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Edp, commande et observation des systèmes
from
Tuesday, October 17, 2023 (8:00 AM)
to
Friday, October 20, 2023 (5:00 PM)
Monday, October 16, 2023
Tuesday, October 17, 2023
1:45 PM
1:45 PM  2:00 PM
Room: Salle de Conférence
2:00 PM
Exponential convergence towards consensus for nonsymmetric linear firstorder systems in finite and infinite dimensions

Emmanuel Trélat
(
Sorbonne Université
)
Exponential convergence towards consensus for nonsymmetric linear firstorder systems in finite and infinite dimensions
Emmanuel Trélat
(
Sorbonne Université
)
2:00 PM  3:00 PM
Room: Salle de Conférence
I will first recall some results on how to achieve consensus for well known classes of systems, like the celebrated CuckerSmale or HegselmannKrause models. When the systems are symmetric, convergence to consensus is classically established by proving, for instance, that the usual variance is an exponentially decreasing Lyapunov function: this is a "L^2 theory". When the systems are not symmetric, no L^2 theory existed until now and convergence was proved by means of a "L^\infty theory". In this talk I will show how to develop a L^2 theory by designing an adequately weighted variance, and how to obtain the sharp rate of exponential convergence to consensus for general finite and infinitedimensional linear firstorder consensus systems. If time allows, I will show applications in which one is interested in controlling vote behaviors in an opinion model. This is a work in collaboration with Laurent Boudin and Francesco Salvarani.
3:00 PM
Repetitive control for nonlinear systems

Daniele Astolfi
(
LAGEPP
)
Repetitive control for nonlinear systems
Daniele Astolfi
(
LAGEPP
)
3:00 PM  4:00 PM
Room: Salle de Conférence
In this talk we revise a series of recent advances on the challenging problem of robust periodic output regulation, that is, the problem of tracking periodic references (and/or rejection periodic disturbances) for nonlinear systems, robustly with respect to model uncertainties. This problem is well understood in the context of linear systems thanks to the celebrated "internalmodel principle" established during the 70's. But, for nonlinear systems, it is still open. This work aim at clarifying challenging and possible solutions, connecting the theory of repetitive control with output regulation by means of infinitedimensional dynamic regulators. In this context, a strong connection between the output regulation problem and the theory of repetitive control is established. Finally, we propose a new feedback design for a repetitive control scheme for minimumphase nonlinear systems. Such a scheme is based on the forwarding approach and allows to deal with systems with highorder relative degree between the input and the regulated output.
4:00 PM
4:00 PM  4:30 PM
Room: Salle de Conférence
4:30 PM
Carlemanbased reconstruction algorithm on a wave network

Julie Valein
(
Université de Lorraine
)
Carlemanbased reconstruction algorithm on a wave network
Julie Valein
(
Université de Lorraine
)
4:30 PM  5:30 PM
Room: Salle de Conférence
In this presentation, we will be interested in an inverse problem set on a tree shaped network where each edge behaves according to the wave equation with potential, external nodes have Dirichlet boundary conditions and internal nodes follow the Kirchoff law. The main goal is the reconstruction of the potential everywhere on the network, from the Neumann boundary measurements at all but one external vertices. Leveraging from the Lipschitz stability of this inverse problem, we aim at providing an efficient reconstruction algorithm based on the use of an appropriate global Carleman estimate. This is a joint work with Lucie Baudouin, Maya de Buhan and Emmanuelle Crépeau.
Wednesday, October 18, 2023
9:00 AM
Controllability criteria for 1D hyperbolic systems

Yacine Chitour
(
L2S
)
Controllability criteria for 1D hyperbolic systems
Yacine Chitour
(
L2S
)
9:00 AM  10:00 AM
Room: Salle de Conférence
This talk deals with the controllability of linear 1D hyperbolic systems. Reformulating the problem in terms of linear difference equations and based on infinitedimensional realization theory, we obtain both necessary and sufficient conditions for the approximate and exact controllability, expressed in the frequency domain as well as an upper bound for the controllability times. The results are applied to dynamic network systems. This is a joint work with S. Fueyo, G. Mazanti and M. Sigalotti.
10:00 AM
10:00 AM  10:30 AM
Room: Salle de Conférence
10:30 AM
Sequential data assimilation for oncology

