Search results for "optimization"

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…

Two applications of geometric optimal control to the dynamics of spin particle

2013

To appear in a volume of "Math and Industry", Springer-Verlag; The purpose of this article is to present the application of methods from geometric optimal control to two problems in the dynamics of spin particles. First, we consider the saturation problem for a single spin system and second, the control of a linear chain of spin particles with Ising couplings. For both problems the minimizers are parameterized using Pontryagin Maximum Principle and the optimal solution is found by a careful analysis of the corresponding equations.

Working Notes on the Time Minimal Saturation of a Pair of Spins and Application in Magnetic Resonance Imaging

2018

In this article, we analyse the time minimal control for the saturation of a pair of spins of the same species but with inhomogeneities of the applied RF-magnetic field, in relation with the contrast problem in Magnetic Resonance Imaging. We make a complete analysis based on geometric control to classify the optimal syntheses in the single spin case to pave the road to analyze the case of two spins. The Bocop software is used to determine local minimizers for physical test cases and Linear Matrix Inequalities approach is applied to estimate the global optimal value and validate the previous computations. This is complemented by numerical computations combining shooting and continuation meth…

A global optimality result with application to orbital transfer

2006

The objective of this note is to present a global optimality result on Riemannian metrics $ds^2=dr^2+(r^2/c^2)(G(\vphi)d\theta^2+d\vphi^2)$. This result can be applied to the averaged energy minimization coplanar orbit transfer problem.