Soha Kanso et William Jussiau

Séminaire jeunes chercheurs Diapro – 21 novembre 2024 – Saint-Jérôme

William Jussiau, jeune docteur de l’ONERA

Titre : Lois de commande pour le contrôle des écoulements oscillateurs

Résumé : Cette thèse porte sur la synthèse de lois de commande pour les écoulements oscillateurs à faible nombre de Reynolds. Nous y étudions deux configurations canoniques en 2D : l’écoulement autour d’un cylindre, et l’écoulement au-dessus d’une cavité ouverte. Ces deux cas d’étude présentent un équilibre stationnaire instable, et un régime d’oscillations auto-entretenues – respectivement, un cycle limite et un attracteur torique. L’objectif principal est la synthèse de lois de commande pour supprimer complètement le régime oscillatoire, pour réduire la traînée moyenne, les vibrations structurelles ou le rayonnement acoustique tonal. En pratique, la synthèse de lois de commande pour ces systèmes est rendue difficile par la diversité des phénomènes dynamiques émergeant des équations de Navier-Stokes, non-linéaires et de dimension infinie. Nous proposons trois méthodes distinctes pour réaliser cette tâche, utilisant respectivement une paramétrisation des correcteurs stabilisants, la continuation numérique et le formalisme de la résolvante moyenne.

Soha KANSO, doctorante, CRAN, Université de Lorraine, Nancy. ATER Polytech Nancy

Titre : Safe Reinforcement Learning and Degradation Tolerant Control Design

Résumé : Safety-critical dynamical systems are essential in various industries, such as aerospace domain, autonomous systems, robots in healthcare area etc., where violating safety constraints and structural or functional failure may lead to catastrophic consequences. A significant challenge in these systems is the degradation of components and actuators, which can compromise safety and stability of systems. As such, incorporating system’s health state within the control design framework is essential to ensure tolerance to functional degradation. Moreover, such system models often involve uncertainties and incomplete knowledge, especially as components degrade, altering system dynamics in a nonlinear manner. This underscores the necessity for the development of learning approaches that incorporate the available data within the control learning paradigm.
In this context, Reinforcement Learning (RL) emerges as a powerful approach, capable of learning optimal control laws for partially or fully unknown dynamic systems, in the presence of input-output data (without the exact knowledge of system models). However, a major challenge in applying RL methods to safety-critical systems lies in ensuring safety during both the exploration and exploitation phases. Exploration involves introducing probing noise to the policy in order to collect informative data across the state space, while exploitation refers to applying the learned policy to optimize performance in real operations.

To this end, this presentation will first explore an off-policy safe RL approach for the regulation and the tracking problem in continuous-time nonlinear systems affine in control input. A novel approach will be presented that ensures system stability and safety during all phases: initialization, exploration, and exploitation. By using quadratic programming with control Lyapunov function (CLF) and control barrier function (CBF), the proposed approach ensures stability and safety of the system during initialization and exploration phases. Furthermore, during exploitation, the safety of the learned policy is ensured by augmenting the cost function with reciprocal CBFs, thus balancing performance optimization and safety. The second part of the talk will focus on addressing actuator degradation, which poses a critical threat to system performance and stability. A degradation-tolerant controller based on RL is introduced for continuous-time nonlinear systems affine in control input. The objectives are twofold: ensuring system stability despite degradation, and decelerating the degradation rate to complete missions and extend actuator life. This is achieved by imposing constraints on degradation rates using CBFs. Furthermore, a cyclic off-policy algorithm is presented, enabling iterative exploration and exploitation across multiple learning cycles. This allows for continuous updates of neural network weights with recent information on degradation levels, ensuring that the learned policy effectively stabilizes the system while accounting for degradation effects.

In the developed approaches, neural networks are used to approximate both the value function and the control policy, thereby enabling efficient learning. Simulation results will be presented to demonstrate the efficiency of the proposed approaches.

Salim Zekraoui et Anes Lazri

Vendredi 8 novembre 9h, Saint-Jérôme

Anes Lazri, L2S, Université Paris Saclay, lien Scholar

Titre : Analyse et contrôle de la synchronisation dans les réseaux de systèmes complexes

Résumé :
Les réseaux complexes sont omniprésents dans notre quotidien, qu’il
s’agisse de réseaux électriques, de réseaux sociaux ou encore de
réseaux biologiques. Ces réseaux interconnectent de nombreux systèmes
individuels, créant ainsi des interactions qui influencent leur
comportement collectif. En plus de la dynamique propre à chaque
système, une dynamique collective émerge, donnant lieu à des
phénomènes tels que la synchronisation ou le regroupement en clusters.

Lors de ce séminaire, nous aborderons deux aspects majeurs influençant
la synchronisation : la force des interconnexions et la topologie du
réseau. Nous explorerons comment ces facteurs impactent la dynamique
des réseaux de systèmes complexes, notamment dans des scénarios où :

  • Le réseau est partitionné en plusieurs groupes capables de communiquer entre eux, permettant à ces groupes de former des « macro-noeuds » qui peuvent atteindre un comportement commun ou un consensus ;
  • Les couplages entre nœuds ne sont pas suffisamment forts pour garantir une synchronisation complète, entraînant l’émergence de clusters distincts au sein du réseau.

