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Two-stage stochastic programming approach to a PDE-constrained steel production problem with the moving interface

Lubomír Klimeš, Pavel Popela, Tomáš Mauder, Josef Štětina, Pavel Charvát (2017)

Kybernetika

The paper is concerned with a parallel implementation of the progressive hedging algorithm (PHA) which is applicable for the solution of stochastic optimization problems. We utilized the Message Passing Interface (MPI) and the General Algebraic Modelling System (GAMS) to concurrently solve the scenario-related subproblems in parallel manner. The standalone application combining the PHA, MPI, and GAMS was programmed in C++. The created software was successfully applied to a steel production problem...

Uncertain input data problems and the worst scenario method

Ivan Hlaváček (2007)

Applications of Mathematics

An introduction to the worst scenario method is given. We start with an example and a general abstract scheme. An analysis of the method both on the continuous and approximate levels is discussed. We show a possible incorporation of the method into the fuzzy set theory. Finally, we present a survey of applications published during the last decade.

Uniform controllability of the linear one dimensional Schrödinger equation with vanishing viscosity

Sorin Micu, Ionel Rovenţa (2012)

ESAIM: Control, Optimisation and Calculus of Variations

This article considers the linear 1-d Schrödinger equation in (0,π) perturbed by a vanishing viscosity term depending on a small parameter ε > 0. We study the boundary controllability properties of this perturbed equation and the behavior of its boundary controls vε as ε goes to zero. It is shown that, for any time T sufficiently large but independent of ε and for each initial datum in H−1(0,π), there exists a uniformly...

Uniform controllability of the linear one dimensional Schrödinger equation with vanishing viscosity

Sorin Micu, Ionel Rovenţa (2012)

ESAIM: Control, Optimisation and Calculus of Variations

This article considers the linear 1-d Schrödinger equation in (0,π) perturbed by a vanishing viscosity term depending on a small parameter ε > 0. We study the boundary controllability properties of this perturbed equation and the behavior of its boundary controls vε as ε goes to zero. It is shown that, for any time T sufficiently large but independent of ε and for each initial datum in H−1(0,π), there exists a uniformly...

Unique continuation principle for systems of parabolic equations

Otared Kavian, Luz de Teresa (2010)

ESAIM: Control, Optimisation and Calculus of Variations

In this paper we prove a unique continuation result for a cascade system of parabolic equations, in which the solution of the first equation is (partially) used as a forcing term for the second equation. As a consequence we prove the existence of ε-insensitizing controls for some parabolic equations when the control region and the observability region do not intersect.

Uniqueness results for Stokes equations and their consequences in linear and nonlinear control problems

Caroline Fabre (2010)

ESAIM: Control, Optimisation and Calculus of Variations

The goal of this article is the study of the approximate controllability for two approximations of Navier Stokes equations with distributed controls. The method of proof combines a suitable linearization of the system with a fixed point argument. We then are led to study the approximate controllability of linear Stokes systems with potentials. We study both the case where there is no constraint on the control and the case where we search a control having one null component. In both cases,...

Viscosity solutions of the Bellman equation for exit time optimal control problems with non-Lipschitz dynamics

Michael Malisoff (2001)

ESAIM: Control, Optimisation and Calculus of Variations

We study the Bellman equation for undiscounted exit time optimal control problems with fully nonlinear lagrangians and fully nonlinear dynamics using the dynamic programming approach. We allow problems whose non-Lipschitz dynamics admit more than one solution trajectory for some choices of open loop controls and initial positions. We prove a uniqueness theorem which characterizes the value functions of these problems as the unique viscosity solutions of the corresponding Bellman equations that satisfy...

Viscosity Solutions of the Bellman Equation for Exit Time Optimal Control Problems with Non-Lipschitz Dynamics

Michael Malisoff (2010)

ESAIM: Control, Optimisation and Calculus of Variations

We study the Bellman equation for undiscounted exit time optimal control problems with fully nonlinear Lagrangians and fully nonlinear dynamics using the dynamic programming approach. We allow problems whose non-Lipschitz dynamics admit more than one solution trajectory for some choices of open loop controls and initial positions. We prove a uniqueness theorem which characterizes the value functions of these problems as the unique viscosity solutions of the corresponding Bellman equations that...

Well-posedness and regularity of hyperbolic boundary control systems on a one-dimensional spatial domain

Hans Zwart, Yann Le Gorrec, Bernhard Maschke, Javier Villegas (2010)

ESAIM: Control, Optimisation and Calculus of Variations

We study a class of hyperbolic partial differential equations on a one dimensional spatial domain with control and observation at the boundary. Using the idea of feedback we show these systems are well-posed in the sense of Weiss and Salamon if and only if the state operator generates a C0-semigroup. Furthermore, we show that the corresponding transfer function is regular, i.e., has a limit for s going to infinity.

Currently displaying 401 – 420 of 441