Controllability of Parabolic Equations by the Flatness Approach

Philippe Martin (1) , Lionel Rosier (2, 1) , Pierre Rouchon (1, 3)

1 CAS - Centre Automatique et Systèmes
2 CAOR - Centre de Robotique
3 QUANTIC - QUANTum Information Circuits

— We consider linear one-dimensional parabolic equations with space dependent coefficients that are only measurable and that may be degenerate or singular. We prove the null controllability with one boundary control by following the flatness approach, which provides explicitly the control and the associated trajectory as series. As an application, we consider the heat equation with a discontinuous coefficient in the principal part. The note ends with a numerical experiment which demonstrates the effectiveness of the method.

Domaines: Mathématiques [math]; Optimisation et contrôle [math.OC]; Sciences de l'ingénieur [physics]; Automatique / Robotique

Philippe Martin, Lionel Rosier, Pierre Rouchon. Controllability of Parabolic Equations by the Flatness Approach. Evolution Equations: Long Time Behavior and Control, Cambridge University Press, pp.161-178, 2017, ⟨10.1017/9781108304023.009⟩. ⟨hal-01769232⟩