Journée thématique "Optimisation et Contrôle"
Journée thématique
"Optimisation et Contrôle"
Marseille, 5 décembre 2014
Conférenciers invités
Marco Caponigro (Paris, CNAM)
Camille Laurent (Paris, LJLL)
Pierre Lissy (Paris, CEREMADE)
Francesco Rossi (Marseille,LSIS)
Organisateurs
Lorenzo Brasco, Morgan Morancey, Enea Parini
Programme
Le workshop, qui consiste de quatre exposés d'une heure chacun, se
déroulera dans la salle de conférences de la FRUMAM située au 2e étage (plan d'accès).
Le repas du midi sera offert aux participants qui se seront inscrits en ligne (formulaire), dans la limite des disponibilités.
- Matin
- 9h30-10h30: exposé de P. Lissy
- 11h00-12h00: exposé de C. Laurent
- Après-midi
- 14h00-15h00: exposé de M. Caponigro
- 15h30-16h30: exposé de F. Rossi
Résumés
Marco Caponigro: "Sparse stabilization of multi-agent systems"
We study controlled alignment models in finite dimension and we explore
how to enforce pattern formation or convergence to consensus in a group
of interacting agents. In particular we focus on the design of control
strategies requiring a small amount of external intervention: we want to
minimize at each instant of time the number of leaders needed to steer
the systems to the desired state. These sparsity features are desirable
in view of practical issues.
Camille Laurent: "Contrôle bilinéaire de l'équation de Schrödinger"
Dans cet exposé, je parlerai de la contrôlabilité de l'équation de
Schrödinger quand le contrôle agit comme un terme de potentiel dans
l'équation. Je présenterai deux cas en expliquant leur liens:
-le cas 1D quand on ne contrôle que l'amplitude du potentiel avec un
potentiel fixe. La preuve utilise un "effet régularisant"
-le cas 2D où le potentiel satisfait une équation de Poisson et le
contrôle est la valeur au bord. On fera le lien avec la théorie plus
standard du contrôle au bord de l'équation de Schrödinger.
Pierre Lissy: "Non-localization of eigenfunctions for some Sturm-Liouville operators "
In this talk, we will study the extremal spectral problem of minimizing
the L2-norm of the eigenfunctions of some Sturm-Liouville operators on
measurable subsets V, with respect both to those V having a prescribed
measure and to the nonnegative bounded potentials a(.) having a
prescribed essentially upper bound (and also possibly a prescribed
L1-norm). We prove the existence of minimizers (V*,a*), and that under
some conditions a* is bang-bang, moreover we give precise upper bounds
on the number of connected components of V* and switches of a*. we also
explain some consequences concerning the control of the corresponding
wave equation in large time. This is a joint work with Thibault Liard
(LJLL, University Pierre and Marie Curie) and Yannick Privat (LJLL,
University Pierre and Marie Curie).
Francesco Rossi: "Control of kinetic models for crowds"
I will show two different models to describe (and control) evolution of
crowds.
In the first part, I will discuss the Cucker-Smale model, that describes
alignement of birds. I will show that its mean-field limit, that is a
transport PDE, can be controlled by an external agent to align all birds
to a given direction.
In the second part, I will discuss more general models for crowds. In
this case, we choose a fixed number of leaders, and study optimal
control problems in which the control acts on these leaders only.
Instead, the number N of other agents, the followers, goes to infinity.
At the limit, we find a coupled ODE-PDE equation, with the ODE for the
leaders and the PDE for the followers. I will show that an optimal
control problem for such ODE-PDE can be solved as the limit for N to
infinity of finite dimensional optimal control problems with each N.
Dernière modification: 02/12/2014