Search results for "optimal"
showing 10 items of 706 documents
Resonance of minimizers forn-level quantum systems with an arbitrary cost
2004
We consider an optimal control problem describing a laser-induced population transfer on a n-level quantum system. For a convex cost depending only on the moduli of controls ( i.e. the lasers intensities), we prove that there always exists a minimizer in resonance. This permits to justify some strategies used in experimental physics. It is also quite important because it permits to reduce remarkably the complexity of the problem (and extend some of our previous results for n=2 and n=3): instead of looking for minimizers on the sphere one is reduced to look just for minimizers on the sphere . Moreover, for the reduced problem, we investigate on the question of existence of strict abnormal mi…
A Simple Operating Strategy of Small-Scale Battery Energy Storages for Energy Arbitrage under Dynamic Pricing Tariffs
2015
Price arbitrage involves taking advantage of an electricity price difference, storing electricity during low-prices times, and selling it back to the grid during high-prices periods. This strategy can be exploited by customers in presence of dynamic pricing schemes, such as hourly electricity prices, where the customer electricity cost may vary at any hour of day, and power consumption can be managed in a more flexible and economical manner, taking advantage of the price differential. Instead of modifying their energy consumption, customers can install storage systems to reduce their electricity bill, shifting the energy consumption from on-peak to off-peak hours. This paper develops a deta…
Symmetry breaking in a constrained cheeger type isoperimetric inequality
2015
We study the optimal constant in a Sobolev inequality for BV functions with zero mean value and vanishing outside a bounded open set. We are interested in finding the best possible embedding constant in terms of the measure of the domain alone. We set up an optimal shape problem and we completely characterize the behavior of optimal domains.
Discretization estimates for an elliptic control problem
1998
An optimal control problem governed by an elliptic equation written in variational form in an abstract functional framework is considered. The control is subject to restrictions. The optimality conditions are established and the Ritz-Galerkin discretization is introduced. If the error estimate corresponding to the elliptic equation is given as a function like where h is the discretization parameter and is an integer, then the error estimates for the optimal control, for the optimal state and for the optimal value are obtained. These results are applied first for a Two-Point BVP and next for a 2D/3D elliptic problem as state equation. Next a spectral method is used in the discretization proc…
Sustainable Management of Tourist Flow Networks: A Mean Field Model
2023
In this article, we propose a mean field game approach for modeling the flows of excursionists within a network of tourist attractions. We prove the existence of an equilibrium within the network using a balance ordinary differential equation together with optimality conditions in terms of the value function. We also propose a bi-level formulation of the problem where we aim at achieving a sustainable-oriented control strategy in the upper level and at maximizing excursionists’ satisfaction in the lower level. Our proposed model may provide an effective management tool for local authorities who deal with the challenging problem of finding an optimal control policy to the often conflicting o…
Guidance Trajectories for Spacecraft Rendezvous
2007
In a previous paper of Miele et al. (J. Optim. Theory Appl. 132(1), 2007), we employed the single-subarc sequential gradient-restoration algorithm to optimize the three-dimensional rendezvous between a target spacecraft in a planar circular orbit and a chaser spacecraft with an initial separation distance and separation velocity. The achieved continuous solutions are characterized by two, three, or four subarcs depending on the performance index (time, fuel) and the constraints. In this paper, based on the solutions in Miele et al. (J. Optim. Theory Appl. 132(1), 2007), we employ the multiple-subarc sequential gradient-restoration algorithm to produce pieced guidance trajectories implementa…
Optimal Trajectories for Spacecraft Rendezvous
2007
The efficient execution of a rendezvous maneuver is an essential component of various types of space missions. This work describes the formulation and numerical investigation of the thrust function required to minimize the time or fuel required for the terminal phase of the rendezvous of two spacecraft. The particular rendezvous studied concerns a target spacecraft in a circular orbit and a chaser spacecraft with an initial separation distance and separation velocity in all three dimensions. First, the time-optimal rendezvous is investigated followed by the fuel-optimal rendezvous for three values of the max-thrust acceleration via the sequential gradient-restoration algorithm. Then, the ti…
Constrained control of a nonlinear two point boundary value problem, I
1994
In this paper we consider an optimal control problem for a nonlinear second order ordinary differential equation with integral constraints. A necessary optimality condition in form of the Pontryagin minimum principle is derived. The proof is based on McShane-variations of the optimal control, a thorough study of their behaviour in dependence of some denning parameters, a generalized Green formula for second order ordinary differential equations with measurable coefficients and certain tools of convex analysis.
Convexities and optimal transport problems on the Wiener space
2013
The aim of this PhD is to study the optimal transportation theory in some abstract Wiener space. You can find the results in four main parts and they are aboutThe convexity of the relative entropy. We will extend the well known results in finite dimension to the Wiener space, endowed with the uniform norm. To be precise the relative entropy is (at least weakly) geodesically 1-convex in the sense of the optimal transportation in the Wiener space.The measures with logarithmic concave density. The first important result consists in showing that the Harnack inequality holds for the semi-group induced by such a measure in the Wiener space. The second one provides us a finite dimensional and dime…
O gulag e a literatura de gulag: um balanço das pesquisas
2017
Resumo: Este artigo apresenta um panorama dos debates historiográficos, antigos e recentes, sobre a literatura produzida no complexo de campos de concentração soviéticos (o "gulag"). São examinados livros, congressos, instituições de pesquisa e organizações de memória dedicadas ao tema. O texto é concluído pela constatação da escassez de pesquisas voltadas às especificidades da literatura do gulag. Abstract: This paper presents an overview of recent and old debates on the literature created in Soviet concentration camp complexes (gulags), and examines books, conferences, research institutions and memory organizations dedicated to the matter. The article concludes with the observation that s…