On the stabilization problem for nonholonomic distributions (2009)
Rifford, Ludovic, Trélat, Emmanuel
Let $M$ be a smooth connected and complete manifold of dimension $n$, and $\Delta$ be a smooth nonholonomic distribution of rank $m\leq n$ on $M$. We prove that, if there exists a smooth Riemannian...
On the stabilization problem for nonholonomic distributions (2009)
Rifford, Ludovic, Trélat, Emmanuel
Let $M$ be a smooth connected and complete manifold of dimension $n$, and $\Delta$ be a smooth nonholonomic distribution of rank $m\leq n$ on $M$. We prove that, if there exists a smooth Riemannian...
Dynamic practical stabilization of sampled-data linear distributed parameter systems (2009)
Tan, Ying, Trélat, Emmanuel, Chitour, Yacine, Nesic, Dragan
In this paper, dynamic practical stability properties of infinite-dimensional sampled-data systems are discussed. A family of finite-dimensional discrete-time controllers are first...
Dynamic practical stabilization of sampled-data linear distributed parameter systems (2009)
Tan, Ying, Trélat, Emmanuel, Chitour, Yacine, Nesic, Dragan
In this paper, dynamic practical stability properties of infinite-dimensional sampled-data systems are discussed. A family of finite-dimensional discrete-time controllers are first...
Smooth regularization of bang-bang optimal control problems (2009)
J. Silva, Cristiana, Trélat, Emmanuel
Consider the minimal time control problem for a single-input control-affine system $\dot{x}=X(x) + u_1 Y_1 (x)$ in $\R^{n}$, where the scalar control $u_1(\cdot)$ satisfies the constraint...
Smooth regularization of bang-bang optimal control problems (2009)
J. Silva, Cristiana, Trélat, Emmanuel
Consider the minimal time control problem for a single-input control-affine system $\dot{x}=X(x) + u_1 Y_1 (x)$ in $\R^{n}$, where the scalar control $u_1(\cdot)$ satisfies the constraint...
Dynamic practical stabilization of sampled-data linear distributed parameter systems (2009)
Tan, Ying, Trélat, Emmanuel, Chitour, Yacine, Nesic, Dragan
In this paper, dynamic practical stability properties of infinite-dimensional sampled-data systems are discussed. A family of finite-dimensional discrete-time controllers are first designed to...
Vazquez, Rafael, Trélat, Emmanuel, Coron, Jean-Michel
We consider the problem of generating and tracking a trajectory between two arbitrary parabolic profiles of a periodic 2D channel flow, which is linearly unstable for high Reynolds numbers. Also...
Vazquez, Rafael, Trélat, Emmanuel, Coron, Jean-Michel
We consider the problem of generating and tracking a trajectory between two arbitrary parabolic profiles of a periodic 2D channel flow, which is linearly unstable for high Reynolds numbers. Also...
Singular trajectories of control-affine systems (2008)
Chitour, Yacine, Jean, Frédéric, Trélat, Emmanuel
When applying methods of optimal control to motion planning or stabilization problems, some theoretical or numerical difficulties may arise, due to the presence of specific trajectories, namely,...
Singular trajectories of control-affine systems (2008)
Chitour, Yacine, Jean, Frédéric, Trélat, Emmanuel
When applying methods of optimal control to motion planning or stabilization problems, some theoretical or numerical difficulties may arise, due to the presence of specific trajectories, namely,...
Numerical study of optimal trajectories with singular arcs for space launcher problems (2008)
Martinon, Pierre, Bonnans, Frédéric, Laurent-Varin, Julien, Trélat, Emmanuel
The subject of this paper is the study of singular arcs (i.e. with a non maximal thrust) for a space launcher problem. We consider a flight to the GTO orbit for a heavy multi-stage launcher (Ariane 5...
Numerical study of optimal trajectories with singular arcs for space launcher problems (2008)
Martinon, Pierre, Bonnans, Frédéric, Laurent-Varin, Julien, Trélat, Emmanuel
The subject of this paper is the study of singular arcs (i.e. with a non maximal thrust) for a space launcher problem. We consider a flight to the GTO orbit for a heavy multi-stage launcher (Ariane 5...
A penalization approach for tomographic reconstruction of binary axially symmetric objects (2008)
Abraham, Romain, Bergounioux, Maïtine, Trélat, Emmanuel
We propose a variational method for tomographic reconstruction of blurred and noised binary images based on a penalization process of a minimization problem settled in the space of bounded variation...
A penalization approach for tomographic reconstruction of binary axially symmetric objects (2008)
Abraham, Romain, Bergounioux, Maïtine, Trélat, Emmanuel
We propose a variational method for tomographic reconstruction of blurred and noised binary images based on a penalization process of a minimization problem settled in the space of bounded variation...
Control of travelling walls in a ferromagnetic nanowire (2008)
Carbou, Gilles, Labbé, Stéphane, Trélat, Emmanuel
We address the problem of control of the magnetic moment in a ferromagnetic nanowire by means of a magnetic field. Based on theoretical results for the 1D Landau-Lifschitz equation, we show a robust...
Control of travelling walls in a ferromagnetic nanowire (2008)
Carbou, Gilles, Labbé, Stéphane, Trélat, Emmanuel
We address the problem of control of the magnetic moment in a ferromagnetic nanowire by means of a magnetic field. Based on theoretical results for the 1D Landau-Lifschitz equation, we show a robust...
Vazquez, Rafael, Trélat, Emmanuel, Coron, Jean-Michel
We consider the problem of generating and tracking a trajectory between two arbitrary parabolic profiles of a periodic 2D channel flow, which is linearly unstable for high Reynolds numbers. Also...
Vazquez, Rafael, Trélat, Emmanuel, Coron, Jean-Michel
We consider the problem of generating and tracking a trajectory between two arbitrary parabolic profiles of a periodic 2D channel flow, which is linearly unstable for high Reynolds numbers. Also...
Control of travelling walls in a ferromagnetic nanowire (2008)
Carbou, Gilles, Labbé, Stéphane, Trélat, Emmanuel
We investigate the problem of controlling the magnetic moment in a ferromagnetic nanowire submitted to an external magnetic field in the direction of the nanowire. The system is modeled with...
Singular arcs in the generalized Goddard’s Problem (2008)
Bonnans, Frédéric, Martinon, Pierre, Trélat, Emmanuel
We investigate variants of Goddard’s problems for nonvertical tra- jectories. The control is the thrust force, and the ob jective is to max imize a certain final cost, typically, the...
Nonlinear optimal control via occupation measures and LMI-relaxations (2008)
Lasserre, Jean-Bernard, Henrion, Didier, Prieur, Christophe, Trélat, Emmanuel
We consider the class of nonlinear optimal control problems (OCP) with polynomial data, i.e., the differential equation, state and control constraints and cost are all described by polynomials,...
Numerical study of optimal trajectories with singular arcs for an Ariane 5 launcher (2008)
Martinon, Pierre, Bonnans, Frédéric, Laurent-Varin, Julien, Trélat, Emmanuel
We consider a flight mission to the geostationary transfer orbit (GTO) for an Ariane 5 launcher, while maximizing the payload or, as a variant, minimizing the fuel consumption. We first...
Control of travelling walls in a ferromagnetic nanowire (2008)
Carbou, Gilles, Labbé, Stéphane, Trélat, Emmanuel
We investigate the problem of controlling the magnetic moment in a ferromagnetic nanowire submitted to an external magnetic field in the direction of the nanowire. The system is modeled with...
Singular arcs in the generalized Goddards Problem (2008)
Bonnans, Frédéric, Martinon, Pierre, Trélat, Emmanuel
We investigate variants of Goddards problems for nonvertical tra- jectories. The control is the thrust force, and the ob jective is to max imize a certain final cost, typically, the...
Nonlinear optimal control via occupation measures and LMI-relaxations (2008)
Lasserre, Jean-Bernard, Henrion, Didier, Prieur, Christophe, Trélat, Emmanuel
We consider the class of nonlinear optimal control problems (OCP) with polynomial data, i.e., the differential equation, state and control constraints and cost are all described by polynomials,...
Numerical study of optimal trajectories with singular arcs for an Ariane 5 launcher (2008)
Martinon, Pierre, Bonnans, Frédéric, Laurent-Varin, Julien, Trélat, Emmanuel
We consider a flight mission to the geostationary transfer orbit (GTO) for an Ariane 5 launcher, while maximizing the payload or, as a variant, minimizing the fuel consumption. We first...
Eight Lissajous orbits in the Earth-Moon system (2008)
Archambeau, Grégory, Augros, Philippe, Trélat, Emmanuel
Euler and Lagrange proved the existence of five equilibrium points in the circular restricted three-body problem. These equilibrium points are known as Lagrange points (Euler points or...
Eight Lissajous orbits in the Earth-Moon system (2008)
Archambeau, Grégory, Augros, Philippe, Trélat, Emmanuel
Euler and Lagrange proved the existence of five equilibrium points in the circular restricted three-body problem. These equilibrium points are known as Lagrange points (Euler points or...
