Null Controllability of the 2D Heat Equation Using Flatness

TL;DR

This paper demonstrates a straightforward flatness-based method to achieve null controllability of the 2D heat equation with boundary control, providing explicit control laws and numerical validation.

Contribution

It introduces a novel flatness approach for boundary control of the 2D heat equation, enabling explicit control law derivation and practical implementation.

Findings

Explicit control law successfully steers the system to zero

Numerical experiments validate the effectiveness of the flatness approach

Method offers a straightforward alternative to existing control techniques

Abstract

We derive in a direct and rather straightforward way the null controllability of a 2-D heat equation with boundary control. We use the so-called flatness approach, which consists in parameterizing the solution and the control by the derivatives of a "flat output". This provides an explicit control law achieving the exact steering to zero. Numerical experiments demonstrate the relevance of the approach.