Exact controllability of a linear Korteweg-de Vries equation by the flatness approach

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

1 Univalle - Universidad del Valle [Cali]
2 CAS - Centre Automatique et Systèmes
3 CAOR - Centre de Robotique

We consider a linear Korteweg-de Vries equation on a bounded domain with a left Dirichlet boundary control. The controllability to the trajectories of such a system was proved in the last decade by using Carleman estimates. Here, we go a step further by establishing the exact controllability in a space of analytic functions with the aid of the flatness approach.

Mots clés: Korteweg-de Vries equation; exact controllability; controllability to the trajectories; flatness approach; Gevrey class

Domaines: Equations aux dérivées partielles [math.AP]

Ivonne Rivas, Philippe Martin, Lionel Rosier, Pierre Rouchon. Exact controllability of a linear Korteweg-de Vries equation by the flatness approach. 2018. ⟨hal-01767971v1⟩