Smooth control of nanowires by means of a magnetic field (2008)
Carbou, Gilles, Labbé, Stéphane, Trélat, Emmanuel
We address the problem of control of the magnetic moment in a ferromagnetic nanowire by means of a magnetic field. Based on theoretical results for the 1D Landau-Lifschitz equation, we show a robust...
Smooth control of nanowires by means of a magnetic field (2008)
Carbou, Gilles, Labbé, Stéphane, Trélat, Emmanuel
We address the problem of control of the magnetic moment in a ferromagnetic nanowire by means of a magnetic field. Based on theoretical results for the 1D Landau-Lifschitz equation, we show a robust...
A penalization approach for tomographic reconstruction of binary axially symmetric objects (2007)
Abraham, Romain, Bergounioux, Maïtine, Trélat, Emmanuel
We propose a variational method for tomographic reconstruction of blurred and noised binary images based on a penalization process of a minimization problem settled in the space of bounded variation...
A penalization approach for tomographic reconstruction of binary axially symmetric objects (2007)
Abraham, Romain, Bergounioux, Maïtine, Trélat, Emmanuel
We propose a variational method for tomographic reconstruction of blurred and noised binary images based on a penalization process of a minimization problem settled in the space of bounded variation...
Singular arcs in the generalized Goddard's Problem (2007)
Bonnans, Frédéric, Martinon, Pierre, Trélat, Emmanuel
We investigate variants of Goddard's problems for nonvertical trajectories. The control is the thrust force, and the objective is to maximize a certain final cost, typically, the final mass. In this...
Singular arcs in the generalized Goddard's Problem (2007)
Bonnans, Frédéric, Martinon, Pierre, Trélat, Emmanuel
We investigate variants of Goddard's problems for nonvertical trajectories. The control is the thrust force, and the objective is to maximize a certain final cost, typically, the final mass. In this...
Singular arcs in the generalized Goddard's Problem (2007)
Bonnans, Frédéric, Martinon, Pierre, Trélat, Emmanuel
We investigate variants of Goddard's problems for nonvertical trajectories. The control is the thrust force, and the objective is to maximize a certain final cost, typically, the final mass. In this...
Nonlinear optimal control via occupation measures and LMI-relaxations (2007)
Lasserre, Jean-Bernard, Henrion, Didier, Prieur, Christophe, Trélat, Emmanuel
We consider the class of nonlinear optimal control problems (OCP) with polynomial data, i.e., the differential equation, state and control con- straints and cost are all described by polynomials, and...
Nonlinear optimal control via occupation measures and LMI-relaxations (2007)
Lasserre, Jean-Bernard, Henrion, Didier, Prieur, Christophe, Trélat, Emmanuel
We consider the class of nonlinear optimal control problems (OCP) with polynomial data, i.e., the differential equation, state and control con- straints and cost are all described by polynomials, and...
Second order optimality conditions with applications (2007)
Bonnard, Bernard, Caillau, Jean-Baptiste, Trélat, Emmanuel
The aim of this article is to present the algorithm to compute the first conjugate point along a smooth extremal curve. Under generic assump- tions, the tra jectory ceases to be optimal at such a...
Second order optimality conditions in the smooth case and applications in optimal control (2007)
Bonnard, Bernard, Caillau, Jean-Baptiste, Trélat, Emmanuel
The aim of this article is to present algorithms to compute the first conjugate time along a smooth extremal curve, where the trajectory ceases to be optimal. It is based on recent theoretical...
Fast Tracking of Poiseuille Trajectories in Navier-Stokes 2D Channel Flow (2007)
Coron, Jean-Michel, Trélat, Emmanuel, Vazquez, Rafael
We consider the problem of generating and tracking a trajectory between two arbitrary parabolic profiles of a periodic 2D channel flow, which is linearly unstable for high Reynolds numbers. Also...
On two hybrid robust optimal stabilization problems (2007)
Prieur, Christophe, Trélat, Emmanuel
We report on some recent results obtained by the authors concerning robust hybrid stabilization of control systems. We stated a result of semi-global minimal time robust stabilization for analytic...
Nonlinear optimal control via occupation measures and LMI-relaxations (2007)
Lasserre, Jean-Bernard, Henrion, Didier, Prieur, Christophe, Trélat, Emmanuel
We consider the class of nonlinear optimal control problems (OCP) with polynomial data, i.e., the differential equation, state and control con- straints and cost are all described by polynomials, and...
Singular arcs in the generalized Goddard's Problem (2007)
Bonnans, Frédéric, Martinon, Pierre, Trélat, Emmanuel
We investigate variants of Goddard's problems for nonvertical trajectories. The control is the thrust force, and the objective is to maximize a certain final cost, typically, the final mass. In this...
Singular arcs in the generalized Goddard's Problem (2007)
Bonnans, Frédéric, Martinon, Pierre, Trélat, Emmanuel
We investigate variants of Goddard's problems for nonvertical trajectories. The control is the thrust force, and the objective is to maximize a certain final cost, typically, the final mass. In this...
Nonlinear optimal control via occupation measures and LMI-relaxations (2007)
Lasserre, Jean-Bernard, Henrion, Didier, Prieur, Christophe, Trélat, Emmanuel
We consider the class of nonlinear optimal control problems (OCP) with polynomial data, i.e., the differential equation, state and control con- straints and cost are all described by polynomials, and...
Second order optimality conditions with applications (2007)
Bonnard, Bernard, Caillau, Jean-Baptiste, Trélat, Emmanuel
The aim of this article is to present the algorithm to compute the first conjugate point along a smooth extremal curve. Under generic assump- tions, the tra jectory ceases to be optimal at such a...
On two hybrid robust optimal stabilization problems (2007)
Prieur, Christophe, Trélat, Emmanuel
We report on some recent results obtained by the authors concerning robust hybrid stabilization of control systems. We stated a result of semi-global minimal time robust stabilization for analytic...
Fast Tracking of Poiseuille Trajectories in Navier-Stokes 2D Channel Flow (2007)
Coron, Jean-Michel, Trélat, Emmanuel, Vazquez, Rafael
We consider the problem of generating and tracking a trajectory between two arbitrary parabolic profiles of a periodic 2D channel flow, which is linearly unstable for high Reynolds numbers. Also...
Second order optimality conditions in the smooth case and applications in optimal control (2007)
Bonnard, Bernard, Caillau, Jean-Baptiste, Trélat, Emmanuel
The aim of this article is to present algorithms to compute the first conjugate time along a smooth extremal curve, where the trajectory ceases to be optimal. It is based on recent theoretical...
On the stabilization problem for nonholonomic distributions (2006)
Rifford, Ludovic, Trélat, Emmanuel
Let $M$ be a smooth connected and complete manifold of dimension $n$, and $\Delta$ be a smooth nonholonomic distribution of rank $m\leq n$ on $M$. We prove that, if there exists a smooth Riemannian...
Second order optimality conditions with applications (2006)
Bonnard, Bernard, Caillau, Jean-Baptiste, Trélat, Emmanuel
The aim of this article is to present the algorithm to compute the first conjugate point along a smooth extremal curve. Under generic assump- tions, the tra jectory ceases to be optimal at such a...
Second order optimality conditions with applications (2006)
Bonnard, Bernard, Caillau, Jean-Baptiste, Trélat, Emmanuel
The aim of this article is to present the algorithm to compute the first conjugate point along a smooth extremal curve. Under generic assump- tions, the tra jectory ceases to be optimal at such a...
On the stabilization problem for nonholonomic distributions (2006)
Rifford, Ludovic, Trélat, Emmanuel
Let $M$ be a smooth connected and complete manifold of dimension $n$, and $\Delta$ be a smooth nonholonomic distribution of rank $m\leq n$ on $M$. We prove that, if there exists a smooth Riemannian...
On the stabilization problem for nonholonomic distributions (2006)
Rifford, Ludovic, Trélat, Emmanuel
Let $M$ be a smooth connected and complete manifold of dimension $n$, and $\Delta$ be a smooth nonholonomic distribution of rank $m\leq n$ on $M$. We prove that, if there exists a smooth Riemannian...
On the stabilization problem for nonholonomic distributions (2006)
Rifford, Ludovic, Trélat, Emmanuel
Let $M$ be a smooth connected and complete manifold of dimension $n$, and $\Delta$ be a smooth nonholonomic distribution of rank $m\leq n$ on $M$. We prove that, if there exists a smooth Riemannian...
On the stabilization problem for nonholonomic distributions (2006)
Rifford, Ludovic, Trélat, Emmanuel
Let $M$ be a smooth connected and complete manifold of dimension $n$, and $\Delta$ be a smooth nonholonomic distribution of rank $m\leq n$ on $M$. We prove that, if there exists a smooth Riemannian...
Generalization of the finite difference method in distributions spaces (2006)
Labbé, Stéphane, Trélat, Emmanuel
The aim of this article is to propose a generalization of the finite difference scheme suitable with solutions of Dirac distribution type. This type of solution is for example encountered in...
