Yannick Privat( )

1 edition published in 2013 in English and held by 2 WorldCat member libraries worldwide

Integral and measure-turnpike properties for infinite-dimensional optimal control systems by Emmanuel Trélat( )

1 edition published in 2018 in English and held by 2 WorldCat member libraries worldwide

Contrôle optimal et métriques de Clairaut-Liouville avec applications by Lionel Jassionnesse( Book )

2 editions published in 2014 in French and held by 2 WorldCat member libraries worldwide

The work of this thesis is about the study of the conjugate and cut loci of 2D riemannian or almost-riemannian metrics. We take the point of view of optimal control to apply the Pontryagin Maximum Principle in the purpose of characterize the extremals of the problem considered.We use geometric, numerical and integrability methods to study some Liouville and Clairaut-Liouville metrics on the sphere. In the degenerate case of revolution, the study of the ellipsoid uses geometric methods to fix the cut locus and the nature of the conjugate locus in the oblate and prolate cases. In the general case, extremals will have two distinct type of comportment which correspond to those observed in the revolution case, and are separated by those which pass by umbilical points. The numerical methods are used to find quickly the Jacobi's Last Geometric Statement : the cut locus is a segment and the conjugate locus has exactly four cusps.The study of an almost-riemannian metric comes from a quantum control problem in which the aim is to transfer in a minimal time the state of one spin through an Ising chain of three spins. After reduction, we obtain a metric with a second first integral so it can be written in the Liouville normal form, which leads us to the equations of geodesics. Outside the particular case of Grushin, of which the caustic is described, we use numerical methods to study the conjugate locus and the cut locus in the general case
Geometric optimal control and applications to aerospace by Jiamin Zhu( )

1 edition published in 2017 in English and held by 2 WorldCat member libraries worldwide

Spectral shape optimization for the Neumann traces of the Dirichlet-Laplacian eigenfunctions by Yannick Privat( )

1 edition published in 2019 in English and held by 2 WorldCat member libraries worldwide

Modélisation mathématique et numérique des comportements sociaux en milieu incertain. Application à l'épidémiologie by Laetitia Laguzet( Book )

2 editions published in 2015 in English and held by 2 WorldCat member libraries worldwide

Cette thèse propose une étude mathématique des stratégies de vaccination.La partie I présente le cadre mathématique, notamment le modèle à compartiments Susceptible - Infected - Recovered.La partie II aborde les techniques mathématiques de type contrôle optimal employées afin de trouver une stratégie optimale de vaccination au niveau de la société. Ceci se fait en minimisant le coût de la société. Nous montrons que la fonction valeur associée peut avoir une régularité plus faible que celle attendue dans la littérature. Enfin, nous appliquons les résultats à la vaccination contre la coqueluche.La partie III présente un modèle où le coût est défini au niveau de l'individu. Nous reformulons le problème comme un équilibre de Nash et comparons le coût obtenu avec celui de la stratégie sociétale. Une application à la grippe A(H1N1) indique la présence de perceptions différentes liées à la vaccination.La partie IV propose une implémentation numérique directe des stratégies présentées
Minimal time spiking in various ChR2-controlled neuron models by Vincent Renault( )

1 edition published in 2017 in English and held by 2 WorldCat member libraries worldwide

Contrôle de systèmes hyperboliques par analyse Lyapunov by Pierre-Olivier Lamare( )

1 edition published in 2015 in English and held by 2 WorldCat member libraries worldwide

In this thesis we have considered different aspects for the control of hyperbolic systems.First, we have studied switched hyperbolic systems. They contain an interaction between a continuous and a discrete dynamics. Thus, the continuous dynamics may evolve in different modes: these modes are imposed by the discrete dynamics. The change in the mode may be controlled (in case of a closed-loop system), or may be uncontrolled (in case of an open-loop system). We have focused our interest on the former case. We procedeed with a Lyapunov analysis, and construct three switching rules. We have shown how to modify them to get robustness and ISS properties. We have shown their effectiveness with numerical tests.Then, we have considered the trajectory generation problem for 2x2 linear hyperbolic systems. We have solved it with backstepping. Then, we have considered the tracking problem with a Proportionnal-Integral controller. We have shown that it stabilizes the error system around the reference trajectory with a new non-diagonal Lyapunov function. The integral action has been shown to be able to reject in-domain, as well as boundary disturbances.Finally, we have considered numerical aspects for the Lyapunov analysis. The conditions for the stability and design of controllers by quadratic Lyapunov functions involve an infinity of matrix inequalities. We have shown how to reduce this complexity by polytopic embeddings of the constraints.Many obtained results have been illustrated by academic examples and physically relevant dynamical systems (as Shallow-Water equations and Aw-Rascle-Zhang equations)
Optimisation de trajectoires spatiales : vol d'un dernier étage de lanceur, nettoyage des débris spatiaux by Max Cerf( Book )

