On Thursday, September 14, at 2:00 pm in room E302 of the CPE building, Swann Marx (GIPSA Lab-LAGEP) will present his thesis work. He will support his thesis on 20 September in Grenoble. His work focuses on the stabilization of EDPs by saturated control.

This is the summary of his presentation.

ABSTRACT :
This thesis provides contributions in stabilization methods for nonlinear dynamical systems. In particular, it focuses on two main subjects: the analysis of infinite-dimensional systems subject to saturated inputs and the design of output feedback laws for either infinite-dimensional or finite-dimensional systems.

The presentation will focus on the first subject.

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 defined by operators generating strongly continuous semigroup of contractions. The attractivity result will be proved by using the LaSalle’s Invariance Principle together with some compactness 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.