# Controllability of some evolution equations by the flatness approach

Authors: Philippe Martin, Lionel Rosier and Pierre Rouchon, Trends in Control and Inverse Problems, 2018, pp. 1-38

The aim of these notes is to introduce the flatness approach for the controllability of PDEs. After discussing the null controllability of the heat equation in dimension one and in dimension N for cylinders, we turn our attention to more general parabolic equation with nonsmooth coefficients. Next we apply the flatness approach to the determination of the reachable states for the heat equation. Finally, we show how to modify the method to deal with the 1D Schro ̈dinger equation. In each situation, the theoretical results are illustrated by numerical simulations. The notes end with some future directions of research.

BibTeX:

@Incollection{,

author = {Philippe Martin, Lionel Rosier and Pierre Rouchon},

title = {Controllability of some evolution equations by the flatness approach},

booktitle = {Trends in Control and Inverse Problems},

editor = {Gerbi, Kaïs Ammari Stéphane},

publisher = {American Institute of Mathematical Sciences},

pages = {1-38},

year = {2018},

abstract = {The aim of these notes is to introduce the flatness approach for the controllability of PDEs. After discussing the null controllability of the heat equation in dimension one and in dimension N for cylinders, we turn our attention to more general parabolic equation with nonsmooth coefficients. Next we apply the flatness approach to the determination of the reachable states for the heat equation. Finally, we show how to modify the method to deal with the 1D Schro ̈dinger equation. In each situation, the theoretical results are illustrated by numerical simulations. The notes end with some future directions of research.}, }

The aim of these notes is to introduce the flatness approach for the controllability of PDEs. After discussing the null controllability of the heat equation in dimension one and in dimension N for cylinders, we turn our attention to more general parabolic equation with nonsmooth coefficients. Next we apply the flatness approach to the determination of the reachable states for the heat equation. Finally, we show how to modify the method to deal with the 1D Schro ̈dinger equation. In each situation, the theoretical results are illustrated by numerical simulations. The notes end with some future directions of research.

BibTeX:

@Incollection{,

author = {Philippe Martin, Lionel Rosier and Pierre Rouchon},

title = {Controllability of some evolution equations by the flatness approach},

booktitle = {Trends in Control and Inverse Problems},

editor = {Gerbi, Kaïs Ammari Stéphane},

publisher = {American Institute of Mathematical Sciences},

pages = {1-38},

year = {2018},

abstract = {The aim of these notes is to introduce the flatness approach for the controllability of PDEs. After discussing the null controllability of the heat equation in dimension one and in dimension N for cylinders, we turn our attention to more general parabolic equation with nonsmooth coefficients. Next we apply the flatness approach to the determination of the reachable states for the heat equation. Finally, we show how to modify the method to deal with the 1D Schro ̈dinger equation. In each situation, the theoretical results are illustrated by numerical simulations. The notes end with some future directions of research.}, }