Annabelle Collin
Sequential data assimilation for oncology
Annabelle Collin
10:30 AM  11:30 AM
Room: Salle de Conférence
The development of PDE models capable of describing tumor growth may help monitor disease progression or predict the efficacy of different therapeutic strategies. However, to be truly informative or predictive, these models need to be corrected and/or parameterized with available observations. The goal of this talk is to present some sequential data assimilation strategies that address these types of problems. More specifically, in the first part we focus on a Luenberger observer that can handle 3D tumor front data. In the second part, we focus on the combination of a Luenberger observer with a populationbased Kalman observer, which allows the use of repeated measurements in configurations with common priors (e.g., multiple subjects in a clinical trial or repeated biological measurements) when data are sparse or corrupted by noise. Theoretical results and numerical illustrations with synthetic and real data are presented for both parts.
11:30 AM
Mortensen observer for subdifferential dynamics

LouisPierre Chaintron
Mortensen observer for subdifferential dynamics
LouisPierre Chaintron
11:30 AM  12:30 PM
Room: Salle de Conférence
In his 1968 article, Mortensen proposed a recursive method to compute a causal estimator for observed deterministic dynamics. Using tools from control theory, his approach relies on a “costtocome’’ value function that solves a HamiltonJacobiBellman (HJB) equation in the viscosity sense. This latter function can also be computed from the stochastic filtering setting using a vanishing noise procedure. This talk proposes an adaptation of Mortensen’s approach to subdifferential dynamics defined through variational inequalities. We introduce a suitable notion of costtocome function that solves a HJB equation with Neumann boundary condition in the viscosity sense, and we define a Mortensen observer from it. We eventually link the costtocome function for this constrained setting to its stochastic filtering counterpart.
12:30 PM
12:30 PM  2:00 PM
Room: Salle de Conférence
2:00 PM
Different approaches to integral action in infinitedimensional nonlinear dynamics

Nicolas Vanspranghe
Different approaches to integral action in infinitedimensional nonlinear dynamics
Nicolas Vanspranghe
2:00 PM  3:00 PM
Room: Salle de Conférence
We discuss some recent advances in setpoint output regulation for nonlinear systems in infinite dimension. We investigate two distinct approaches: (i) passivity arguments and constrained integral control; (ii) Lyapunov techniques and forwardingbased control. For nonlinear plants modelled by monotone differential inclusions, the passivitybased approach allows us to achieve constant reference tracking with simple output feedback control. Additionally, the integrator state can be constrained into a desired convex subset of the output space. On the other hand, the forwardingLyapunov approach does not require impedance passivity of the system, and relies instead on the existence of a suitable invariant manifold for the plantintegrator cascade. This motivates the introduction of a new class of nonlinear operator Sylvester equations, which we are able to handle in some relevant particular cases. Both approaches are applied to selected nonlinear PDE models. Joint work with Lucas Brivadis, Pietro Lorenzetti, Lassi Paunonen and George Weiss.
3:00 PM
Stabilization results for KdV equations with delay

Emmanuelle Crépeau
Stabilization results for KdV equations with delay
Emmanuelle Crépeau
3:00 PM  4:00 PM
Room: Salle de Conférence
In this talk, the exponential stability of the nonlinear Kortewegde Vries equation with delayed terms is considered both in the case of a bounded interval and a treeshape network. We will give two types of proof, one constructive with some Lyapunov techniques and the other more general with observability results. We will also discuss the results from a numerical point of view. This is joint work with L. Baudouin, J. Valein, C. Prieur and H. Parada.
4:00 PM
4:00 PM  4:30 PM
Room: Salle de Conférence
4:30 PM
Global stabilization of the cubic defocusing nonlinear Schrödinger equation on the torus

Kevin Le Balch
Global stabilization of the cubic defocusing nonlinear Schrödinger equation on the torus
Kevin Le Balch
4:30 PM  5:30 PM
Room: Salle de Conférence
In this talk, I will focus on the stabilization of defocusing nonlinear Schrödinger equations on manifolds, arising naturally as models of wave propagation in fiber optics. I will first recall local and semiglobal results that have been obtained since the beginning of the 2000's. Then, I will introduce a method that I have developed in collaboration with Jérémy Martin to prove the (uniform) global stabilization of the cubic defocusing nonlinear Schrödinger equation on the ddimensional torus, d=1, 2 or 3.
8:00 PM
8:00 PM  11:00 PM
Room: Salle de Conférence
Thursday, October 19, 2023
9:00 AM
Lie brackets and interpolation for controllability