Generalization of the finite difference method in distributions spaces (2006)
Labbé, Stéphane, Trélat, Emmanuel
The aim of this article is to propose a generalization of the finite difference scheme suitable with solutions of Dirac distribution type. This type of solution is for example encountered in...
Control of travelling walls in a ferromagnetic nanowire (2006)
Carbou, Gilles, Labbé, Stéphane, Trélat, Emmanuel
We investigate the problem of controlling the magnetic moment in a ferromagnetic nanowire submitted to an external magnetic field in the direction of the nanowire. The system is modeled with the one...
Control of travelling walls in a ferromagnetic nanowire (2006)
Carbou, Gilles, Labbé, Stéphane, Trélat, Emmanuel
We investigate the problem of controlling the magnetic moment in a ferromagnetic nanowire submitted to an external magnetic field in the direction of the nanowire. The system is modeled with the one...
Control of travelling walls in a ferromagnetic nanowire (2006)
Carbou, Gilles, Labbé, Stéphane, Trélat, Emmanuel
We investigate the problem of controlling the magnetic moment in a ferromagnetic nanowire submitted to an external magnetic field in the direction of the nanowire. The system is modeled with the one...
Control of travelling walls in a ferromagnetic nanowire (2006)
Carbou, Gilles, Labbé, Stéphane, Trélat, Emmanuel
We investigate the problem of controlling the magnetic moment in a ferromagnetic nanowire submitted to an external magnetic field in the direction of the nanowire. The system is modeled with the one...
Second order optimality conditions in optimal control with applications (2006)
Bonnard, Bernard, Caillau, Jean-Baptiste, Trélat, Emmanuel
The aim of this article is to present the algorithm to compute the first conjugate point along a smooth extremal curve. Under generic assumptions, the trajectory ceases to be optimal at such a point....
Second order optimality conditions in optimal control with applications (2006)
Bonnard, Bernard, Caillau, Jean-Baptiste, Trélat, Emmanuel
The aim of this article is to present the algorithm to compute the first conjugate point along a smooth extremal curve. Under generic assumptions, the trajectory ceases to be optimal at such a point....
Stackelberg strategy with closed-loop information structure for linear-quadratic games (2006)
Jungers, Marc, Trélat, Emmanuel, Abou-Kandil, Hisham
This paper deals with the Stackelberg strategy in the case of a closed-loop information structure. Two players differential games are considered with one leader and one follower. The Stackelberg...
Stackelberg strategy with closed-loop information structure for linear-quadratic games (2006)
Jungers, Marc, Trélat, Emmanuel, Abou-Kandil, Hisham
This paper deals with the Stackelberg strategy in the case of a closed-loop information structure. Two players differential games are considered with one leader and one follower. The Stackelberg...
Singular trajectories of control-affine systems (2006)
Chitour, Yacine, Jean, Frédéric, Trélat, Emmanuel
When applying methods of optimal control to motion planning or stabilization problems, some theoretical or numerical difficulties may arise, due to the presence of specific trajectories, namely,...
Quasi-optimal robust stabilization of control systems (2006)
Prieur, Christophe, Trélat, Emmanuel
In this paper, we investigate the problem of semi-global minimal time robust stabilization of analytic control systems with controls entering linearly, by means of a hybrid state feedback law. It is...
Le thème central de cette thèse est l'étude et le rôle des trajectoires anormales en théorie du contrôle optimal. Après avoir rappelé quelques résultats fondamentaux en contrôle optimal, on...
Contrôle en dimension finie et infinie (2006)
Ce mémoire présente les travaux que j'ai effectués, tout d'abord, à l'Institut de Mathématiques de l'Université de Dijon, pendant ma thèse de 1998 à 2000, puis dans l'équipe d'Analyse...
Singular trajectories of control-affine systems (2006)
Chitour, Yacine, Jean, Frédéric, Trélat, Emmanuel
When applying methods of optimal control to motion planning or stabilization problems, some theoretical or numerical difficulties may arise, due to the presence of specific trajectories, namely,...
A Stackelberg Game Approach to Mixed $H_2/H_\infty$ Control (2006)
Jungers, Marc, Trélat, Emmanuel, Abou-Kandil, Hisham
The $H_2/H_\infty$ robust control problem is formulated as a Stackelberg differential game where the leader minimizes an $H_2$criterion while the follower deals with the $H_\infty$ constraint. For a...
Commande mixte $H_2/H_\infty$ : une approche par la stratégie de Stackelberg (2006)
Jungers, Marc, Trélat, Emmanuel, Abou-Kandil, Hisham
La commande mixte $H_2/H_\infty$ consiste à déterminer une commande minimisant la norme $H_2$ d'un système tout en respectant une contrainte sous optimale sur une norme $H_\infty$. Il s'agit d'un...
Singular trajectories of control-affine systems (2006)
Chitour, Yacine, Jean, Frédéric, Trélat, Emmanuel
When applying methods of optimal control to motion planning or stabilization problems, some theoretical or numerical difficulties may arise, due to the presence of specific trajectories, namely,...
A Stackelberg Game Approach to Mixed $H_2/H_\infty$ Control (2006)
Jungers, Marc, Trélat, Emmanuel, Abou-Kandil, Hisham
The $H_2/H_\infty$ robust control problem is formulated as a Stackelberg differential game where the leader minimizes an $H_2$criterion while the follower deals with the $H_\infty$ constraint. For a...
Commande mixte $H_2/H_\infty$ : une approche par la stratégie de Stackelberg (2006)
Jungers, Marc, Trélat, Emmanuel, Abou-Kandil, Hisham
La commande mixte $H_2/H_\infty$ consiste à déterminer une commande minimisant la norme $H_2$ d'un système tout en respectant une contrainte sous optimale sur une norme $H_\infty$. Il s'agit d'un...
Let $T>0$ fixed. We consider the optimal control problem for analytic affine systems: $\ds{\dot{x}=f\_0(x)+\sum\_{i=1}^m u\_if\_i(x)}$, with a cost of the form: $\ds{C(u)=\int\_0^T \sum\_{i=1}^m...
Asymptotics of accessibility sets along an abnormal trajectory (2006)
We describe precisely, under generic conditions, the contact of the accessibility set at time $T$ with an abnormal direction, first for a single-input affine control system with constraint on the...
On the role of abnormal minimizers in sub-Riemannian geometry (2006)
Bonnard, Bernard, Trélat, Emmanuel
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...
Uniform controllability of semidiscrete approximations of parabolic control systems (2006)
Labbé, Stéphane, Trélat, Emmanuel
Controlling an approximation model of a controllable infinite dimensional linear control system does not necessarily yield a good approximation of the control needed for the continuous model. In the...
Controllability of partial differential equations (2006)
Chitour, Yacine, Trélat, Emmanuel
This is the notes of a FAP 2005 course (for CTS PhD and posdoc students, and for researchers) about controllability of partial differential equations, with the following items: # m-dissipative...
Controllability of Couette flows (2006)
Schmidt, Michael, Trélat, Emmanuel
In this article, we investigate the problem of controlling Navier-Stokes equations between two infinite rotating coaxial cylinders. We prove that it is possible to move from a given Couette flow,...
Singular trajectories and subanalyticity in optimal control and Hamilton-Jacobi theory (2006)
This survey paper presents several works of the author in optimal control theory. Under some general assumptions on an analytic optimal control problem, and assuming the absence of singular...
Genericity results for singular curves (2006)
Chitour, Yacine, Jean, Frédéric, Trélat, Emmanuel
Let $M$ be a smooth manifold and ${\cal D}_m$, $m\geq 2$, be the set of rank $m$ distributions on $M$ endowed with the Whitney $C^\infty$ topology. We show the existence of an open set $O_m$ dense in...
Robust stabilization in the Martinet case (2006)
Prieur, Christophe, Trélat, Emmanuel
In a previous work, 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...
Second order optimality conditions in the smooth case and applications in optimal control (2006)
Bonnard, Bernard, Caillau, Jean-Baptiste, Trélat, Emmanuel
The aim of this article is to present algorithms to compute the first conjugate time along a smooth extremal curve, where the trajectory ceases to be optimal. It is based on recent theoretical...
Global subanalytic solutions of Hamilton-Jacobi type equations (2006)
In the 80's, Crandall and Lions introduced the concept of viscosity solution, in order to get existence and/or uniqueness results for Hamilton-Jacobi equations. In this work, we first investigate the...
Geometric analysis of minimum time Keplerian orbit transfers (2006)
Bonnard, Bernard, Caillau, Jean-Baptiste, Trélat, Emmanuel
The minimum time control of the Kepler equation is considered. The typical application is the transfer of a satellite from an orbit around the Earth to another one, both orbits being elliptic. We...
Global steady-state stabilization and controllability of 1-D semilinear wave equations (2006)
Coron, Jean-Michel, Trélat, Emmanuel
This paper is concerned with the exact boundary controllability of semilinear wave equations in one space dimension. We prove that it is possible to move from any steady-state to any other one by...
