GLOBAL STABILIZATION OF A KORTEWEG-DE6WRIES EQUATION WITH SATURATING DISTRIBUTED CONTROL

Séance du jeudi 4 Février 2016, Salle L 224, 14h00
Swann MARX, Gipsa-Lab, Grenoble
This presentation deals with the design of saturated controls in the context of partial differential equations. It focuses on a Korteweg-de Vries equation, which is a nonlinear mathematical model of waves on shallow water surfaces. In this article, we close the loop with a saturating localized control. We study two different types of saturation. The well-posedness is proven applying a Banach fixed point theorem, using some estimates of this equation and some properties of the saturation function. The proof of the asymptotic stability of the closed-loop system is separated in two cases: i) when the control acts on all the domain, a Lyapunov function together with a sector condition describing the saturating input is used to conclude on the stability; ii) when the control is localized, we argue by contradiction. Some numerical simulations illustrate the stability of the closed-loop nonlinear partial differential equation.