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

Abstract : 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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Submitted on : Tuesday, September 6, 2016 - 11:39:59 AM
Last modification on : Thursday, August 22, 2019 - 11:32:03 AM

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  • HAL Id : hal-01360576, version 2
  • ARXIV : 1609.01447

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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. 10th IFAC Symposium on Nonlinear Control Systems (NOLCOS 2016), Aug 2016, Monterey, CA, United States. ⟨hal-01360576v2⟩

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