Jean-Paul Gauthier

Brief paper: An adaptive high-gain observer for nonlinear systems

In this paper the authors provide a solution to the noise sensitivity of high-gain observers. The resulting nonlinear observer possesses simultaneously (1) extended Kalman filters good noise filtering properties, and (2) the reactivity of the high-gain extended Kalman filter with respect to large perturbations. The authors introduce innovation as the quantity that drives the gain adaptation. They prove a general convergence result, propose guidelines to practical implementation and show simulation results for an example.

Optimal control in laser-induced population transfer for two- and three-level quantum systems

We apply the techniques of control theory and of sub-Riemannian geometry to laser-induced population transfer in two- and three-level quantum systems. The aim is to induce complete population transfer by one or two laser pulses minimizing the pulse fluences. Sub-Riemannian geometry and singular-Riemannian geometry provide a natural framework for this minimization, where the optimal control is expressed in terms of geodesics. We first show that in two-level systems the well-known technique of “π-pulse transfer” in the rotating wave approximation emerges naturally from this minimization. In three-level systems driven by two resonant fields, we also find the counterpart of the “π-pulse transfer.” This geometrical picture also allows one to analyze the population transfer by adiabatic passage.

On the K + P Problem for a Three-Level Quantum System: Optimality Implies Resonance

We apply techniques of subriemannian geometry on Lie groups to laser-induced population transfer in a three-level quantum system. The aim is to induce transitions by two laser pulses, of arbitrary shape and frequency, minimizing the pulse energy. We prove that the Hamiltonian system given by the Pontryagin maximum principle is completely integrable, since this problem can be stated as a “k ⊕ p problem” on a simple Lie group. Optimal trajectories and controls are exhausted. The main result is that optimal controls correspond to lasers that are “in resonance”.

Anthropomorphic Image Reconstruction via Hypoelliptic Diffusion

In this paper we study a model of geometry of vision due to Petitot, Citti, and Sarti. One of the main features of this model is that the primary visual cortex V1 lifts an image from

On the subanalyticity of Carnot–Caratheodory distances

\mathbb{R}^2

An FPGA-based accelerator for Fourier Descriptors computing for color object recognition using SVM

to the bundle of directions of the plane. Neurons are grouped into orientation columns, each of them corresponding to a point of this bundle. In this model a corrupted image is reconstructed by minimizing the energy necessary for the activation of the orientation columns corresponding to regions in which the image is corrupted. The minimization process intrinsically defines a hypoelliptic heat equation on the bundle of directions of the plane. In the original model, directions are considered both with and without orientation, giving rise, respectively, to a problem on the group of rototranslations of the plane

SUB-RIEMANNIAN METRICS AND ISOPERIMETRIC PROBLEMS IN THE CONTACT CASE

SE(2)

On the Dido Problem and Plane Isoperimetric Problems

or on the projective tangent bundle of the plane

On Sub-Riemannian Caustics and Wave Fronts for Contact Distributions in the Three-Space

PT\mathbb{R}^2

A biomechanical inactivation principle

. We provide a mathematical proof of several important facts for this model. We first prove that the model is mathematically consis...