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

International audienceThis 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