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Null controllability of the 2D heat equation using flatness

Abstract : 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 param-eterizing 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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Philippe Martin, Lionel Rosier, Pierre Rouchon. Null controllability of the 2D heat equation using flatness. Automatica, Elsevier, 2014, 50 (12), pp.3067--3076. ⟨10.1016/j.automatica.2014.10.049⟩. ⟨hal-01112044⟩

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