Séminaire d'Automatique du plateau de Saclay : Stabilization of nonlinear infinite-dimensional systems subject to saturations

Séminaire le 19 Octobre 2017, 10h00 à CentraleSupelec (Gif-sur-Yvette) Salle du conseil du L2S - B4.40
Swann Marx (Postdoctoral researcher, LAAS-CNRS)

This presentation provides contributions in stabilization methods for nonlinear dynamical systems. In particular, it focuses on the analysis of infinite-dimensional systems subject to saturated inputs.

In the first part, we will introduce a more general class of saturations than the one known for finite-dimensional systems. When bounding a linear stabilizing feedback law with such nonlinearity, a well-posedness result together with an attractivity result will be stated for systems whose open-loop is described by (possibly nonlinear) operators generating strongly continuous semigroup of contractions. The attractivity result will be proved by using the LaSalle's Invariance Principle together with some precompactness properties. 

In the second part, a particular nonlinear partial differential equation is studied, namely the Korteweg-de Vries equation, that models long waves in water of relatively shallow depth. A control actuating on a small part of the channel will be considered. This control will be modified with two different types of saturations. The attractivity result will be proved by using Lyapunov argument and a contradiction argument. Finally, the results will be illustrated with some numerical simulations.

Bio. Swann Marx graduated in 2014 from "Ecole Supérieure de Cachan", France. He got his Ph.D. in the Departement of Automatic at the GIPSA-lab, in Grenoble, France. He is currently a postdoctoral researcher at the LAAS-CNRS, in Toulouse, France. His main research interests are stabilization of partial differential equations with constrained inputs, output feedback stabilization and optimal control of nonlinear partial differential equations.