Fast Tracking of Poiseuille Trajectories in Navier-Stokes 2D Channel Flow (2006)
Coron, Jean-Michel, Trélat, Emmanuel, Vazquez, Rafael
We consider the problem of generating and tracking a trajectory between two arbitrary parabolic profiles of a periodic 2D channel flow, which is linearly unstable for high Reynolds numbers. Also...
Stable Poiseuille flow transfer for a Navier-Stokes system (2006)
Vazquez, Rafael, Trélat, Emmanuel, Coron, Jean-Michel
We consider the problem of generating and tracking a trajectory between two arbitrary parabolic profiles of a periodic 2D channel flow, which is linearly unstable for high Reynolds numbers. Also...
On two hybrid robust optimal stabilization problems (2006)
Prieur, Christophe, Trélat, Emmanuel
We report on some recent results obtained by the authors concerning robust hybrid stabilization of control systems. We stated a result of semi-global minimal time robust stabilization for analytic...
Controllability of partial differential equations (2006)
Chitour, Yacine, Trélat, Emmanuel
This is the notes of a FAP 2005 course (for CTS PhD and posdoc students, and for researchers) about controllability of partial differential equations, with the following items: # m-dissipative...
Controllability of Couette flows (2006)
Schmidt, Michael, Trélat, Emmanuel
In this article, we investigate the problem of controlling Navier-Stokes equations between two infinite rotating coaxial cylinders. We prove that it is possible to move from a given Couette flow,...
Singular trajectories and subanalyticity in optimal control and Hamilton-Jacobi theory (2006)
This survey paper presents several works of the author in optimal control theory. Under some general assumptions on an analytic optimal control problem, and assuming the absence of singular...
Genericity results for singular curves (2006)
Chitour, Yacine, Jean, Frédéric, Trélat, Emmanuel
Let $M$ be a smooth manifold and ${\cal D}_m$, $m\geq 2$, be the set of rank $m$ distributions on $M$ endowed with the Whitney $C^\infty$ topology. We show the existence of an open set $O_m$ dense in...
Robust stabilization in the Martinet case (2006)
Prieur, Christophe, Trélat, Emmanuel
In a previous work, 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...
Second order optimality conditions in the smooth case and applications in optimal control (2006)
Bonnard, Bernard, Caillau, Jean-Baptiste, Trélat, Emmanuel
The aim of this article is to present algorithms to compute the first conjugate time along a smooth extremal curve, where the trajectory ceases to be optimal. It is based on recent theoretical...
Global subanalytic solutions of Hamilton-Jacobi type equations (2006)
In the 80's, Crandall and Lions introduced the concept of viscosity solution, in order to get existence and/or uniqueness results for Hamilton-Jacobi equations. In this work, we first investigate the...
Geometric analysis of minimum time Keplerian orbit transfers (2006)
Bonnard, Bernard, Caillau, Jean-Baptiste, Trélat, Emmanuel
The minimum time control of the Kepler equation is considered. The typical application is the transfer of a satellite from an orbit around the Earth to another one, both orbits being elliptic. We...
Global steady-state stabilization and controllability of 1-D semilinear wave equations (2006)
Coron, Jean-Michel, Trélat, Emmanuel
This paper is concerned with the exact boundary controllability of semilinear wave equations in one space dimension. We prove that it is possible to move from any steady-state to any other one by...
Fast Tracking of Poiseuille Trajectories in Navier-Stokes 2D Channel Flow (2006)
Coron, Jean-Michel, Trélat, Emmanuel, Vazquez, Rafael
We consider the problem of generating and tracking a trajectory between two arbitrary parabolic profiles of a periodic 2D channel flow, which is linearly unstable for high Reynolds numbers. Also...
Stable Poiseuille flow transfer for a Navier-Stokes system (2006)
Vazquez, Rafael, Trélat, Emmanuel, Coron, Jean-Michel
We consider the problem of generating and tracking a trajectory between two arbitrary parabolic profiles of a periodic 2D channel flow, which is linearly unstable for high Reynolds numbers. Also...
On two hybrid robust optimal stabilization problems (2006)
Prieur, Christophe, Trélat, Emmanuel
We report on some recent results obtained by the authors concerning robust hybrid stabilization of control systems. We stated a result of semi-global minimal time robust stabilization for analytic...
Uniform controllability of semidiscrete approximations of parabolic control systems (2006)
Labbé, Stéphane, Trélat, Emmanuel
Controlling an approximation model of a controllable infinite dimensional linear control system does not necessarily yield a good approximation of the control needed for the continuous model. In the...
Generalization of the finite difference method in distributions spaces (2006)
Labbé, Stéphane, Trélat, Emmanuel
The aim of this article is to propose a generalization of the finite difference scheme suitable with solutions of Dirac distribution type. This type of solution is for example encountered in...
Control of travelling walls in a ferromagnetic nanowire (2006)
Carbou, Gilles, Labbé, Stéphane, Trélat, Emmanuel
We investigate the problem of controlling the magnetic moment in a ferromagnetic nanowire submitted to an external magnetic field in the direction of the nanowire. The system is modeled with the one...
Second order optimality conditions in optimal control with applications (2006)
Bonnard, Bernard, Caillau, Jean-Baptiste, Trélat, Emmanuel
The aim of this article is to present the algorithm to compute the first conjugate point along a smooth extremal curve. Under generic assumptions, the trajectory ceases to be optimal at such a point....
Stackelberg strategy with closed-loop information structure for linear-quadratic games (2006)
Jungers, Marc, Trélat, Emmanuel, Abou-Kandil, Hisham
This paper deals with the Stackelberg strategy in the case of a closed-loop information structure. Two players differential games are considered with one leader and one follower. The Stackelberg...
A Stackelberg Game Approach to Mixed $H_2/H_\infty$ Control (2006)
Jungers, Marc, Trélat, Emmanuel, Abou-Kandil, Hisham
The $H_2/H_\infty$ robust control problem is formulated as a Stackelberg differential game where the leader minimizes an $H_2$criterion while the follower deals with the $H_\infty$ constraint. For a...
Commande mixte $H_2/H_\infty$ : une approche par la stratégie de Stackelberg (2006)
Jungers, Marc, Trélat, Emmanuel, Abou-Kandil, Hisham
La commande mixte $H_2/H_\infty$ consiste à déterminer une commande minimisant la norme $H_2$ d'un système tout en respectant une contrainte sous optimale sur une norme $H_\infty$. Il s'agit d'un...
Controllability of partial differential equations (2006)
Chitour, Yacine, Trélat, Emmanuel
This is the notes of a FAP 2005 course (for CTS PhD and posdoc students, and for researchers) about controllability of partial differential equations, with the following items: # m-dissipative...
Controllability of Couette flows (2006)
Schmidt, Michael, Trélat, Emmanuel
In this article, we investigate the problem of controlling Navier-Stokes equations between two infinite rotating coaxial cylinders. We prove that it is possible to move from a given Couette flow,...
Singular trajectories and subanalyticity in optimal control and Hamilton-Jacobi theory (2006)
This survey paper presents several works of the author in optimal control theory. Under some general assumptions on an analytic optimal control problem, and assuming the absence of singular...
Genericity results for singular curves (2006)
Chitour, Yacine, Jean, Frédéric, Trélat, Emmanuel
Let $M$ be a smooth manifold and ${\cal D}_m$, $m\geq 2$, be the set of rank $m$ distributions on $M$ endowed with the Whitney $C^\infty$ topology. We show the existence of an open set $O_m$ dense in...
Robust stabilization in the Martinet case (2006)
Prieur, Christophe, Trélat, Emmanuel
In a previous work, 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...
Global subanalytic solutions of Hamilton-Jacobi type equations (2006)
In the 80's, Crandall and Lions introduced the concept of viscosity solution, in order to get existence and/or uniqueness results for Hamilton-Jacobi equations. In this work, we first investigate the...
Geometric analysis of minimum time Keplerian orbit transfers (2006)
Bonnard, Bernard, Caillau, Jean-Baptiste, Trélat, Emmanuel
The minimum time control of the Kepler equation is considered. The typical application is the transfer of a satellite from an orbit around the Earth to another one, both orbits being elliptic. We...
Global steady-state stabilization and controllability of 1-D semilinear wave equations (2006)
Coron, Jean-Michel, Trélat, Emmanuel
This paper is concerned with the exact boundary controllability of semilinear wave equations in one space dimension. We prove that it is possible to move from any steady-state to any other one by...
Stable Poiseuille flow transfer for a Navier-Stokes system (2006)
Vazquez, Rafael, Trélat, Emmanuel, Coron, Jean-Michel
We consider the problem of generating and tracking a trajectory between two arbitrary parabolic profiles of a periodic 2D channel flow, which is linearly unstable for high Reynolds numbers. Also...
Uniform controllability of semidiscrete approximations of parabolic control systems (2006)
Labbé, Stéphane, Trélat, Emmanuel
Controlling an approximation model of a controllable infinite dimensional linear control system does not necessarily yield a good approximation of the control needed for the continuous model. In the...
