Output feedback stabilization of the Korteweg-de Vries equation

Swann Marx (1) , Eduardo Cerpa (2)

1 GIPSA-SYSCO - GIPSA - Systèmes non linéaires et complexité
2 UTFSM - Universidad Tecnica Federico Santa Maria [Valparaiso]

This paper presents an output feedback control law for the Korteweg-de Vries equation. The control design is based on the backstepping method and the introduction of an appropriate observer. The local exponential stability of the closed-loop system is proven. Some numerical simulations are shown to illustrate this theoretical result.

Mots clés: Korteweg-de Vries equation; output feedback; backstepping; nonlinear system

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

Swann Marx, Eduardo Cerpa. Output feedback stabilization of the Korteweg-de Vries equation. Automatica, 2018, 28, pp.210-217. ⟨10.1016/j.automatica.2017.07.057⟩. ⟨hal-01367650v3⟩