Control of Kawahara equation using flat outputs

TL;DR

This paper introduces a novel flatness-based control method for the linear Kawahara equation, achieving exact controllability in analytic function spaces, extending previous Hilbert uniqueness and Carleman estimate techniques.

Contribution

It applies the flatness approach to a higher-order dispersive PDE, providing a new method for exact controllability in analytic function spaces.

Findings

Achieved exact controllability of the Kawahara equation using flat outputs.

Extended controllability results to analytic function spaces.

Demonstrated the flatness approach as a new tool for higher-order PDE control.

Abstract

In this study we focused on the linear Kawahara equation in a bounded domain, employing two boundary controls. The controllability of this system has been previously demonstrated over the past decade using the Hilbert uniqueness method which involves proving an observability inequality, in general, demonstrated via Carleman estimates. Here, we extend this understanding by achieving the exact controllability within a space of analytic functions, employing the flatness approach which is a new approach for higher-order dispersive systems.