Caractérisation d'un espace fonctionnel intervenant en contrôle optimal
Jacques Simon (1983)
Annales de la Faculté des sciences de Toulouse : Mathématiques
Guy Bouchitté, Giuseppe Buttazzo (2001)
Journal of the European Mathematical Society
We study some problems of optimal distribution of masses, and we show that they can be characterized by a suitable Monge-Kantorovich equation. In the case of scalar state functions, we show the equivalence with a mass transport problem, emphasizing its geometrical approach through geodesics. The case of elasticity, where the state function is vector valued, is also considered. In both cases some examples are presented.
Farag, M.H. (2009)
Surveys in Mathematics and its Applications
Philippe Michel (1977)
Bulletin de la Société Mathématique de France
Madalina Petcu, Roger Temam (2004)
ESAIM: Control, Optimisation and Calculus of Variations
In this article we apply the optimal and the robust control theory to the sine-Gordon equation. In our case the control is given by the boundary conditions and we work in a finite time horizon. We present at the beginning the optimal control problem and we derive a necessary condition of optimality and we continue by formulating a robust control problem for which existence and uniqueness of solutions are derived.
Madalina Petcu, Roger Temam (2010)
ESAIM: Control, Optimisation and Calculus of Variations
In this article we apply the optimal and the robust control theory to the sine-Gordon equation. In our case the control is given by the boundary conditions and we work in a finite time horizon. We present at the beginning the optimal control problem and we derive a necessary condition of optimality and we continue by formulating a robust control problem for which existence and uniqueness of solutions are derived.
Hoda A. Ali (2006)
Mathematica Slovaca
Rinaldo M. Colombo, Michael Herty, Magali Mercier (2011)
ESAIM: Control, Optimisation and Calculus of Variations
This paper focuses on the analytical properties of the solutions to the continuity equation with non local flow. Our driving examples are a supply chain model and an equation for the description of pedestrian flows. To this aim, we prove the well posedness of weak entropy solutions in a class of equations comprising these models. Then, under further regularity conditions, we prove the differentiability of solutions with respect to the initial datum and characterize this derivative. A necessary ...
Rinaldo M. Colombo, Michael Herty, Magali Mercier (2011)
ESAIM: Control, Optimisation and Calculus of Variations
This paper focuses on the analytical properties of the solutions to the continuity equation with non local flow. Our driving examples are a supply chain model and an equation for the description of pedestrian flows. To this aim, we prove the well posedness of weak entropy solutions in a class of equations comprising these models. Then, under further regularity conditions, we prove the differentiability of solutions with respect to the initial datum and characterize this derivative. A necessary ...
Iftode, Vasile (2002)
Balkan Journal of Geometry and its Applications (BJGA)
Olivier Pironneau (2002)
ESAIM: Control, Optimisation and Calculus of Variations
We wish to show how the shock position in a nozzle could be controlled. Optimal control theory and algorithm is applied to the transonic equation. The difficulty is that the derivative with respect to the shock position involves a Dirac mass. The one dimensional case is solved, the two dimensional one is analyzed .
Olivier Pironneau (2010)
ESAIM: Control, Optimisation and Calculus of Variations
We wish to show how the shock position in a nozzle could be controlled. Optimal control theory and algorithm is applied to the transonic equation. The difficulty is that the derivative with respect to the shock position involves a Dirac mass. The one dimensional case is solved, the two dimensional one is analyzed .
Phuong Anh Nguyen, Jean-Pierre Raymond (2001)
ESAIM: Control, Optimisation and Calculus of Variations
We consider optimal control problems for convection-diffusion equations with a pointwise control or a control localized on a smooth manifold. We prove optimality conditions for the control variable and for the position of the control. We do not suppose that the coefficient of the convection term is regular or bounded, we only suppose that it has the regularity of strong solutions of the Navier–Stokes equations. We consider functionals with an observation on the gradient of the state. To obtain optimality...
Phuong Anh Nguyen, Jean-Pierre Raymond (2010)
ESAIM: Control, Optimisation and Calculus of Variations
We consider optimal control problems for convection-diffusion equations with a pointwise control or a control localized on a smooth manifold. We prove optimality conditions for the control variable and for the position of the control. We do not suppose that the coefficient of the convection term is regular or bounded, we only suppose that it has the regularity of strong solutions of the Navier–Stokes equations. We consider functionals with an observation on the gradient of the state. To obtain...
F. Mignot, J. P. Puel (1981/1982)
Séminaire Équations aux dérivées partielles (Polytechnique)
Anton Schiela, Daniel Wachsmuth (2013)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
In the article an optimal control problem subject to a stationary variational inequality is investigated. The optimal control problem is complemented with pointwise control constraints. The convergence of a smoothing scheme is analyzed. There, the variational inequality is replaced by a semilinear elliptic equation. It is shown that solutions of the regularized optimal control problem converge to solutions of the original one. Passing to the limit in the optimality system of the regularized problem...
Piotr Holnicki, Jan Sokołowski, Antoni Żochowski (1987)
Aplikace matematiky
The convex optimal control problem for a system described by the parabolic equation is considered. The form of the right derivative of an optimal solution with respect to the parameter is derived. The applications to an air quality control problem are discussed. Numerical result are provided.
Maria Emilia Amendola, Giuliano Gargiulo, Elvira Zappale (2014)
ESAIM: Control, Optimisation and Calculus of Variations
A 3D-2D dimension reduction for −Δ1 is obtained. A power law approximation from −Δp as p → 1 in terms of Γ-convergence, duality and asymptotics for least gradient functions has also been provided.
Nadir Arada (2013)
ESAIM: Control, Optimisation and Calculus of Variations
The aim of this paper is to establish necessary optimality conditions for optimal control problems governed by steady, incompressible Navier-Stokes equations with shear-dependent viscosity. The main difficulty derives from the fact that equations of this type may exhibit non-uniqueness of weak solutions, and is overcome by introducing a family of approximate control problems governed by well posed generalized Stokes systems and by passing to the limit in the corresponding optimality conditions.
Lee, Mi Jin, Park, Jong Yeoul, Kwon, Young Chel (2003)
International Journal of Mathematics and Mathematical Sciences