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Null controllability of the heat equation using flatness

Authors: P. Martin, L. Rosier and P. Rouchon, Automatica, Vol 50, pp. 3067--3076, 2014
We derive in a direct and rather straightforward way the null controllability of the N-dimensional heat equation in a bounded cylinder with boundary control at one end of the cylinder. We use the so-called flatness approach, which consists in parameterizing the solution and the control by the derivatives of a “flat output”. This yields an explicit control law achieving the exact steering to zero. Replacing the involved series by partial sums we obtain a simple numerical scheme for which we give explicit error bounds. Numerical experiments demonstrate the relevance of the approach.
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author = {L. Rosier and P. Rouchon P. Martin},
title = {Null controllability of the heat equation using flatness},
journal = {Automatica},
volume = {50},
number = {},
pages = {3067-3067},
year = {2014},