Quasi-optimal robust stabilization of control systems (2006)
Prieur, Christophe, Trélat, Emmanuel
In this paper, we investigate the problem of semi-global minimal time robust stabilization of analytic control systems with controls entering linearly, by means of a hybrid state feedback law. It is...
Quasi-optimal robust stabilization of control systems (2006)
Prieur, Christophe, Trélat, Emmanuel
In this paper, we investigate the problem of semi-global minimal time robust stabilization of analytic control systems with controls entering linearly, by means of a hybrid state feedback law. It is...
Generalization of the finite difference method in distributions spaces (2006)
Labbé, Stéphane, Trélat, Emmanuel
The aim of this article is to propose a generalization of the finite difference scheme suitable with solutions of Dirac distribution type. This type of solution is for example encountered in...
Control of travelling walls in a ferromagnetic nanowire (2006)
Carbou, Gilles, Labbé, Stéphane, Trélat, Emmanuel
We investigate the problem of controlling the magnetic moment in a ferromagnetic nanowire submitted to an external magnetic field in the direction of the nanowire. The system is modeled with the one...
Second order optimality conditions in optimal control with applications (2006)
Bonnard, Bernard, Caillau, Jean-Baptiste, Trélat, Emmanuel
The aim of this article is to present the algorithm to compute the first conjugate point along a smooth extremal curve. Under generic assumptions, the trajectory ceases to be optimal at such a point....
Stackelberg strategy with closed-loop information structure for linear-quadratic games (2006)
Jungers, Marc, Trélat, Emmanuel, Abou-Kandil, Hisham
This paper deals with the Stackelberg strategy in the case of a closed-loop information structure. Two players differential games are considered with one leader and one follower. The Stackelberg...
Controllability of partial differential equations (2006)
Chitour, Yacine, Trélat, Emmanuel
This is the notes of a FAP 2005 course (for CTS PhD and posdoc students, and for researchers) about controllability of partial differential equations, with the following items: # m-dissipative...
Stable Poiseuille flow transfer for a Navier-Stokes system (2006)
Vazquez, Rafael, Trélat, Emmanuel, Coron, Jean-Michel
We consider the problem of generating and tracking a trajectory between two arbitrary parabolic profiles of a periodic 2D channel flow, which is linearly unstable for high Reynolds numbers. Also...
Global steady-state stabilization and controllability of 1-D semilinear wave equations (2006)
Coron, Jean-Michel, Trélat, Emmanuel
This paper is concerned with the exact boundary controllability of semilinear wave equations in one space dimension. We prove that it is possible to move from any steady-state to any other one by...
Commande mixte $H_2/H_\infty$ : une approche par la stratégie de Stackelberg (2006)
Jungers, Marc, Trélat, Emmanuel, Abou-Kandil, Hisham
La commande mixte $H_2/H_\infty$ consiste à déterminer une commande minimisant la norme $H_2$ d'un système tout en respectant une contrainte sous optimale sur une norme $H_\infty$. Il s'agit d'un...
Geometric analysis of minimum time Keplerian orbit transfers (2006)
Bonnard, Bernard, Caillau, Jean-Baptiste, Trélat, Emmanuel
The minimum time control of the Kepler equation is considered. The typical application is the transfer of a satellite from an orbit around the Earth to another one, both orbits being elliptic. We...
A Stackelberg Game Approach to Mixed $H_2/H_\infty$ Control (2006)
Jungers, Marc, Trélat, Emmanuel, Abou-Kandil, Hisham
The $H_2/H_\infty$ robust control problem is formulated as a Stackelberg differential game where the leader minimizes an $H_2$criterion while the follower deals with the $H_\infty$ constraint. For a...
Global subanalytic solutions of Hamilton-Jacobi type equations (2006)
In the 80's, Crandall and Lions introduced the concept of viscosity solution, in order to get existence and/or uniqueness results for Hamilton-Jacobi equations. In this work, we first investigate the...
Robust stabilization in the Martinet case (2006)
Prieur, Christophe, Trélat, Emmanuel
In a previous work, 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...
Genericity results for singular curves (2006)
Chitour, Yacine, Jean, Frédéric, Trélat, Emmanuel
Let $M$ be a smooth manifold and ${\cal D}_m$, $m\geq 2$, be the set of rank $m$ distributions on $M$ endowed with the Whitney $C^\infty$ topology. We show the existence of an open set $O_m$ dense in...
Singular trajectories and subanalyticity in optimal control and Hamilton-Jacobi theory (2006)
This survey paper presents several works of the author in optimal control theory. Under some general assumptions on an analytic optimal control problem, and assuming the absence of singular...
Controllability of Couette flows (2006)
Schmidt, Michael, Trélat, Emmanuel
In this article, we investigate the problem of controlling Navier-Stokes equations between two infinite rotating coaxial cylinders. We prove that it is possible to move from a given Couette flow,...
Uniform controllability of semidiscrete approximations of parabolic control systems (2006)
Labbé, Stéphane, Trélat, Emmanuel
Controlling an approximation model of a controllable infinite dimensional linear control system does not necessarily yield a good approximation of the control needed for the continuous model. In the...
Contrôle en dimension finie et infinie (2005)
Ce mémoire présente les travaux que j'ai effectués, tout d'abord, àl'Institut de Mathématiques de l'Université de Dijon, pendant ma thèse de1998 à 2000, puis dans l'équipe d'Analyse...
Cotcot: short reference manual (2005)
This reference introduces the Matlab package COTCOT designed to compute extremals in the case of smooth Hamiltonian systems, and to obtain the associated conjugate points with respect to the index...
Prieur, Christophe, Trélat, Emmanuel
We investigate the problem of semi-global minimal time robust stabilization of analytic driftless control-affine systems, by means of a hybrid state feedback law. Our main result is that, in the...
Morse-Sard type results in sub-Riemannian geometry (2005)
Rifford, Ludovic, Trélat, Emmanuel
Let $(M,\Delta,g)$ be a sub-Riemannian manifold and $x_0\in M$. Assuming that Chow's condition holds and that $M$ endowed with the sub-Riemannian distance is complete, we prove that there exists a...
Bonnard, Bernard, Faubourg, Ludovic, Trélat, Emmanuel
This article, continuation of previous works, presents the applications of geometric optimal control theory to the analysis of the Earth re-entry problem for a space shuttle where the control is the...
Geometric optimal control of elliptic Keplerian orbits (2005)
Bonnard, Bernard, Caillau, Jean-Baptiste, Trélat, Emmanuel
This article deals with the transfer of a satellite between Keplerian orbits. We study the controllability properties of the system and make a preliminary analysis of the time optimal control using...
Robust optimal stabilization of the Brockett integrator via a hybrid feedback (2005)
Prieur, Christophe, Trélat, Emmanuel
The problem of semi-global minimal time robust stabilization of the Brockett integrator (also called Heisenberg system) is addressed and solved by means of a hybrid state feedback law. It is shown...
Quasi-optimal robust stabilization of control systems (2005)
Prieur, Christophe, Trélat, Emmanuel
In this paper, we investigate the problem of semi-global minimal time robust stabilization of analytic control systems with controls entering linearly, by means of a hybrid state feedback law. It is...
Coron, Jean-Michel, Trélat, Emmanuel
We report the problem of feedback stabilization along a path of steady-states, and of exact boundary controllability of semilinear one-dimensional heat and wave equations. The main result is that it...
Computation of conjugate times in smooth optimal control: the COTCOT algorithm (2005)
Bonnard, Bernard, Caillau, Jean-Baptiste, Trélat, Emmanuel
Conjugate point type second order optimality conditions for extremals associated to smooth Hamiltonians are evaluated by means of a new algorithm. Two kinds of standard control problems fit in this...
Singular trajectories of driftless and control-affine systems (2005)
Chitour, Yacine, Jean, Frédéric, Trélat, Emmanuel
We establish generic properties for singular trajectories, first for driftless, and then for control-affine systems. We show that, generically -- for the Whitney topology -- nontrivial singular...
Contrôle en dimension finie et infinie (2005)
Ce mémoire présente les travaux que j'ai effectués, tout d'abord, à l'Institut de Mathématiques de l'Université de Dijon, pendant ma thèse de 1998 à 2000, puis dans l'équipe d'Analyse...
Cotcot: short reference manual (2005)
This reference introduces the Matlab package COTCOT designed to compute extremals in the case of smooth Hamiltonian systems, and to obtain the associated conjugate points with respect to the index...
Prieur, Christophe, Trélat, Emmanuel
We investigate the problem of semi-global minimal time robust stabilization of analytic driftless control-affine systems, by means of a hybrid state feedback law. Our main result is that, in the...
Morse-Sard type results in sub-Riemannian geometry (2005)
Rifford, Ludovic, Trélat, Emmanuel
Let $(M,\Delta,g)$ be a sub-Riemannian manifold and $x_0\in M$. Assuming that Chow's condition holds and that $M$ endowed with the sub-Riemannian distance is complete, we prove that there exists a...
