Search results for "CONST"

Regularization of chattering phenomena via bounded variation controls

2018

In control theory, the term chattering is used to refer to strong oscillations of controls, such as an infinite number of switchings over a compact interval of times. In this paper we focus on three typical occurences of chattering: the Fuller phenomenon, referring to situations where an optimal control switches an infinite number of times over a compact set; the Robbins phenomenon, concerning optimal control problems with state constraints, meaning that the optimal trajectory touches the boundary of the constraint set an infinite number of times over a compact time interval; the Zeno phenomenon, referring as well to an infinite number of switchings over a compact set, for hybrid optimal co…

Solving chance constrained optimal control problems in aerospace via Kernel Density Estimation

2017

International audience; The goal of this paper is to show how non-parametric statistics can be used to solve some chance constrained optimization and optimal control problems. We use the Kernel Density Estimation method to approximate the probability density function of a random variable with unknown distribution , from a relatively small sample. We then show how this technique can be applied and implemented for a class of problems including the God-dard problem and the trajectory optimization of an Ariane 5-like launcher.

Optimal control with state constraints and the space shuttle re-entry problem

2003

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 to evaluate \textit{the small time reachable set} and necessary optimality conditions. Our work is motivated by the \textit{optimal control of the atmospheric arc for the re-entry of a space shuttle}, where the vehicle is subject to constraints on the thermal flux and on the normal acceleration. A \textit{multiple shooting technique} is finally applied to compute the optimal longitudinal arc.

Analysis of highly excited 'hot' bands in the SO2 molecule: ν2 + 3ν3 - ν2 and 2ν1 + ν2 + ν3 - ν2

2010

International audience; We set up a variational procedure of assignments of transitions and we applied it to the analysis very weak 'hot' bands, v(2) + 3v(3) - v(2) and 2v(1) + v(2) + v(3) - v(2), of the SO2 molecule. As the first step of the study, the 'cold' bands, 3v(3) and 2v(1) + v(3), are re-analysed and transitions belonging to those bands are assigned up to the values of quantum numbers J(max.) = 60, K-a(max.) = 19, and J(max.) = 69, K-a(max.) = 20 for the bands 3v(3) and 2v(1) + v(3), respectively. After 'cleaning' the experimental spectrum from transitions belonging to the 3v(3) and 2v(1) + v(3) bands, a variational procedure was used that allowed us to assign 230 and 115 transiti…

Le tuffeau, un matériau apprécié dans la construction

2018

Quelques problèmes relatifs au mariage dans les lois des Wisigoths et des Burgondes

2009

International audience

La construction historique de l’Etat culturel

2017

International audience

Territoires et terroirs du vin du 18e au 21e siècles : approche internationale d'une construction historique

2011

International audience

La reconstruction de la mémoire dans Valse avec Bachir d'Ari Folman

2015

International audience

A new invariant-based method for building biomechanical behavior laws - Application to an anisotropic hyperelastic material with two fiber families

2013

Abstract In this article, we present a general constructive and original approach that allows us to calculate the invariants associated with an anisotropic hyperelastic material made of two families of collagen fibers. This approach is based on mathematical techniques from the theory of invariants: • Definition of the material symmetry group. • Analytical calculation of a set of generators using the Noether’s theorem. • Analytical calculation of an integrity basis. • Comparison between the proposed invariants and the classical ones.