Null controllability of the 2D heat equation using flatness

Philippe Martin (1) , Lionel Rosier (1, 2) , Pierre Rouchon (1)

1 CAS - Centre Automatique et Systèmes
2 IECL - Institut Élie Cartan de Lorraine

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.

Mots clés: Partial differential equations; heat equation; boundary control; motion planning; flatness; null controllability

Domaines: Automatique / Robotique; Mathématiques générales [math.GM]

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