Search results for "optimization"
showing 10 items of 2824 documents
Minimum fuel control of the planar circular restricted three-body problem
2012
The circular restricted three-body problem is considered to model the dynamics of an artificial body submitted to the attraction of two planets. Minimization of the fuel consumption of the spacecraft during the transfer, e.g. from the Earth to the Moon, is considered. In the light of the controllability results of Caillau and Daoud (SIAM J Control Optim, 2012), existence for this optimal control problem is discussed under simplifying assumptions. Thanks to Pontryagin maximum principle, the properties of fuel minimizing controls is detailed, revealing a bang-bang structure which is typical of L1-minimization problems. Because of the resulting non-smoothness of the Hamiltonian two-point bound…
Constrained differential inclusions with nonlocal initial conditions
2017
International audience; We show existence for the perturbed sweeping process with nonlocal initial conditions under very general hypotheses. Periodic, anti-periodic, mean value and multipoints conditions are included in this study. We give abstract results for differential inclusions with nonlocal initial conditions through bounding functions and tangential conditions. Some applications to differential complementarity systems and to vector hysteresis are given.
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.
A combination of algebraic, geometric and numerical methods in the contrast problem by saturation in magnetic resonance imaging
2014
In this article, the contrast imaging problem by saturation in nuclear magnetic resonance is modeled as a Mayer problem in optimal control. The optimal solution can be found as an extremal solution of the Maximum Principle and analyzed with the recent advanced techniques of geometric optimal control. This leads to a numerical investigation based on shooting and continuation methods implemented in the HamPath software. The results are compared with a direct approach to the optimization problem and implemented within the Bocop toolbox. In complement lmi techniques are used to estimate a global optimum. It is completed with the analysis of the saturation problem of an ensemble of spin particle…
Geometric optimal control of elliptic Keplerian orbits
2005
This article deals with the transfer of a satellite between Keplerian orbits. We study the controllability properties of the system and make a preliminary analysis of the time optimal control using the maximum principle. Second order sufficient conditions are also given. Finally, the time optimal trajectory to transfer the system from an initial low orbit with large eccentricity to a terminal geostationary orbit is obtained numerically.
Minimum Time Control of the Restricted Three-Body Problem
2012
The minimum time control of the circular restricted three-body problem is considered. Controllability is proved on an adequate submanifold. Singularities of the extremal flow are studied by means of a stratification of the switching surface. Properties of homotopy maps in optimal control are framed in a simple case. The analysis is used to perform continuations on the two parameters of the problem: The ratio of the masses, and the magnitude of the 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.