Stabilization of a linear Korteweg-de Vries equation with a saturated internal control

Swann Marx (1) , Eduardo Cerpa (2) , Christophe Prieur (1) , Vincent Andrieu (3, 4)

1 GIPSA-SYSCO - GIPSA - Systèmes non linéaires et complexité
2 Departamento de Matematica, Universidad Tecnica Federico Santa Maria
3 LAGEP - Laboratoire d'automatique et de génie des procédés
4 Bergische Universität Wuppertal

— This article deals with the design of saturated controls in the context of partial differential equations. It is focused on a linear Korteweg-de Vries equation, which is a mathematical model of waves on shallow water surfaces. In this article, we close the loop with a saturating input that renders the equation nonlinear. The well-posedness is proven thanks to the nonlinear semigroup theory. The proof of the asymptotic stability of the closed-loop system uses a Lyapunov function.

Domaines: Equations aux dérivées partielles [math.AP]; Automatique / Robotique

Swann Marx, Eduardo Cerpa, Christophe Prieur, Vincent Andrieu. Stabilization of a linear Korteweg-de Vries equation with a saturated internal control. ECC 2015 - 14th European Control Conference, Jul 2015, Linz, Austria. ⟨hal-01193019⟩