Global stabilization of a Korteweg-de Vries equation with saturating distributed control - Archive ouverte HAL
Pré-Publication, Document De Travail Année : 2016

Global stabilization of a Korteweg-de Vries equation with saturating distributed control

Résumé

This article 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. Two different types of saturated controls are considered. 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.
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Dates et versions

hal-01367622 , version 1 (16-09-2016)
hal-01367622 , version 2 (20-09-2016)
hal-01367622 , version 3 (29-06-2017)

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Swann Marx, Eduardo Cerpa, Christophe Prieur, Vincent Andrieu. Global stabilization of a Korteweg-de Vries equation with saturating distributed control. 2016. ⟨hal-01367622v2⟩
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