Bonnard, Bernard, Faubourg, Ludovic, Trélat, Emmanuel
This article, continuation of previous works, presents the applications of geometric optimal control theory to the analysis of the Earth re-entry problem for a space shuttle where the control is the...
Geometric optimal control of elliptic Keplerian orbits (2005)
Bonnard, Bernard, Caillau, Jean-Baptiste, Trélat, Emmanuel
This article deals with the transfer of a satellite between Keplerian orbits. We study the controllability properties of the system and make a preliminary analysis of the time optimal control using...
Robust optimal stabilization of the Brockett integrator via a hybrid feedback (2005)
Prieur, Christophe, Trélat, Emmanuel
The problem of semi-global minimal time robust stabilization of the Brockett integrator (also called Heisenberg system) is addressed and solved by means of a hybrid state feedback law. It is shown...
Quasi-optimal robust stabilization of control systems (2005)
Prieur, Christophe, Trélat, Emmanuel
In this paper, we investigate the problem of semi-global minimal time robust stabilization of analytic control systems with controls entering linearly, by means of a hybrid state feedback law. It is...
Coron, Jean-Michel, Trélat, Emmanuel
We report the problem of feedback stabilization along a path of steady-states, and of exact boundary controllability of semilinear one-dimensional heat and wave equations. The main result is that it...
Computation of conjugate times in smooth optimal control: the COTCOT algorithm (2005)
Bonnard, Bernard, Caillau, Jean-Baptiste, Trélat, Emmanuel
Conjugate point type second order optimality conditions for extremals associated to smooth Hamiltonians are evaluated by means of a new algorithm. Two kinds of standard control problems fit in this...
Singular trajectories of driftless and control-affine systems (2005)
Chitour, Yacine, Jean, Frédéric, Trélat, Emmanuel
We establish generic properties for singular trajectories, first for driftless, and then for control-affine systems. We show that, generically -- for the Whitney topology -- nontrivial singular...
Cotcot: short reference manual (2005)
This reference introduces the Matlab package COTCOT designed to compute extremals in the case of smooth Hamiltonian systems, and to obtain the associated conjugate points with respect to the index...
Prieur, Christophe, Trélat, Emmanuel
We investigate the problem of semi-global minimal time robust stabilization of analytic driftless control-affine systems, by means of a hybrid state feedback law. Our main result is that, in the...
Morse-Sard type results in sub-Riemannian geometry (2005)
Rifford, Ludovic, Trélat, Emmanuel
Let $(M,\Delta,g)$ be a sub-Riemannian manifold and $x_0\in M$. Assuming that Chow's condition holds and that $M$ endowed with the sub-Riemannian distance is complete, we prove that there exists a...
Bonnard, Bernard, Faubourg, Ludovic, Trélat, Emmanuel
This article, continuation of previous works, presents the applications of geometric optimal control theory to the analysis of the Earth re-entry problem for a space shuttle where the control is the...
Geometric optimal control of elliptic Keplerian orbits (2005)
Bonnard, Bernard, Caillau, Jean-Baptiste, Trélat, Emmanuel
This article deals with the transfer of a satellite between Keplerian orbits. We study the controllability properties of the system and make a preliminary analysis of the time optimal control using...
Robust optimal stabilization of the Brockett integrator via a hybrid feedback (2005)
Prieur, Christophe, Trélat, Emmanuel
The problem of semi-global minimal time robust stabilization of the Brockett integrator (also called Heisenberg system) is addressed and solved by means of a hybrid state feedback law. It is shown...
Coron, Jean-Michel, Trélat, Emmanuel
We report the problem of feedback stabilization along a path of steady-states, and of exact boundary controllability of semilinear one-dimensional heat and wave equations. The main result is that it...
Computation of conjugate times in smooth optimal control: the COTCOT algorithm (2005)
Bonnard, Bernard, Caillau, Jean-Baptiste, Trélat, Emmanuel
Conjugate point type second order optimality conditions for extremals associated to smooth Hamiltonians are evaluated by means of a new algorithm. Two kinds of standard control problems fit in this...
Singular trajectories of driftless and control-affine systems (2005)
Chitour, Yacine, Jean, Frédéric, Trélat, Emmanuel
We establish generic properties for singular trajectories, first for driftless, and then for control-affine systems. We show that, generically -- for the Whitney topology -- nontrivial singular...
Contrôle en dimension finie et infinie (2005)
Ce mémoire présente les travaux que j'ai effectués, tout d'abord, à l'Institut de Mathématiques de l'Université de Dijon, pendant ma thèse de 1998 à 2000, puis dans l'équipe d'Analyse...
Cotcot: short reference manual (2005)
This reference introduces the Matlab package COTCOT designed to compute extremals in the case of smooth Hamiltonian systems, and to obtain the associated conjugate points with respect to the index...
Computation of conjugate times in smooth optimal control: the COTCOT algorithm (2005)
Bonnard, Bernard, Caillau, Jean-Baptiste, Trélat, Emmanuel
Conjugate point type second order optimality conditions for extremals associated to smooth Hamiltonians are evaluated by means of a new algorithm. Two kinds of standard control problems fit in this...
Coron, Jean-Michel, Trélat, Emmanuel
We report the problem of feedback stabilization along a path of steady-states, and of exact boundary controllability of semilinear one-dimensional heat and wave equations. The main result is that it...
Robust optimal stabilization of the Brockett integrator via a hybrid feedback (2005)
Prieur, Christophe, Trélat, Emmanuel
The problem of semi-global minimal time robust stabilization of the Brockett integrator (also called Heisenberg system) is addressed and solved by means of a hybrid state feedback law. It is shown...
Geometric optimal control of elliptic Keplerian orbits (2005)
Bonnard, Bernard, Caillau, Jean-Baptiste, Trélat, Emmanuel
This article deals with the transfer of a satellite between Keplerian orbits. We study the controllability properties of the system and make a preliminary analysis of the time optimal control using...
Bonnard, Bernard, Faubourg, Ludovic, Trélat, Emmanuel
This article, continuation of previous works, presents the applications of geometric optimal control theory to the analysis of the Earth re-entry problem for a space shuttle where the control is the...
Morse-Sard type results in sub-Riemannian geometry (2005)
Rifford, Ludovic, Trélat, Emmanuel
Let $(M,\Delta,g)$ be a sub-Riemannian manifold and $x_0\in M$. Assuming that Chow's condition holds and that $M$ endowed with the sub-Riemannian distance is complete, we prove that there exists a...
Prieur, Christophe, Trélat, Emmanuel
We investigate the problem of semi-global minimal time robust stabilization of analytic driftless control-affine systems, by means of a hybrid state feedback law. Our main result is that, in the...
Contrôle en dimension finie et infinie (2005)
Ce mémoire présente les travaux que j'ai effectués, tout d'abord, à l'Institut de Mathématiques de l'Université de Dijon, pendant ma thèse de 1998 à 2000, puis dans l'équipe d'Analyse...
Singular trajectories of driftless and control-affine systems (2005)
Chitour, Yacine, Jean, Frédéric, Trélat, Emmanuel
We establish generic properties for singular trajectories, first for driftless, and then for control-affine systems. We show that, generically -- for the Whitney topology -- nontrivial singular...
Global steady-state controllability of 1-D semilinear heat equations (2004)
Coron, Jean-Michel, Trélat, Emmanuel
We investigate the problem of exact boundary controllability of semilinear one-dimensional heat equations. We prove that it is possible to move from any steady-state to any other one by means of a...
Robust optimal stabilization of the Brockett integrator via a hybrid feedback (2004)
Prieur, Christophe, Trélat, Emmanuel
The problem of semi-global robust stabilization of the Brockett integrator (also called Heisenberg system) in minimal time is addressed and solved by means of a hybrid feedback law. It is shown that...
Contrôle optimal appliqué au problème de rentrée atmosphérique (2004)
On s'intéresse au problème de contrôle optimal d'une navette spatiale en phase de rentrée atmosphérique, où le contrôle est l'angle de gîte, et le coût est le flux thermique total (facteur...
Global steady-state controllability of 1-D semilinear heat equations (2004)
Coron, Jean-Michel, Trélat, Emmanuel
We investigate the problem of exact boundary controllability of semilinear one-dimensional heat equations. We prove that it is possible to move from any steady-state to any other one by means of a...
Robust optimal stabilization of the Brockett integrator via a hybrid feedback (2004)
Prieur, Christophe, Trélat, Emmanuel
The problem of semi-global robust stabilization of the Brockett integrator (also called Heisenberg system) in minimal time is addressed and solved by means of a hybrid feedback law. It is shown that...
Contrôle optimal appliqué au problème de rentrée atmosphérique (2004)
On s'intéresse au problème de contrôle optimal d'une navette spatiale en phase de rentrée atmosphérique, où le contrôle est l'angle de gîte, et le coût est le flux thermique total (facteur...
Global steady-state controllability of 1-D semilinear heat equations (2004)
Coron, Jean-Michel, Trélat, Emmanuel
We investigate the problem of exact boundary controllability of semilinear one-dimensional heat equations. We prove that it is possible to move from any steady-state to any other one by means of a...
