Bonjour à toutes et tous,
La prochaine séance du Groupe de Travail Contrôle se tiendra le vendredi 17 octobre dans la salle de séminaire du Laboratoire Jacques-Louis Lions (salle 309, 3ème étage du couloir 15-16, Sorbonne Université), avec lien Zoom posté sur la page web du GT Contrôle.
Voici les résumés :
Vendredi 17 octobre 2025
15h30 : M. Krstic (UC San Diego).
Nonholonomic Stabilization: Global, Time-Invariant, Optimal, Robust, and Finite-Time.
From parking, to spacecraft docking, to missile guidance -- nonholonomic models are arguably the most ubiquitous nonlinear control class in today's technology. In concordance with Brockett's 1983 necessary condition, and its Coron-Rosier sharpening in 1994, which deny the stabilizability of nonlinear systems by static state feedback in Cartesian coordinates, the control designs of the past four decades have focused on many workarounds, which either rely on local stabilization of open-loop trajectories or are impractical in certain ways. However, in the polar coordinates (smoothly but not continuously invertibly transformable to Cartesian), no barrier exists for stabilization -- even global. I present feedbacks for a diverse collection of unicycle stabilization problems. For steering-controlled, constant-velocity unicycles, finite-time stable parking is achieved, as well as pursuit of a moving, kinematically inferior evader, which is captured in spite of its arbitrarily vigorous evasive maneuvering. For parking and spacecraft docking, with steering and direction-reversible velocity control, global asymptotic stabilization is achieved using integrator forwarding and backstepping, with strict Lyapunov functions, which, thanks to the drifless nature of the unicycle, yields (1) optimality without solving HJB PDEs (2) infinite "gain margins,” and (3) prescribed/fixed-time parking.
17h : H. Lhachemi (CNRS CentraleSupelec, Paris-Saclay).
Controllability and output feedback stabilization of PDE cascades.
Cascaded systems of partial differential equations (PDEs) have attracted significant attention in recent years due to their relevance in various applications. In this talk, I will present recent results obtained in collaboration with Christophe Prieur and Emmanuel Trélat concerning the controllability and output feedback stabilization of PDE cascades, possibly involving equations of different types.
The focus will be on a prototypical example: a heat-wave PDE cascade with boundary coupling. I will first discuss the controllability properties of this system, namely exact, null exact, and approximate controllability, in suitable Hilbert spaces, under sharp assumptions. Our analysis relies on an Ingham-Müntz-type inequality, which enables us to establish a precise observability estimate for the adjoint system. Interestingly, the resulting controllable subspace, characterized through spectral methods, does not correspond to a standard functional space.
In the second part of the talk, I will exploit the spectral structure of the system to design a systematic and explicit output feedback control law for the heat-wave cascade. I will also briefly present analogous results for other configurations, such as heat-heat cascades and more generally, cascades involving N heat equations.
Notez que le GT Contrôle sera précédé par un exposé de Miroslav Krstic au séminaire hebdomadaire du LJLL, à 14h : https://www.ljll.fr/event/seminaire-du-ljll-miroslav-krstic-universite-de-californie-san-diego/
(thème: Neural operators for PDEs that stabilize PDEs)
Pour plus d'informations, voir page web :
https://www.ljll.fr/gdt-controle/
Bien cordialement,
Le comité scientifique du GT Contrôle,
F. Alabau, C. Bardos, U. Boscain, J.-M. Coron, B. Geshkovski, O. Glass, K. Le Balc'h, J. Le Rousseau, H.-M. Nguyen, J.-P. Puel, M. Sigalotti, E. Trélat
PS: Celles et ceux souhaitant s'abonner aux annonces du GT Contrôle peuvent envoyer un mail à Emmanuel Trélat, emmanuel.trelat@sorbonne-universite.fr
