0000000000075350
AUTHOR
Jean-paul Gauthier
Observer for a thick layer of solid deuterium-tritium using backlit optical shadowgraphy and interferometry.
Our work is in the context of the French "laser megajoule" project, about fusion by inertial confinement. The project leads to the problem of characterizing the inner surface, of the approximately spherical target, by optical shadowgraphy techniques. Our work is entirely based on the basic idea that optical shadowgraphy produces "caustics" of systems of optical rays, which contain a great deal of 3D information about the surface to be characterized. We develop a method of 3D reconstruction based upon this idea plus a "small perturbations" technique. Although computations are made in the special "spherical" case, the method is in fact general and may be extended to several other situations.
New Results on Identifiability of Nonlinear Systems
Abstract In this paper, we recall definition of identifiability of nonlinear systems. We prove equivalence between identifiability and smooth identifiability. This new result justifies our definition of identifiability. In a previous paper (Busvelle and Gauthier, 2003), we have established that • If the number of observations is three or more, then, systems are generically identifiable. • If the number of observations is 1 or 2, then the situation is reversed. Identifiability is not at all generic. Also, we have completely classified infinitesimally identifiable systems in the second case, and in particular, we gave normal forms for identifiable systems. Here, we will give similar results i…
Observation and identification tools for non-linear systems: application to a fluid catalytic cracker
In this paper we recall general methodologies we developed for observation and identification in non-linear systems theory, and we show how they can be applied to real practical problems. In a previous paper, we introduced a filter which is intermediate between the extended Kalman filter in its standard version and its high-gain version, and we applied it to certain observation problems. But we were missing some important cases. Here, we show how to treat these cases. We also apply the same technique in the context of our identifiability theory. As non-academic illustrations, we treat a problem of observation and a problem of identification, for a fluid catalytic cracker (FCC). This FCC uni…
Simulation of a UAV ground control station
International audience; In this article we present the development of a UAV ground control station simulator. We propose a module based description of the architecture of this simulator. We recall the nonlinear model of a fixed-wing aircraft. Finally, we outline ideas for improved path planning tasks. The approach is made clearthrough several diagrams, figures of the resulting station are displayed.
On determining unknown functions in differential systems, with an application to biological reactors.
In this paper, we consider general nonlinear systems with observations, containing a (single) unknown function φ . We study the possibility to learn about this unknown function via the observations: if it is possible to determine the [values of the] unknown function from any experiment [on the set of states visited during the experiment], and for any arbitrary input function, on any time interval, we say that the system is “identifiable”. For systems without controls, we give a more or less complete picture of what happens for this identifiability property. This picture is very similar to the picture of the “observation theory” in [7]: Contrarily to the case of the observability property, i…
On complexity and motion planning for co-rank one sub-Riemannian metrics
In this paper, we study the motion planning problem for generic sub-Riemannian metrics of co-rank one. We give explicit expressions for the metric complexity (in the sense of Jean (10,11)), in terms of the elementary invariants of the problem. We construct asymptotic optimal syntheses. It turns out that among the results we show, the most complicated case is the 3-dimensional. Besides the generic C ∞ case, we study some non-generic generalizations in the analytic case.
Nonholonomic Interpolation for Kinematic Problems, Entropy and Complexity
Here we present the main lines of a theory we developed in a series of previous papers, about the motion planning problem in robotics. We illustrate the theory with a few academic examples.
Adaptive-gain extended Kalman filter: Extension to the continuous-discrete case
In the present article we propose a nonlinear observer that merges the behaviors 1) of an extended Kalman filter, mainly designed to smooth off noise , and 2) of high-gain observers devoted to handle large perturbations in the state estimation. We specifically aim at continuous-discrete systems. The strategy consists in letting the high-gain self adapt according to the innovation. We define innovation computed over a time window and justify its usage via an important lemma. We prove the general convergence of the resulting observer.
Finding Invariants of Group Actions on Function Spaces, a General Methodology from Non-Abelian Harmonic Analysis
In this paper, we describe a general method using the abstract non-Abelian Fourier transform to construct “rich” invariants of group actions on functional spaces.
Spatial Reconstruction Algorithm of DT Layer in Cryogenic Targets Using Optical Techniques
The measurements of the solid DT layer, in terms of thickness and roughness, in the LMJ geometry (i.e. in a hohlraum) are not trivial. The DT layer measurements will be done using a Matsukov-Cassegrain telescope placed 39 cm away from the target. This telescope will be used to acquire shadowgraphy images on equators, and interferometric measurements on pole areas using optical coherence tomography (OCT). Optical coherence tomography allows determining the DT layer thickness on a few points, in the polar regions of the target. By scanning around the poles, several points can be acquired in order to calculate the roughness and the local shape of the DT layer at the pole. Both techniques were …
Optimal control of the Schrödinger equation with two or three levels
In this paper, we present how techniques of “control theory”, “sub-Riemannian geometry” and “singular Riemannian geometry” can be applied to some classical problems of quantum mechanics and yield improvements to some previous results.
Adaptive-gain extended Kalman filter: application to a series connected DC motor
International audience
EMERGENCE OF TRAVELLING WAVES IN SMOOTH NERVE FIBRES
International audience; An approximate analytical solution characterizing initial condi- tions leading to action potential ¯ring in smooth nerve ¯bres is determined, using the bistable equation. In the ¯rst place, we present a non-trivial sta- tionary solution wave. Then, we extract the main features of this solution to obtain a frontier condition between the initiation of the travelling waves and a decay to the resting state. This frontier corresponds to a separatrix in the projected dynamics diagram depending on the width and the amplitude of the stationary wave.
The Inactivation Principle: Mathematical Solutions Minimizing the Absolute Work and Biological Implications for the Planning of Arm Movements
An important question in the literature focusing on motor control is to determine which laws drive biological limb movements. This question has prompted numerous investigations analyzing arm movements in both humans and monkeys. Many theories assume that among all possible movements the one actually performed satisfies an optimality criterion. In the framework of optimal control theory, a first approach is to choose a cost function and test whether the proposed model fits with experimental data. A second approach (generally considered as the more difficult) is to infer the cost function from behavioral data. The cost proposed here includes a term called the absolute work of forces, reflecti…