Exact controllability of a linear Korteweg-de Vries equation by the flatness approach

TL;DR

This paper demonstrates exact controllability of a linear Korteweg-de Vries equation within an analytic function space using the flatness approach, advancing beyond previous Carleman estimate methods.

Contribution

It introduces the flatness approach to achieve exact controllability of the linear Korteweg-de Vries equation in an analytic function space, extending prior results.

Findings

Exact controllability achieved in an analytic function space.

Flatness approach effectively used for control design.

Advances beyond Carleman estimate techniques.

Abstract

We consider a linear Korteweg-de Vries equation on a bounded domain with a left Dirichlet boundary control.The controllability to the trajectories of such a system was proved in the last decade by using Carleman estimates.Here, we go a step further by establishing the exact controllability in a space of analytic functions with the aid of the flatness approach.