Null controllability of the 1D 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 straightforward way the null controllability of a 1-D heat equation with boundary control. We use the so-called {\em 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.

Domaines: Optimisation et contrôle [math.OC]; Equations aux dérivées partielles [math.AP]

Philippe Martin, Lionel Rosier, Pierre Rouchon. Null controllability of the 1D heat equation using flatness. 1st IFAC workshop on Control of Systems Governed by Partial Differential Equations (CPDE2013), Sep 2013, Paris, France. pp.1-7. ⟨hal-00971487⟩