Search results for " and Control"

On some Riemannian aspects of two and three-body controlled problems

2009

The flow of the Kepler problem (motion of two mutually attracting bodies) is known to be geodesic after the work of Moser [20], extended by Belbruno and Osipov [2, 21]: Trajectories are reparameterizations of minimum length curves for some Riemannian metric. This is not true anymore in the case of the three-body problem, and there are topological obstructions as observed by McCord et al. [19]. The controlled formulations of these two problems are considered so as to model the motion of a spacecraft within the influence of one or two planets. The averaged flow of the (energy minimum) controlled Kepler problem with two controls is shown to remain geodesic. The same holds true in the case of o…

Chance constrained optimization of a three-stage launcher

2015

Journées SMAI-MODE 2016 (Toulouse)

Characterization of the Clarke regularity of subanalytic sets

2017

International audience; In this note, we will show that for a closed subanalytic subset $A \subset \mathbb{R}^n$, the Clarke tangential regularity of $A$ at $x_0 \in A$ is equivalent to the coincidence of the Clarke's tangent cone to $A$ at $x_0$ with the set \\$$\mathcal{L}(A, x_0):= \bigg\{\dot{c}_+(0) \in \mathbb{R}^n: \, c:[0,1]\longrightarrow A\;\;\mbox{\it is Lipschitz}, \, c(0)=x_0\bigg\}.$$Where $\dot{c}_+(0)$ denotes the right-strict derivative of $c$ at $0$. The results obtained are used to show that the Clarke regularity of the epigraph of a function may be characterized by a new formula of the Clarke subdifferential of that function.

A Context-Based Adaptation In Mobile Learning

2013

International audience; Recent developments on mobile devices and wireless technologies enable new technical capabilities for the learning domain. Nowadays, learners are able to learn anywhere and at any time. The dynamic and continually changing learning setting in learner's mobile environment gives rise to many different learning contexts. The challenge in context-aware mobile learning is to develop an approach building the best learning content according to dynamic learning situations. This paper aims to develop an adaptive system based on the semantic modeling of the learning content and the learning context. The behavioral part of this approach is made up of rules and metaheuristics to…

Minimum time control of the Kepler equation

2004

Convexity of injectivity domains on the ellipsoid of revolution: The oblate case (addendum)

2011

Addendum to: Bonnard, B.; Caillau, J.-B.; Rifford, L. Convexity of injectivity domains on the ellipsoid of revolution: The oblate case. C. R. Acad. Sci. Paris, Ser. I 348 (2010), 1315–1318.

Mécanique céleste et contrôle de systèmes spatiaux

2006

Mécanique céleste et contrôle de systèmes spatiaux

Classification of local optimal syntheses for time minimal control problems with state constraints

2003

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 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.

Geometric analysis of minimum time Keplerian orbit transfers

2006

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 recall the standard model to represent the system. Its Lie algebraic structure is first analyzed, and controllability is established for two different single-input subsystems, the control being oriented by the velocity or by the orthoradial direction. In both cases, a preliminary analysis of singular and regular extremals is also given, using the usual concept of order to classify the contacts. Moreover, the singularity of the multi-input model---which is a particular case of a subriemannian system…

The transcendence needed to compute the sphere and wave front in Martinet sub-Riemannian geometry

2001

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 $Ker \,\omega$, $\omega =dz-\f{y^2}{2}dx$, $q=(x,y,z)$ and $g$ is a \it{metric on $D$} which can be taken in the normal form : \mbox{$a(q)dx^2+c(q)dy^2$}, \mbox{$a=1+yF(q)$}, \mbox{$c=1+G(q)$}, \mbox{$G_{|x=y=0}=0$}. In a previous article we analyzed the \it{flat case} : \mbox{$a=c=1$} ; we showed that the set of geodesics is integrable using \it{elliptic integrals} of the \it{first and second kind} ; moreover we described the sphere and the wave front near the abnormal direction using the \it{\mbox{exp-log} category}. The objective o…