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

Abstract : 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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SIAM Journal on Control and Optimization, Society for Industrial and Applied Mathematics, 2017, 55 (3), pp.1452-1480. 〈http://epubs.siam.org/doi/abs/10.1137/16M1061837〉
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Dernière modification le : vendredi 15 février 2019 - 16:34:03
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  • HAL Id : hal-01367622, version 3
  • ARXIV : 1609.05728

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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, Society for Industrial and Applied Mathematics, 2017, 55 (3), pp.1452-1480. 〈http://epubs.siam.org/doi/abs/10.1137/16M1061837〉. 〈hal-01367622v3〉

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