Experimental Study of the HUM Control Operator for Linear Waves

Gilles Lebeau (1) , Maëlle Nodet (2)

1 JAD - Laboratoire Jean Alexandre Dieudonné
2 MOISE - Modelling, Observations, Identification for Environmental Sciences

We consider the problem of the numerical approximation of the linear controllability of waves. All our experiments are done in a bounded domain Ω of the plane, with Dirichlet boundary conditions and internal control. We use a Galerkin approximation of the optimal control operator of the continuous model, based on the spectral theory of the Laplace operator in Ω. This allows us to obtain surprisingly good illustrations of the main theoretical results available on the controllability of waves, and to formulate some questions for the future analysis of optimal control theory of waves.

Mots clés: controllability; numerical control; linear wave equations

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

Gilles Lebeau, Maëlle Nodet. Experimental Study of the HUM Control Operator for Linear Waves. 2008. ⟨inria-00316195v1⟩