Alessandro Scagliotti

TUM Munich

30 novembre 2023, 14.00
Salle X133
Campus Toulon

Ensemble optimal control: ResNets, diffeomorphisms approximation and
Normalizing Flows

In the last years it was observed that Residual Neural
Networks (ResNets) can be interpreted as discretizations of control
systems, bridging ResNets (and, more generally, Deep Learning) with
Control Theory. In the first part of this seminar we formulate the task
of a data-driven reconstruction of a diffeomorphism as an ensemble
optimal control problem. In the second part we adapt this machinery to
address the problem of Normalizing Flows: after observing some samplings
of an unknown probability measure, we want to (approximately) construct
a transport map that brings a “simple” distribution (e.g., a Gaussian)
onto the unknown target distribution. In both the problems we use tools
from $\Gamma$-convergence to study the limiting case when the size of
the data-set tends to infinity.

This talk is based on the papers

Deep Learning approximation of diffeomorphisms via linear-control systems.

Normalizing flows as approximations of optimal transport maps via
linear-control neural ODEs

Térence Bayen

LMA (Avignon)

19 janvier 2023, 11.00
Salle X 133
Campus Toulon

A hybrid maximum principle including regional switching parameters.

 In this presentation, we consider a Mayer optimal control problem where the controlled system is defined over a partition of the euclidean space, and we assume that the dynamics depends on some additional regionally switching parameter. This means that the parameter should remain constant as long as the trajectory belongs to a given stratum, but, in contrast with optimal control problems including (constant) parameters, it is now authorized to change its value each time the system enters into a new stratum. This framework is motivated by several applications arising in the context of aerospace engineering or in epidemiology (typically when a loss of control occurs). In this presentation, we give the necessary optimality conditions in this framework in the spirit of a hybrid maximum principle. The necessary optimality conditions involve a jump of the covector at the interface between two strata and also an averaged gradient condition related to the regionally switching parameter. We shall also give some insights how to obtain such a result using needle’s type variations. 

Eugenio Pozzoli

Eugenio Pozzoli

20 octobre 2022, 14.30
Salle X 133
Campus Toulon

Contrôlabilité des systèmes quantiques en dimension infinie

L’étude des propriétés de contrôlabilité d’un système quantique joue un rôle important dans les applications en physique et en chimie, comme par example la spectroscopie et l’information quantique. Les questions que j’aborderai dans cet exposé sont principalement deux : (i) le système (fermé) peut-il être contrôlé parmi tous ses états ? (ii) quels états peuvent être atteints en temps petit ? La question (i) est un problème de contrôlabilité bilinéaire (globale). La question (ii) est un problème d’accessibilité bilinéaire en petit temps, lié au problème du temps minimal. Dans le cadre où l’état évolue dans un espace infini-dimensionnel, je présenterai quelques réponses aux questions (i) en utilisant des approximations fini-dimensionnelles avec des contrôles périodiques et (ii) en utilisant une technique de saturation issue du contrôle géométrique avec des contrôles pas bornés. Je montrerai aussi des applications de ces résultats au contrôle de la dynamique rotationelle des molécules, vues comme des corps rigides quantiques.

Angelo Alessandri (DIPTEM, Università degli Studi di Genova)

Angelo Alessandri
Università degli Studi di Genova


25 Avril 2019, 14.00
salle X133
Campus Toulon

Moving Horizon Methods for Constrained and Unconstrained Estimation of Dynamic Systems


Moving-horizon estimation (MHE) for dynamic systems relies on the simple idea of using a limited amount of most recent information to estimate the state variables at the current time instant, thus ensuring intrinsic robustness. The literature on MHE is vast since it has followed a favorable trend induced by the success of the model predictive control. MHE has been applied to estimation of many kind of systems in different application fields. The talk will concern the various approaches adopted to perform MHE to systems with linear, nonlinear, and switching dynamics and different optimization tools.