Global stabilization of a Korteweg-de Vries equation with saturating distributed control - Archive ouverte HAL
Article Dans Une Revue SIAM Journal on Control and Optimization Année : 2017

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 partialdifferential equations. It focuses on a Korteweg–de Vries equation, which is a nonlinear mathematicalmodel 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 thisequation and some properties of the saturation function. The proof of the asymptotic stability of theclosed-loop system is separated in two cases: (i) when the control acts on all the domain, a Lyapunovfunction together with a sector condition describing the saturating input is used to conclude on thestability; (ii) when the control is localized, we argue by contradiction. Some numerical simulationsillustrate 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)

Identifiants

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Swann Marx, Eduardo Cerpa, Christophe Prieur, Vincent Andrieu. Global stabilization of a Korteweg-de Vries equation with saturating distributed control. SIAM Journal on Control and Optimization, 2017, 55 (3), pp.1452-1480. ⟨10.1137/16M1061837⟩. ⟨hal-01367622v3⟩
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