Karine Beauchard
Lie brackets and interpolation for controllability
Karine Beauchard
9:00 AM  10:00 AM
Room: Salle de Conférence
This talk will survey old and recent results on the local controllability of control systems modeled by ODEs, focussing on results stated using Lie brackets of the vector fields defining the dynamics. We will propose a unified approach to determine and prove obstructions to local controllability. This approach relies on a recent Magnustype representation formula of the state, a new Hall basis of the free Lie algebra over two generators and GagliardoNirenberg interpolation inequalities. This approach allows to recover the known necessary conditions, but also to prove a conjecture of 1986 due to Kawski and many other new necessary conditions. Finally, we will see how these results translate for PDEs. This is a joint work with Frederic Marbach, Jeremy Le Borgne and Mégane Bournissou.
10:00 AM
10:00 AM  10:30 AM
Room: Salle de Conférence
10:30 AM
Placement partiel des pôles de systèmes de dimension infinie : nouvelles perspectives de fonctions hypergéométriques

Islam Boussaada
Placement partiel des pôles de systèmes de dimension infinie : nouvelles perspectives de fonctions hypergéométriques
Islam Boussaada
10:30 AM  11:30 AM
Room: Salle de Conférence
Récemment, dans le cadre de l’étude de la stabilité exponentielle des systèmes gouvernés par des équations différentielles fonctionnelles, un nouveau lien entre les fonctions hypergéométriques dégénérées et la distribution des zéros de la fonction caractéristique associée aux équations différentielles linéaires à retard a été mis en évidence. Cela a permis la caractérisation d’une propriété des systèmes à retard connue sous le nom de "la dominance induite par la multiplicité", ce qui a ouvert une nouvelle direction dans la conception de commande de faible complexité non seulement pour les systèmes à retard mais aussi pour certaines classes d’équations aux dérivées partielles en utilisant une idée de placement partiel des pôles. Dans cet exposé, après avoir rappelé quelques prérequis, les fondements d’une méthodologie de placement de pôles seront présentés, puis des questions ouvertes seront abordées. Certaines applications telles que le contrôle actif des vibrations intervenant dans les structures flexibles et la modélisation de l’action du système nerveux central sur l’équilibre humain mettront l’accent sur les bénéfices de la stratégie de contrôle proposée. Enfin, des fonctionnalités d’un nouveau logiciel dédié appelé "P3δ" (https://cutt.ly/p3delta) seront présentées. Cet exposé reprend essentiellement des résultats de travaux méthodologiques en commun avec Silviu Niculescu (L2S, Université ParisSaclay), Guilherme Mazanti (L2S, Université ParisSaclay) et Wim Michiels (NUMA, KU Leuven), et des résultats de travaux applicatifs en commun avec Sami Tliba (L2S, Université ParisSaclay), Tamas Insperger ( MTABME, Budapest University of Technology and Economics) et Tomas Vyhlidal (Czech Technical University in Prague).
11:30 AM
Setvalued KKL observer design for non observable systems

Pauline Bernard
Setvalued KKL observer design for non observable systems
Pauline Bernard
11:30 AM  12:30 PM
Room: Salle de Conférence
We present the theory of KKL observer design, which consists in finding a smooth change of coordinates transforming the system dynamics into a linear filter of the output. Its interest is that the state of the original system can then be reconstructed by implementing this filter from any initial condition and leftinverting the transformation, if the system is backwarddistinguishable. But we show that this theory is still relevant when the latter assumption does not hold, namely when distinct solutions may generate the same output, and thus be indistinguishable : the system state could then be reconstructed modulo its indistinguishable class. More precisely, the KKL transformation is no longer injective and its “leftinverse” is allowed to be setvalued, yielding a setvalued KKL observer. Assuming the transformation is fullrank and its preimage has constant cardinality, we show the existence of a globally defined setvalued leftinverse that is Lipschitz in the Hausdorff sense and that is linked to the backwardindistinguishable sets, so that the setvalued KKL observer converges in the Hausdorff sense to the backwardindistinguishable set of the system solution. When, additionally, a given output is generated by a specific number of solutions not converging to each other, we show that the designed observer asymptotically reconstructs each of those solutions.
12:30 PM
12:30 PM  2:00 PM
Room: Salle de Conférence
2:00 PM
Design of lowdimensional controllers for highdimensional systems

Mathieu Bajodek
Design of lowdimensional controllers for highdimensional systems
Mathieu Bajodek
2:00 PM  3:00 PM
Room: Salle de Conférence
This talk presents the design of reducedorder controllers for largescale dynamical systems. The objective is to develop efficient control strategies that ensure stability and robustness with reduced computational complexity. By leveraging the concept of partial pole placement, which involves placing a subset of the closedloop system's poles, this study aims to strike a balance between reducedorder modeling and control effectiveness. The proposed approach addresses the challenges posed by highdimensional systems and provides a systematic framework for controller design. Two case studies are investigated in detail: timedelay systems and ODEreactiondiffusion interconnections.
3:00 PM
Nullcontrollability of underactuated linear parabolictransport systems with constant coefficients

