CONTROLLABILITY OF A COUPLED WAVE SYSTEM WITH A SINGLE CONTROL AND DIFFERENT SPEEDS

Pierre Lissy (1) , Jingrui Niu (2)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
2 LJLL (UMR_7598) - Laboratoire Jacques-Louis Lions

We consider an exact controllability problem in a smooth bounded domain Ω of R d , d ∈ N * , for a coupled wave system, with two different speeds and a single control acting on an open subset ω satisfying the Geometric Control Condition and acting on one speed only. Actions for the wave equations with the second speed are obtained through a coupling term. Firstly, we construct appropriate state spaces with compatibility conditions associated with the coupling structure. Secondly, in these well-prepared spaces, we prove that the coupled wave system is exactly controllable if and only if the coupling structure satisfies an operator Kalman rank condition.

Mots clés: Wave equation, controllability, unique continuation, coupled system

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

Pierre Lissy, Jingrui Niu. CONTROLLABILITY OF A COUPLED WAVE SYSTEM WITH A SINGLE CONTROL AND DIFFERENT SPEEDS. 2022. ⟨hal-03682501⟩