Robust optimal stabilization of the Brockett integrator via a hybrid feedback (2004)
Prieur, Christophe, Trélat, Emmanuel
The problem of semi-global robust stabilization of the Brockett integrator (also called Heisenberg system) in minimal time is addressed and solved by means of a hybrid feedback law. It is shown that...
Contrôle optimal appliqué au problème de rentrée atmosphérique (2004)
On s'intéresse au problème de contrôle optimal d'une navette spatiale en phase de rentrée atmosphérique, où le contrôle est l'angle de gîte, et le coût est le flux thermique total (facteur...
Robust optimal stabilization of the Brockett integrator via a hybrid feedback (2004)
Prieur, Christophe, Trélat, Emmanuel
The problem of semi-global robust stabilization of the Brockett integrator (also called Heisenberg system) in minimal time is addressed and solved by means of a hybrid feedback law. It is shown that...
Global steady-state controllability of 1-D semilinear heat equations (2004)
Coron, Jean-Michel, Trélat, Emmanuel
We investigate the problem of exact boundary controllability of semilinear one-dimensional heat equations. We prove that it is possible to move from any steady-state to any other one by means of a...
Contrôle optimal appliqué au problème de rentrée atmosphérique (2004)
On s'intéresse au problème de contrôle optimal d'une navette spatiale en phase de rentrée atmosphérique, où le contrôle est l'angle de gîte, et le coût est le flux thermique total (facteur...
Generic properties of singular trajectories (2003)
Chitour, Yacine, Jean, Frédéric, Trélat, Emmanuel
We give genericity results for singular trajectories in sub-Riemannian geometry: generically (in the sense of the Whitney topology), every singular trajectory is of minimal order and of corank 1 and...
Optimal control with state constraints and the space shuttle re-entry problem (2003)
Bonnard, Bernard, Faubourg, Ludovic, Launay, Geneviève, Trélat, Emmanuel
In this article, we initialize the analysis under generic assumptions of the small \textit{time optimal synthesis} for single input systems with \textit{state constraints}. We use geometric methods...
Optimal control of a space shuttle and numerical simulations (2003)
We study the Earth re-entry problem of a space shuttle where the control is the angle of bank, the cost is the total amount of thermal flux, and the system is subject to state constraints on the...
Conjugate times for smooth singular trajectories and bang-bang extremals (2003)
Bonnard, Bernard, Faubourg, Ludovic, Trélat, Emmanuel
In this paper we discuss the problem of estimating conjugate times along smooth singular or bang-bang extremals. For smooth extremals conjugate times can be defined in the generic case by using the...
Bonnard, Bernard, Faubourg, Ludovic, Trélat, Emmanuel
This paper describes the analysis under generic assumptions of the small \textit{time minimal syntheses} for single input affine control systems in dimension $3$, submitted to \textit{state...
Optimal control with state constraints and the space shuttle re-entry problem (2003)
Bonnard, Bernard, Faubourg, Ludovic, Launay, Geneviève, Trélat, Emmanuel
In this article, we initialize the analysis under generic assumptions of the small \textit{time optimal synthesis} for single input systems with \textit{state constraints}. We use geometric methods...
Optimal control of a space shuttle and numerical simulations (2003)
We study the Earth re-entry problem of a space shuttle where the control is the angle of bank, the cost is the total amount of thermal flux, and the system is subject to state constraints on the...
Conjugate times for smooth singular trajectories and bang-bang extremals (2003)
Bonnard, Bernard, Faubourg, Ludovic, Trélat, Emmanuel
In this paper we discuss the problem of estimating conjugate times along smooth singular or bang-bang extremals. For smooth extremals conjugate times can be defined in the generic case by using the...
Bonnard, Bernard, Faubourg, Ludovic, Trélat, Emmanuel
This paper describes the analysis under generic assumptions of the small \textit{time minimal syntheses} for single input affine control systems in dimension $3$, submitted to \textit{state...
Generic properties of singular trajectories (2003)
Chitour, Yacine, Jean, Frédéric, Trélat, Emmanuel
We give genericity results for singular trajectories in sub-Riemannian geometry: generically (in the sense of the Whitney topology), every singular trajectory is of minimal order and of corank 1 and...
Optimal control with state constraints and the space shuttle re-entry problem (2003)
Bonnard, Bernard, Faubourg, Ludovic, Launay, Geneviève, Trélat, Emmanuel
In this article, we initialize the analysis under generic assumptions of the small \textit{time optimal synthesis} for single input systems with \textit{state constraints}. We use geometric methods...
Optimal control of a space shuttle and numerical simulations (2003)
We study the Earth re-entry problem of a space shuttle where the control is the angle of bank, the cost is the total amount of thermal flux, and the system is subject to state constraints on the...
Conjugate times for smooth singular trajectories and bang-bang extremals (2003)
Bonnard, Bernard, Faubourg, Ludovic, Trélat, Emmanuel
In this paper we discuss the problem of estimating conjugate times along smooth singular or bang-bang extremals. For smooth extremals conjugate times can be defined in the generic case by using the...
Bonnard, Bernard, Faubourg, Ludovic, Trélat, Emmanuel
This paper describes the analysis under generic assumptions of the small \textit{time minimal syntheses} for single input affine control systems in dimension $3$, submitted to \textit{state...
Generic properties of singular trajectories (2003)
Chitour, Yacine, Jean, Frédéric, Trélat, Emmanuel
We give genericity results for singular trajectories in sub-Riemannian geometry: generically (in the sense of the Whitney topology), every singular trajectory is of minimal order and of corank 1 and...
Bonnard, Bernard, Faubourg, Ludovic, Trélat, Emmanuel
This paper describes the analysis under generic assumptions of the small \textit{time minimal syntheses} for single input affine control systems in dimension $3$, submitted to \textit{state...
Conjugate times for smooth singular trajectories and bang-bang extremals (2003)
Bonnard, Bernard, Faubourg, Ludovic, Trélat, Emmanuel
In this paper we discuss the problem of estimating conjugate times along smooth singular or bang-bang extremals. For smooth extremals conjugate times can be defined in the generic case by using the...
Optimal control of a space shuttle and numerical simulations (2003)
We study the Earth re-entry problem of a space shuttle where the control is the angle of bank, the cost is the total amount of thermal flux, and the system is subject to state constraints on the...
Optimal control with state constraints and the space shuttle re-entry problem (2003)
Bonnard, Bernard, Faubourg, Ludovic, Launay, Geneviève, Trélat, Emmanuel
In this article, we initialize the analysis under generic assumptions of the small \textit{time optimal synthesis} for single input systems with \textit{state constraints}. We use geometric methods...
Generic properties of singular trajectories (2003)
Chitour, Yacine, Jean, Frédéric, Trélat, Emmanuel
We give genericity results for singular trajectories in sub-Riemannian geometry: generically (in the sense of the Whitney topology), every singular trajectory is of minimal order and of corank 1 and...
Description of accessibility sets near an abnormal trajectory and consequences (2002)
We describe precisely, under generic conditions, the contact of the accessibility set at time $T$ with an abnormal direction, first for a single-input affine control system with constraint on the...
We investigate minimization problems along a singular trajectory of a single-input affine control system with constraint on the control, and then as an application of a sub-Riemannian system of rank...
Une approche géométrique du contrôle optimal de l'arc atmosphérique de la navette spatiale (2002)
Bonnard, Bernard, Trélat, Emmanuel
L'objectif de ce travail est de faire quelques remarques géométriques et des calculs préliminaires pour construire l'arc atmosphérique optimal d'une navette spatiale (problème de rentrée sur...
Description of accessibility sets near an abnormal trajectory and consequences (2002)
We describe precisely, under generic conditions, the contact of the accessibility set at time $T$ with an abnormal direction, first for a single-input affine control system with constraint on the...
We investigate minimization problems along a singular trajectory of a single-input affine control system with constraint on the control, and then as an application of a sub-Riemannian system of rank...
Une approche géométrique du contrôle optimal de l'arc atmosphérique de la navette spatiale (2002)
Bonnard, Bernard, Trélat, Emmanuel
L'objectif de ce travail est de faire quelques remarques géométriques et des calculs préliminaires pour construire l'arc atmosphérique optimal d'une navette spatiale (problème de rentrée sur...
Description of accessibility sets near an abnormal trajectory and consequences (2002)
We describe precisely, under generic conditions, the contact of the accessibility set at time $T$ with an abnormal direction, first for a single-input affine control system with constraint on the...
We investigate minimization problems along a singular trajectory of a single-input affine control system with constraint on the control, and then as an application of a sub-Riemannian system of rank...
Une approche géométrique du contrôle optimal de l'arc atmosphérique de la navette spatiale (2002)
Bonnard, Bernard, Trélat, Emmanuel
L'objectif de ce travail est de faire quelques remarques géométriques et des calculs préliminaires pour construire l'arc atmosphérique optimal d'une navette spatiale (problème de rentrée sur...