Pierre LISSY
Nullcontrollability of underactuated linear parabolictransport systems with constant coefficients
Pierre LISSY
3:00 PM  4:00 PM
Room: Salle de Conférence
I will present controllability properties of mixed systems of linear parabolictransport equations, with possibly nondiagonalizable diffusion matrix, on the 1D torus, coupled by constant coupling terms. The distributed control acts through a constant matrix, with possibly less controls than equations. In small time or for not regular enough initial data, these systems are never controllable, whereas in large time, nullcontrollability holds, for regular initial data, iff a spectral Kalman rank condition is verified. This is a joint work with Armand Koenig.
4:00 PM
4:00 PM  4:30 PM
Room: Salle de Conférence
4:30 PM
Stabilization of networks of hyperbolic systems with a chain structure

Jean Auriol
(
L2S  CNRS
)
Stabilization of networks of hyperbolic systems with a chain structure
Jean Auriol
(
L2S  CNRS
)
4:30 PM  5:30 PM
Room: Salle de Conférence
In this talk, we focus on recent developments for the stabilization of networks of elementary hyperbolic systems with a chain structure. Such a structure arises in multiple industrial processes such as electric power transmission systems, traffic networks, or torsional vibrations in drilling devices. The objective is to design output feedback control laws that stabilize the chain using the available actuators and sensors. The different systems composing the network are called elementary in the sense that when taken alone, we know how to design stabilizing outputfeedback control laws. We will first consider the case where the actuators and sensors are available at one end of the chain. Using appropriate state predictors, we will present a recursive approach to stabilize the whole chain. Then, we will focus on the case where the actuators and sensors are only available at the junction between two subsystems composing the chain. We will show that such a configuration does not always guarantee the controllability of the chain. Under appropriate controllability/observability conditions, we will design simple stabilizing control laws. Our approach will be based on rewriting the system as Integral Delay Equations (IDEs) with pointwise and distributed control terms. Finally, we will show how the proposed techniques can be used to develop output feedback control laws for traffic flow on two cascaded freeway segments connected by a junction.
Friday, October 20, 2023
9:00 AM
Clustering in large language models: an interacting particle systems perspective

Borjan Geshkovski
Clustering in large language models: an interacting particle systems perspective
Borjan Geshkovski
9:00 AM  10:00 AM
Room: Salle de Conférence
With remarkable empirical success, Transformers enable large language models to compute succinct representations of data using the selfattention mechanism. We model these architectures as interacting particle systems in the spirit of models in collective behaviour and opinion dynamics, allowing us to show the appearance of various clustering/coagulation phenomena. Associated control problems will also be discussed. Based on joint work with Cyril Letrouit, Yury Polyanskiy, and Philippe Rigollet.
10:00 AM
10:00 AM  10:30 AM
Room: Salle de Conférence
10:30 AM
Exponentially stable uncertain systems in infinite dimension: converse Lyapunov characterization and some applications

Mario Sigalotti
(
Inria, Laboratoire JacquesLouis Lions
)
Exponentially stable uncertain systems in infinite dimension: converse Lyapunov characterization and some applications
Mario Sigalotti
(
Inria, Laboratoire JacquesLouis Lions
)
10:30 AM  11:30 AM
Room: Salle de Conférence
We discuss infinitedimensional forward complete dynamical systems which are subject to uncertainties, representing switching parameters or external disturbances. We characterize the uniform (with respect to uncertainties) local, semiglobal, and global exponential stability, in terms of coercive and noncoercive Lyapunov functionals. We illustrate the potential usefulness of the result discussing exponential stability of nonlinear retarded systems with uncertainties and exponential stability preservation under sampling for semilinear control switching systems.
11:30 AM
Systems subject to input saturation: from ODEs to PDEs

Sophie Tarbouriech
Systems subject to input saturation: from ODEs to PDEs
Sophie Tarbouriech
11:30 AM  12:30 PM
Room: Salle de Conférence
In this talk some results dealing with the control of some PDEs (such as the wave equation) subject to input nonlinearities (such as saturations) are considered. Leveraging the results obtained in the ODE context, stability analysis and control design conditions are proposed by using adequate Lyapunov functions and quadratic abstractions of the input nonlinearity. Static and dynamic controllers are discussed. Recent extensions to the more complex case resulting from the cascade of an ODE, a nonlinearity and a PDE are also discussed.