Control of Kawahara equation using flat outputs

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.