Michel Fliess

LIX – Palaiseau

7 décembre 2023, 14.30
Salle X133
Campus Toulon

Atténuer les congestions internet grâce aux outils de l’automatique

Active Queue Management (AQM) for mitigating Internet congestion has been addressed via various feedback control syntheses, especially P, PI, and PID regulators, by using a linear approximation where the round trip time, i.e., the delay, is assumed to be constant. This constraint is lifted here by using a nonlinear modeling with a variable delay, introduced more than 20 years ago. This delay, intimately linked to the congestion phenomenon, may be viewed as a flat output. All other system variables, especially the control variable, i.e., the packet loss ratio, are expressed as a function of the delay and its derivatives: they are frozen if the delay is kept constant. This flatness-like property, which demonstrates the mathematical discrepancy of the linear approximation adopted until today, yields also our control strategy in two steps: Firstly, designing an open-loop control, thanks to straightforward Flatness-Based Control (FBC) techniques, and secondly, closing the loop via Model-Free Control (MFC) in order to take into account severe model mismatches, like, here, the number of TCP sessions. Several convincing computer simulations, which are easily implementable, are presented and discussed.

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

Hassan Haghighi


12 octobre 2023, 14.00
Salle des commissions
Campus St. Jérôme

Path Planning According to the Fault Tolerance and Modeling. Application in: Autonomous Emergency Landing for Aircraft

 In the field of controlling complex systems, a key focus is on developing strategies to handle technical, dynamic, structural defects, and faults. This study analyzes equation stability and state-space structure changes to identify stable system poles despite the presence of defects. Additionally, it employs Dubin’s equations to swiftly devise emergency landing routes. To implement in a case study project, we construct sample sets of stable poles for the system according to the defects and calculate corresponding path as admissible set. From these samples, we design a path planning system to select specific points. Our concept integrates Dubin’s path for emergency landings, enabling an optimization system to choose from admissible stable routes.

Swann Marx

L2SN (UMR CNRS 6004) Nantes

27 avril 2023, 14.00
Salle des commissions
Campus St. Jérôme

Singular perturbation analysis for a coupled KdV-ODE system

This talk will be about the singular perturbation analysis of
a Korteweg-de Vries equation, which is a nonlinear PDE modeling waves on
shallow water surfaces, coupled with an ODE. The coupled system may
admit different time-scales, and this particular feature will be taken
into account when analysing the asymptotic stability of the coupled
system. To introduce our methodology, we will first explain how it can
be applied on scalar ODEs. We will then give some insights on the
difficulties when applying it on already known coupled PDE-ODE systems.
Finally, we will show how one can apply this methodology for the KdV-ODE
system under consideration. This talk is based on a joint work with
Eduardo Cerpa, professor at the Universidad Catolica de Chile.

David Hill

LIMOS (UMR CNRS 6158 – UCA – Clermont Auvergne INP)

30 mars 2023, 14.00
Salle des commissions
Campus St. Jérôme

Reproductibilité et répétabilité des simulations stochastiques.

L’un des critères majeurs de la scientificité d’une étude de recherche est la reproductibilité. Dans cet exposé, nous présenterons les principales définitions autour de la reproductibilité, elles ont évolué récemment à l’ACM en 2020. Nous examinerons dans quelle mesure les travaux d’informatique et de simulation sont concernés. Nous donnerons quelques exemples d’applications incluant des simulations stochastiques parallèles, qui sont trop souvent présentées comme non reproductibles. Toute personne souhaitant produire un travail scientifique en simulation a intérêt à prêter attention à la reproductibilité numérique de ses résultats. Des différences significatives peuvent être observées dans les résultats de simulations parallèles si les meilleures pratiques ne sont pas appliquées. Nous verrons que même dans ce contexte, il est possible de reproduire les mêmes résultats numériques en mettant en œuvre une méthode rigoureuse testée jusqu’à un milliard de threads. Il est ainsi possible de vérifier les résultats parallèles avec leurs contreparties séquentielles et ce avant un passage « à l’échelle », gagnant ainsi en confiance dans les modèles développés. Ce séminaire présentera quelques bonnes pratiques pour des simulations stochastiques parallèles, permettant même de faire face erreurs silencieuses qui impactent les supercalculateurs (dont la machine Exascale présentée l’an passé à Hambourg). 

Biographie :

David Hill est professeur à l’Université Clermont Auvergne, il effectue ses recherches au LIMOS (UMR CNRS 6158 – UCA – Clermont Auvergne INP). Après un doctorat en 1993 et une Habilitation à diriger les recherches en 2000 dans le domaine de la simulation stochastique à événements discrets appliquée à l’environnement ou aux Sciences Fondamentales, il a servi à l’Université Blaise Pascal en tant que Vice-Président délégué au TIC, à la direction du centre Régional de Calcul (CRRI) et 2 fois en tant que directeur adjoint de l’ISIMA (école d’ingénieur clermontoise membre de Clermont Auvergne INP). David Hill s’occupe actuellement de la Graduate Track de l’INP. Il s’intéresse à la thématique de la recherche reproductible à partir de 2014 et a récemment supervisé des recherches au CERN en calcul à hautes performances. 

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.