Papers by Emmanuel Trélat
On the role of abnormal minimizers in sub-riemannian geometry
Annales de la faculté des sciences de Toulouse Mathématiques, 2001
ABSTRACT Consider a sub-Riemannian geometry $(U,D,g)$ where $U$ is a neighborhood at 0 in $\R^n,$... more ABSTRACT Consider a sub-Riemannian geometry $(U,D,g)$ where $U$ is a neighborhood at 0 in $\R^n,$ $D$ is a rank-2 smooth $(C^\infty $ or $C^\omega)$ distribution and $g$ is a smooth metric on $D$. The objective of this article is to explain the role of abnormal minimizers in SR-geometry. It is based on the analysis of the Martinet SR-geometry.
Commande mixte H 2 /H ∞ . Une approche par la stratégie de Stackelberg
Journal Européen des Systèmes Automatisés, 2006
... {Marc.Jungers,Hisham.Abou-Kandil}@satie.ens-cachan.fr ** Université Paris-Sud, Laboratoire de... more ... {Marc.Jungers,Hisham.Abou-Kandil}@satie.ens-cachan.fr ** Université Paris-Sud, Laboratoire de Mathématique, UMR 8628, Bât. ... x = Ax + B∞w∞ + B2w2 + Bu = f(x, w∞,w2,u), z∞ = C∞x + D∞w∞ + D∞uu, z2 = C2x + D2uu, y = Cx. [1] Système que l'on pourra noter ...
Sparse stabilization and optimal control of the Cucker-Smale model
Mathematical Control and Related Fields, 2013
ABSTRACT
In a previous work, Prieur, Trelat (2006), we derived a result of semi-global minimal time robust... more In a previous work, Prieur, Trelat (2006), we derived a result of semi-global minimal time robust stabilization for analytic control systems with controls entering linearly, by means of a hybrid state feedback law, under the main assumption of the absence of minimal time singular trajectories. In this paper, we investigate the Martinet case, which is a model case in IR3,
Quantum ergodicity and quantum limits for sub-Riemannian Laplacians
Séminaire Laurent Schwartz — EDP et applications, 2014
Mécanique céleste et contrôle de systemes spatiaux
... HAL : hal-00086408, version 1. Fiche détaillée, Récupérer au format: BibTeX -. EndNote -. TEI... more ... HAL : hal-00086408, version 1. Fiche détaillée, Récupérer au format: BibTeX -. EndNote -. TEI -. RefWorks -. Mécanique céleste et contrôle de systèmes spatiaux (2006) 276 pages. Mécanique céleste et contrôle de systèmes spatiaux. Bernard Bonnard 2 , Ludovic Faubourg 2 ...
Optimality of singular trajectories and asymptotics of accessibility sets under generic assumptions
... dET (u)= 0. Definition 1.3. L et ube a singu lar control on[0,T] . Th e sub sp ace Im dET (u)... more ... dET (u)= 0. Definition 1.3. L et ube a singu lar control on[0,T] . Th e sub sp ace Im dET (u) is called t hefirstPontryagin' s cone along u(or along xu) . ... h e control .It comes from t h efact t h at singular reference controlbelongs to t h e interiorof t h e domain ofconstraints. 7 Page 8. \ ...
Let M be a smooth manifold and D m , m 2, be the set of rank m distributions on M endowed with th... more Let M be a smooth manifold and D m , m 2, be the set of rank m distributions on M endowed with the Whitney C ∞ topology. We show the existence of an open set O m dense in D m , so that, every nontrivial singular curve of a distribution D of O m is of minimal order and of corank one. In particular, for m 3, every distribution of O m does not admit nontrivial rigid curves. As a consequence, for generic sub-Riemannian structures of rank greater than or equal to three, there does not exist nontrivial minimizing singular curves.
Optimal control theory and some applications to aerospace problems
European Congress of Mathematics Kraków, 2 – 7 July, 2012, 2013
Bifurcations of Reachable Sets Near an Abnormal Direction and Consequences
Lecture Notes in Control and Information Sciences, 2002
Global subanalytic solutions of Hamilton–Jacobi type equations
Annales de l'Institut Henri Poincare (C) Non Linear Analysis, 2006
Asymptotics of accessibility sets along an abnormal trajectory
ESAIM: Control, Optimisation and Calculus of Variations, 2001
Comptes Rendus de l'Académie des Sciences - Series I - Mathematics, 2001
Consider the sub-Riemannian Martinet structure (M, ∆, g) where M = R 3 , ∆ = Ker(dz − y 2 2 dx) a... more Consider the sub-Riemannian Martinet structure (M, ∆, g) where M = R 3 , ∆ = Ker(dz − y 2 2 dx) and g is the general gradated metric of order 0: g = (1 + αy) 2 dx 2 + (1 + βx + γy) 2 dy 2 . We prove that if α = 0 then the sub-Riemannian spheres S(0, r) with small radii are not subanalytic. 2001 Académie des sciences/Éditions scientifiques et médicales Elsevier SAS
Solutions sous-analytiques globales de certaines équations d'Hamilton–Jacobi
Comptes Rendus Mathematique, 2003
... 3 Page 4. Emmanuel Trélat et soit : & 1¥ yg zW { 8 3 5& s ¦87@9 ! ) 5& & ¨ Al... more ... 3 Page 4. Emmanuel Trélat et soit : & 1¥ yg zW { 8 3 5& s ¦87@9 ! ) 5& & ¨ Alors est continue sur ¡ et est l'unique solution de viscosité du probl`eme de Dirichlet : ¦ % @(7Q % && @¤ 14 3 T)V ¡ ¡ £¢ 7 {©1¥¤ ¨ Si de plus le syst`eme 1WV D " D © D ...
Control and stabilization of steady-states in a finite-length ferromagnetic nanowire
ESAIM: Control, Optimisation and Calculus of Variations, 2015
Optimal Shape and Location of Sensors for Parabolic Equations with Random Initial Data
Archive for Rational Mechanics and Analysis, 2014
Complexity and regularity of maximal energy domains for the wave equation with fixed initial data
Discrete and Continuous Dynamical Systems, 2015
On the best observation of wave and Schrödinger equations in quantum ergodic billiards
Journées Équations aux dérivées partielles, 2012
Journal of the Institute of Mathematics of Jussieu, 2015
In this paper, we define and study strong right-invariant sub-Riemannian structures on the group ... more In this paper, we define and study strong right-invariant sub-Riemannian structures on the group of diffeomorphisms of a manifold with bounded geometry. We establish some approximate and exact reachability properties, and we derive the Hamiltonian geodesic equations for such structures. We provide examples of normal and of abnormal geodesics in that infinitedimensional context.
Optimal shape and location of sensors or actuators in PDE models
2014 American Control Conference, 2014
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Papers by Emmanuel Trélat