Global stabilization of a Korteweg-de Vries equation with a distributed control saturated in L 2 -norm - Archive ouverte HAL
Communication Dans Un Congrès Année : 2016

Global stabilization of a Korteweg-de Vries equation with a distributed control saturated in L 2 -norm

Résumé

This article deals with the design of saturated controls in the context of partial differential equations. It is focused on a Korteweg-de Vries equation, which is a nonlinear mathematical model of waves on shallow water surfaces. The aim of this article is to study the influence of a saturating in L 2-norm distributed control on the well-posedness and the stability of this equation. The well-posedness is proven applying a Banach fixed point theorem. The proof of the asymptotic stability of the closed-loop system is tackled with a Lyapunov function together with a sector condition describing the saturating input. Some numerical simulations illustrate the stability of the closed-loop nonlinear partial differential equation.
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Dates et versions

hal-01360576 , version 1 (06-09-2016)
hal-01360576 , version 2 (06-09-2016)

Identifiants

Citer

Swann Marx, Eduardo Cerpa, Christophe Prieur, Vincent Andrieu. Global stabilization of a Korteweg-de Vries equation with a distributed control saturated in L 2 -norm. NOLCOS 2016 - 10th IFAC Symposium on Nonlinear Control Systems, Aug 2016, Monterey, CA, United States. ⟨10.1016/j.ifacol.2016.10.150⟩. ⟨hal-01360576v2⟩
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