Null controllability of the 2D heat equation using flatness

Philippe Martin (1) , Lionel Rosier (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 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.

Domaines: Automatique / Robotique

Philippe Martin, Lionel Rosier, Pierre Rouchon. Null controllability of the 2D heat equation using flatness. Decision and Control (CDC), 2013 IEEE 52nd Annual Conference on, Dec 2013, Firenze, Italy. pp.3738 - 3743, ⟨10.1109/CDC.2013.6760459⟩. ⟨hal-00971484⟩