2 editions published in 2012 in English and held by 2 WorldCat member libraries worldwide

The work addresses two space trajectories optimization problems : the flight of a launcher upper stage and the collecting of space debris. For these two problems the goal is to develop resolution methods and softwares usable in an industrial framework. Flight of a launcher upper stage. For the problem of a launcher upper stage flight, two continuation approaches are envisioned from models simplifications. The first approach consists in solving the flat Earth problem with uniform gravity, then to come back to the round Earth problem through a double continuation on the gravity and on the earth curvature. The second approach consists in solving the impulsive problem, corresponding to an infinite thrust level, then to come back to the continuous thrust problem through a continuation on the thrust level. The goal is to define a solving procedure as automatic as possible for various instances of the real problem : launcher configuration, targeted orbit. Space debris collecting. The selection of the debris and the visiting order is a shortest path problem in a time-dependent valuated graph. A generic strategy reduces the optimal control problem to a nonlinear programming problem of finite dimension, which can be coupled to the path problem. A local linearization around an initial solution allows to set up a Branch and Bound algorithm. The reference solution is then updated with the linearized solution. Iterating on the linearization-resolution process from the pre-optimized initialization allows converging to the solution of the global problem
Contrôle géométrique et méthodes numériques : application au problème de montée d'un avion. by Damien Goubinat( )

1 edition published in 2017 in French and held by 1 WorldCat member library worldwide

Ce travail s'intéresse à la phase de montée d'un aéronef civil. Les trajectoires minimisant le temps de montée ainsi que que celles minimisant la consommation de carburant sont étudiées au travers du contrôle optimal géométrique. La dynamique associée à la phase de montée possède un phénomène dit de perturbation singulière. Ce phénomène, présent dans les systèmes multi-échelle, rend difficile la résolution numérique du problème de contrôle associé. La réduction desystème hamiltonien, permettant de s'affranchir de la difficulté numérique introduite par la perturbation singulière, est étudiée d'un point de vue théorique puis numérique. Dans un second temps, le système réduit est étudié géométriquement. L'utilisation des outils du contrôle géométrique combinée à celui des synthèses à temps court permet de déterminer des familles de trajectoires localement temps-optimales pour des temps courts. Cette étude est complétée par une étude des trajectoires temps-optimales en présence de contraintes d'état. D'un point de vue plus numérique, les méthodes directes et indirectes sont utilisées pour résoudre les différents problèmes. Une synthèse locale est alors réalisée en partant des familles de trajectoires déterminées pour des temps courts. Une étude des trajectoires minimisant la consommation de carburant est également réalisée
Une nouvelle méthode de décomposition polynomiale d'un front d'onde oculaire by Damien Gatinel( )

1 edition published in 2017 in French and held by 1 WorldCat member library worldwide

The eye vision defaults are analyzed and classified by studyingthe corresponding eye wavefront. After presenting the orthogonal basis, called the Zernike basis, that is currently used for the medical diagnosis, a new decomposition basis is built. It is based on the use of the space of polynomials of valuation greater or equal to L+1 (for L a natural integer). It allows to uniquely decompose a polynomial wavefront into the sum of a polynomial of low degree (lesser or equal to L) and a polynomial of high valuation (greater or equal to L +1). By choosing L = 2, a new decomposition, called D2V3, is obtained where the polynomial wavefront of high degree does not include terms of radial degree lesser or equal to 2. In particular, it allows to quantify perfectly the aberrations that can be corrected by eyeglasses or not. Various clinical examples clearly show the interest of this new basis compared to a diagnosis based on the Zernike decomposition
 
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Mécanique céleste et contrôle des véhicules spatiaux
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Active particles
Alternative Names
Emmanuel Trélat Frans wiskundige

Emmanuel Trélat fransk matematikar

Emmanuel Trélat fransk matematiker

Emmanuel Trélat französischer Mathematiker

Emmanuel Trélat French mathematician

Emmanuel Trélat matemàtic francès

Emmanuel Trélat matemático francés

Emmanuel Trélat matemáticu francés

Emmanuel Trelat matematikan francez

Emmanuel Trélat mathematician from France

Emmanuel Trélat mathématicien français

에마뉘엘 트렐라 프랑스 수학자

Languages
French (25)

English (15)