Nous examinerons ces phénomènes avec un certain degré de
généralité, mais aussi à travers des exemples concrets tels que les
réseaux d’oscillateurs. Le but de cette présentation est de discuter
des algorithmes de contrôle et des outils d’analyse permettant
d’assurer la synchronisation et le consensus dans ces réseaux. Nous
mettrons également en lumière des cas particuliers où le
multi-consensus émerge, et nous analyserons différents types de
topologies et de connexions dans ce contexte.

Salim Zekraoui, LAGEPP, Université Lyon 1, lien Scholar

Titre : Finite-time control of LTI/PDE systems with input delay using a PDE-based approach.

Abstract :
Time-delay systems are ubiquitous in control engineering. As time delays may cause performance degradation or instability of the closed-loop system, control design becomes a central issue; however, due to the infinite-dimensional nature of those systems, control continues to be challenging. Moreover, in many applications, like rendezvous and missile guidance, the transient process must occur within a given time while also managing the effect of the delay. The need to meet these time constraints and to increase temporal performance has motivated non-asymptotic stabilization (stabilization + convergence in finite time). In this talk, we will focus on the non-asymptotic stabilization of some classes of infinite-dimensional systems, namely LTI systems with input delays and reaction-diffusion PDEs with boundary input delays, utilizing a PDE backstepping-based approach. The approach consists mainly of rewriting the initial delayed LTI/PDE system as an ODE/PDE-PDE cascade system; and then transforming the resulting cascaded system, using an invertible transformation, into a well-chosen non-asymptotically stable target system. We show that the inverse transformation transfers the non-asymptotic stability property back to the initial ODE/PDE-PDE cascade system. 

In addition, we consider the problem of boundary state-dependent finite/fixed-time stabilization of reaction-diffusion PDEs. To the best of our knowledge, this problem has remained open in the literature for a considerable long time. We tackled this challenging problem using classical methods related to Control Lyapunov functions.

Tarek Ahmed-Ali

LINEACT-CESI, ENSICAEN

vendredi 20 septembre 2024, 10h
Salle des commissions
Campus Saint-Jérôme

Adaptive observers: From finite to infinite dimensional systems

Abstract:
This talk is devoted to adaptive observers for some classes of distributed parameters systems. We will show that several existing results for finite dimensional systems can be extended to infinite dimensional systems More precisely, new finite-dimensional adaptive observers are proposed for uncertain heat equation and a class of linear Kuramoto-Sivashinsky equation (KSE) with local output. The observers are based on the modal decomposition approach and use a classical persistent excitation condition to ensure prac tical exponential convergence of both states and parameters estimation. An important challenge of this work is that it treats the case when the function φ1(·,t) of the unknown part in the PDE model, depends on the spatial variable and φ1(·,t) ∈ L2(0,1) .

Pere Colet and Damia Gomila

Instituto de Física Interdisciplinar y Sistemas Complejos, IFISC (CSIC-UIB)

11 juillet 2024, 14h
Salle des commissions
Campus Saint-Jérôme
https://univ-amu-fr.zoom.us/j/88505334444?pwd=38rJZyBA8Df7TDvy1nCra7u0QstRaV.1

Pere Colet
Power grid frequency fluctuations in scenarios of large penetration of renewables


As the transition towards a sustainable energy system accelerates, conventional power plants are progressively replaced by variable renewable energy sources. This reduces the overall flexibility of the grid, requiring additional control strategies to ensure stable operation. We consider a model for the high-voltage grid including conventional and variable renewable generation, as well as demand variations. By assimilating load and generation data, the model reproduces frequency fluctuations with the current power mix with a high degree of accuracy. Moreover, it allows to simulate the frequency dynamics for different scenarios with a very high penetration of renewable energy. As a case study, we analyze the power grid of Gran Canaria, which is isolated, and the Balearic Islands, connected to mainland with a DC cable, considering an increasing share of, respectively wind and solar generation.

Damia Gomila
Power grid frequency fluctuations and smart devices with dynamic demand control

The increase of electric demand and the progressive integration of renewable sources threatens the stability of the power grid. To solve this issue, several methods have been proposed to control the demand side instead of increasing the spinning reserve in the supply side. Here we focus on dynamic demand control (DDC), a method in which smart devices can autonomously delay its scheduled operation if the electric frequency is outside a suitable range. DDC can effectively reduce small and medium size frequency fluctuations but, due to the need of recovering pending tasks, the probability of large demand peaks, and hence large frequency fluctuations, may actually increase. Although these events are very rare they can potentially trigger a failure of the system and therefore strategies to avoid them have to be addressed. We show also that an improved method including communication among DDC devices belonging to a given group, such that they can coordinate opposite actions to keep the group demand more stable can reduce the amount of pending tasks by a factor 10 while large frequency fluctuations are significantly reduced or even completely avoided.

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

LIS (UMR CNRS 7020)

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.