Global stabilization of a Korteweg-de Vries equation with a distributed control saturated in L2-norm. Issue 18 (2016)

• Record Type: Journal Article
• Authors: Marx, Swann; Cerpa, Eduardo; Prieur, Christophe; Andrieu, Vincent
• Is Part Of: IFAC-PapersOnLine. Volume 49:Issue 18(2016)
• Page Start: 122
• Page End: 127
• Publication Date: 2016
• Subjects: Partial differential equation -- saturation control -- nonlinear control system -- global stability -- Lyapunov function; Automatic control -- Periodicals; 629.805
• DOI: 10.1016/j.ifacol.2016.10.150
• Languages: English
• ISSNs: 2405-8963

Abstract

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.