Edp, commande et observation des systèmes

Résumés

2. Exponential convergence towards consensus for non-symmetric linear first-order systems in finite and infinite dimensions

Emmanuel Trélat (Sorbonne Université)

17/10/2023 14:00

I will first recall some results on how to achieve consensus for well known classes of systems, like the celebrated Cucker-Smale or Hegselmann-Krause 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...

1. Repetitive control for nonlinear systems

Daniele Astolfi (LAGEPP)

17/10/2023 15:00

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 "internal-model principle"...

9. Carleman-based reconstruction algorithm on a wave network

Julie Valein (Université de Lorraine)

17/10/2023 16:30

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...

8. Controllability criteria for 1D hyperbolic systems

Yacine Chitour (L2S)

18/10/2023 09:00

This talk deals with the controllability of linear 1D hyperbolic systems. Reformulating the problem in terms of linear difference equations and based on infinite-dimensional 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...

20. Sequential data assimilation for oncology

Annabelle Collin

18/10/2023 10:30

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...

7. Mortensen observer for sub-differential dynamics

Louis-Pierre Chaintron

18/10/2023 11:30

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 “cost-to-come’’ value function that solves a Hamilton-Jacobi-Bellman (HJB) equation in the viscosity sense. This latter function can also be computed from the stochastic filtering setting using a vanishing noise...

11. Different approaches to integral action in infinite-dimensional nonlinear dynamics

Nicolas Vanspranghe

18/10/2023 14:00

We discuss some recent advances in set-point output regulation for nonlinear systems in infinite dimension. We investigate two distinct approaches: (i) passivity arguments and constrained integral control; (ii) Lyapunov techniques and forwarding-based control. For nonlinear plants modelled by monotone differential inclusions, the passivity-based approach allows us to achieve constant reference...

12. Stabilization results for KdV equations with delay

Emmanuelle Crépeau

18/10/2023 15:00

In this talk, the exponential stability of the nonlinear Korteweg-de Vries equation with delayed terms is considered both in the case of a bounded interval and a tree-shape 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 ...

13. Global stabilization of the cubic defocusing nonlinear Schrödinger equation on the torus

Kevin Le Balch

18/10/2023 16:30

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 semi-global 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)...

16. Lie brackets and interpolation for controllability

Karine Beauchard

19/10/2023 09:00

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 Magnus-type representation formula of the state, a new Hall basis...

17. Placement partiel des pôles de systèmes de dimension infinie : nouvelles perspectives de fonctions hypergéométriques

Islam Boussaada

19/10/2023 10:30

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...

19. Set-valued KKL observer design for non observable systems

Pauline Bernard

19/10/2023 11:30

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 left-inverting the transformation, if the system is backward-distinguishable. But we...

10. Design of low-dimensional controllers for high-dimensional systems

Mathieu Bajodek

19/10/2023 14:00

This talk presents the design of reduced-order controllers for large-scale 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 closed-loop system's poles, this study aims to strike a balance between...

14. Null-controllability of underactuated linear parabolic-transport systems with constant coefficients

Pierre LISSY

19/10/2023 15:00

I will present controllability properties of mixed systems of linear parabolic-transport 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...

5. Stabilization of networks of hyperbolic systems with a chain structure

Jean Auriol (L2S - CNRS)

19/10/2023 16:30

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...

6. Clustering in large language models: an interacting particle systems perspective

Borjan Geshkovski

20/10/2023 09:00

With remarkable empirical success, Transformers enable large language models to compute succinct representations of data using the self-attention 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...

4. Exponentially stable uncertain systems in infinite dimension: converse Lyapunov characterization and some applications

Mario Sigalotti (Inria, Laboratoire Jacques-Louis Lions)

20/10/2023 10:30

We discuss infinite-dimensional forward complete dynamical systems which are subject to uncertainties, representing switching parameters or external disturbances. We characterize the uniform (with respect to uncertainties) local, semi-global, and global exponential stability, in terms of coercive and non-coercive Lyapunov functionals. We illustrate the potential usefulness of the result...

15. Systems subject to input saturation: from ODEs to PDEs

Sophie Tarbouriech

20/10/2023 11:30

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...