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Null Controllability of the 1D Heat Equation Using Flatness

Authors: Martin, P. Rosier, L. and Rouchon P., 1st IFAC workshop on Control of Systems Governed by Partial Differential Equations (CPDE2013), September 25-27, 2013, Paris
We derive in a straightforward way the null controllability of a 1-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. We also give accurate error estimates when the various series involved are replaced by their partial sums, which is paramount for an actual numerical scheme. Numerical experiments demonstrate the relevance of the approach.
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BibTeX:
@Proceedings{,
author = {Martin, P. Rosier, L. and Rouchon P.},
editor = {},
title = {Null Controllability of the 1D Heat Equation Using Flatness},
booktitle = {1st IFAC workshop on Control of Systems Governed by Partial Differential Equations (CPDE2013)},
volume = {},
publisher = {},
address = {Paris},
pages = {},
year = {2013},
abstract = {We derive in a straightforward way the null controllability of a 1-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. We also give accurate error estimates when the various series involved are replaced by their partial sums, which is paramount for an actual numerical scheme. Numerical experiments demonstrate the relevance of the approach.},
keywords = {Partial differential equations, heat equation, boundary control, null controllability, path planning, flatness.}}