Une approche géométrique du contrôle optimal de l'arc atmosphérique de la navette spatiale (2002)
Bonnard, Bernard, Trélat, Emmanuel
L'objectif de ce travail est de faire quelques remarques géométriques et des calculs préliminaires pour construire l'arc atmosphérique optimal d'une navette spatiale (problème de rentrée sur...
We investigate minimization problems along a singular trajectory of a single-input affine control system with constraint on the control, and then as an application of a sub-Riemannian system of rank...
Description of accessibility sets near an abnormal trajectory and consequences (2002)
We describe precisely, under generic conditions, the contact of the accessibility set at time $T$ with an abnormal direction, first for a single-input affine control system with constraint on the...
On the role of abnormal minimizers in sub-Riemannian geometry (2001)
Bonnard, Bernard, Trélat, Emmanuel
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...
Asymptotics of accessibility sets along an abnormal trajectory (2001)
We describe precisely, under generic conditions, the contact of the accessibility set at time $T$ with an abnormal direction, first for a single-input affine control system with constraint on the...
Bonnard, Bernard, Launay, Geneviève, Trélat, Emmanuel
Consider a \it{sub-Riemannian geometry} $(U,D,g)$ where $U$ is a neighborhood of $O$ in $\mathbb{R}^3$, $D$ is a \it{Martinet type distribution} identified to $Ker \,\omega$, $\omega...
Stratification du secteur anormal dans la sphère de Martinet de petit rayon (2001)
Bonnard, Bernard, Trélat, Emmanuel
L'objectif de cet article est de fournir le cadre géométrique pour faire une analyse de la singularité de l'application exponentielle le long d'une direction anormale en géométrie...
Non subanalyticity of sub-Riemannian Martinet spheres (2001)
Consider the sub-Riemannian Martinet structure $(M,\Delta,g)$ where $M=\R^3$, $\Delta={\rm{Ker }}(dz-{{y^2}\over{2}}dx)$ and $g$ is the general gradated metric of order $0$~: $g=(1+\alpha...
Stratification du secteur anormal dans la sphère de Martinet de petit rayon (2001)
Bonnard, Bernard, Trélat, Emmanuel
L'objectif de cet article est de fournir le cadre géométrique pour faire une analyse de la singularité de l'application exponentielle le long d'une direction anormale en géométrie...
Non subanalyticity of sub-Riemannian Martinet spheres (2001)
Consider the sub-Riemannian Martinet structure $(M,\Delta,g)$ where $M=\R^3$, $\Delta={\rm{Ker }}(dz-{{y^2}\over{2}}dx)$ and $g$ is the general gradated metric of order $0$~: $g=(1+\alpha...
On the role of abnormal minimizers in sub-Riemannian geometry (2001)
Bonnard, Bernard, Trélat, Emmanuel
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...
Asymptotics of accessibility sets along an abnormal trajectory (2001)
We describe precisely, under generic conditions, the contact of the accessibility set at time $T$ with an abnormal direction, first for a single-input affine control system with constraint on the...
Bonnard, Bernard, Launay, Geneviève, Trélat, Emmanuel
Consider a \it{sub-Riemannian geometry} $(U,D,g)$ where $U$ is a neighborhood of $O$ in $\mathbb{R}^3$, $D$ is a \it{Martinet type distribution} identified to $Ker \,\omega$, $\omega...
Stratification du secteur anormal dans la sphère de Martinet de petit rayon (2001)
Bonnard, Bernard, Trélat, Emmanuel
L'objectif de cet article est de fournir le cadre géométrique pour faire une analyse de la singularité de l'application exponentielle le long d'une direction anormale en géométrie...
Non subanalyticity of sub-Riemannian Martinet spheres (2001)
Consider the sub-Riemannian Martinet structure $(M,\Delta,g)$ where $M=\R^3$, $\Delta={\rm{Ker }}(dz-{{y^2}\over{2}}dx)$ and $g$ is the general gradated metric of order $0$~: $g=(1+\alpha...
On the role of abnormal minimizers in sub-Riemannian geometry (2001)
Bonnard, Bernard, Trélat, Emmanuel
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...
Asymptotics of accessibility sets along an abnormal trajectory (2001)
We describe precisely, under generic conditions, the contact of the accessibility set at time $T$ with an abnormal direction, first for a single-input affine control system with constraint on the...
Bonnard, Bernard, Launay, Geneviève, Trélat, Emmanuel
Consider a \it{sub-Riemannian geometry} $(U,D,g)$ where $U$ is a neighborhood of $O$ in $\mathbb{R}^3$, $D$ is a \it{Martinet type distribution} identified to $Ker \,\omega$, $\omega...
Non subanalyticity of sub-Riemannian Martinet spheres (2001)
Consider the sub-Riemannian Martinet structure $(M,\Delta,g)$ where $M=\R^3$, $\Delta={\rm{Ker }}(dz-{{y^2}\over{2}}dx)$ and $g$ is the general gradated metric of order $0$~: $g=(1+\alpha...
Stratification du secteur anormal dans la sphère de Martinet de petit rayon (2001)
Bonnard, Bernard, Trélat, Emmanuel
L'objectif de cet article est de fournir le cadre géométrique pour faire une analyse de la singularité de l'application exponentielle le long d'une direction anormale en géométrie...
On the role of abnormal minimizers in sub-Riemannian geometry (2001)
Bonnard, Bernard, Trélat, Emmanuel
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...
Asymptotics of accessibility sets along an abnormal trajectory (2001)
We describe precisely, under generic conditions, the contact of the accessibility set at time $T$ with an abnormal direction, first for a single-input affine control system with constraint on the...
Bonnard, Bernard, Launay, Geneviève, Trélat, Emmanuel
Consider a \it{sub-Riemannian geometry} $(U,D,g)$ where $U$ is a neighborhood of $O$ in $\mathbb{R}^3$, $D$ is a \it{Martinet type distribution} identified to $Ker \,\omega$, $\omega...
Le thème central de cette thèse est l'étude et le rôle destrajectoires anormales en théorie du contrôle optimal.Après avoir rappelé quelques résultats fondamentaux en contrôleoptimal, on...
Let $T>0$ fixed. We consider the optimal control problem for analytic affine systems~: $\ds{\dot{x}=f_0(x)+\sum_{i=1}^m u_if_i(x)}$, with a cost of the form~: $\ds{C(u)=\int_0^T \sum_{i=1}^m...
Le thème central de cette thèse est l'étude et le rôle des trajectoires anormales en théorie du contrôle optimal. Après avoir rappelé quelques résultats fondamentaux en contrôle optimal, on...
Let $T>0$ fixed. We consider the optimal control problem for analytic affine systems~: $\ds{\dot{x}=f_0(x)+\sum_{i=1}^m u_if_i(x)}$, with a cost of the form~: $\ds{C(u)=\int_0^T \sum_{i=1}^m...
Let $T>0$ fixed. We consider the optimal control problem for analytic affine systems~: $\ds{\dot{x}=f_0(x)+\sum_{i=1}^m u_if_i(x)}$, with a cost of the form~: $\ds{C(u)=\int_0^T \sum_{i=1}^m...
Le thème central de cette thèse est l'étude et le rôle des trajectoires anormales en théorie du contrôle optimal. Après avoir rappelé quelques résultats fondamentaux en contrôle optimal, on...
Le thème central de cette thèse est l'étude et le rôle des trajectoires anormales en théorie du contrôle optimal. Après avoir rappelé quelques résultats fondamentaux en contrôle optimal, on...
Let $T>0$ fixed. We consider the optimal control problem for analytic affine systems~: $\ds{\dot{x}=f_0(x)+\sum_{i=1}^m u_if_i(x)}$, with a cost of the form~: $\ds{C(u)=\int_0^T \sum_{i=1}^m...
Bonnard, Bernard, Launay, Geneviève, Trélat, Emmanuel
Consider a \it{sub-Riemannian geometry} $(U,D,g)$ where $U$ is a neighborhood of $O$ in $\mathbb{R}^3$, $D$ is a \it{Martinet type distribution} identified to $Ker \,\omega$, $\omega...
Bonnard, Bernard, Launay, Geneviève, Trélat, Emmanuel
Consider a \it{sub-Riemannian geometry} $(U,D,g)$ where $U$ is a neighborhood of $O$ in $\mathbb{R}^3$, $D$ is a \it{Martinet type distribution} identified to $Ker \,\omega$, $\omega...
Bonnard, Bernard, Launay, Geneviève, Trélat, Emmanuel
Consider a \it{sub-Riemannian geometry} $(U,D,g)$ where $U$ is a neighborhood of $O$ in $\mathbb{R}^3$, $D$ is a \it{Martinet type distribution} identified to $Ker \,\omega$, $\omega...
Bonnard, Bernard, Launay, Geneviève, Trélat, Emmanuel
Consider a \it{sub-Riemannian geometry} $(U,D,g)$ where $U$ is a neighborhood of $O$ in $\mathbb{R}^3$, $D$ is a \it{Martinet type distribution} identified to $Ker \,\omega$, $\omega...