Jeudi 24 Mai, Jean Auriol et Amaury Hayat vont venir pour présenter leurs travaux de recherche qui concernent (pour parti) le contrôle d’équations hyperboliques.
Sur cette journée du 24 Mai, nous allons en profiter pour faire une journée Control@Lyon autour de cette thématique.
La journée commencera à 11h00 par une présentation d’Alexandre Terrand-Jeanne. Les deux invités donneront alors une présentation dans l’après midi.
Plus d’informations sur Jean et Amaury sur leur page web:
11h00 Alexandre Terrand-Jeanne, (LAGEP, Lyon).
Title : Regulation of linear PDE’s by P-I controller using a Lyapunov approach inspired by forwarding methods. Theory and application to the drilling case
Abstract : Most of the existing results for the regulation of PDE’s are based on semi-group and spectral theory. However, these results impose bounds on the control and the measurement operators. For instance, the boundary regulation by boundary control of hyperbolic PDE can not be addressed. In order to deals with more general systems, we introduce a novel Lyapunov functionnal inspired by nonlinear forwarding technics. Our approach is then illustrated in the case of a drilling system.
13h30 Jean Auriol, ENSMP, Paris
Title : Delay-robust stabilization of first-order linear hyperbolic PDEs.
Abstract: In this talk we solve the problem of delay-robust stabilization for systems composed of two linear first order hyperbolic equations. More precisely, one must go back to the classical trade-off between convergence rate and delay-robustness: we prove that, for systems with strong reflections, canceling the reflection at the actuated boundary will yield zero delay-robustness. The proof is based on the equivalence between the considered class of PDEs and neutral-differential equations with distributed delays. This equivalence is obtained using the backstepping approach as an analysis tool. Finally, some extensions for the robust stabilization in presence of delays, but also uncertainties on the parameters and disturbances are proposed.
14h30 Amaury Hayat, UPMC Paris
Title : Stabilization of 1-D nonlinear hyperbolic systems with boundary controls, and application to Burgers and Saint-Venant equations
Abstract: In this talk, we will review several methods to stabilize such systems with very simple controls at the boundaries, based on a Lyapunov approach. In particular, we will show that the general Saint-Venant system, a well-known model for shallow waters used in practice for the regulation of navigable rivers, has a particular structure that enables the stabilization of any of its regular steady-states by simple boundary controls, whatever the source term is. This remains true even if the source term and the physical data associated (bathymetry, friction, section width, etc.) are unknown. This feat comes from the existence of a remarkable local entropy that we will discuss. We will see how to stabilize a shock steady-state for the Burgers equation and a hydraulic jump modeled by the Saint-Venant equations. Finally, we will talk about the design of Proportional-Integral controllers which are very much used in practice while remaining quite hard to handle mathematically for nonlinear infinite dimensional systems.
Room location: CPE Lyon, 3 rue victor Grignard, 69622 Villeurbanne, Room F101 – Batiment CPE.
Pour rappel, vous pouvez retrouver toutes ces informations sur la page web :