Rapid stabilization for a Korteweg-de Vries equation from the left Dirichlet boundary condition

Eduardo Cerpa (1) , Jean-Michel Coron (2)

1 Departamento de Matematica [Valparaiso]
2 LJLL - Laboratoire Jacques-Louis Lions

This paper deals with the stabilization problem for the Korteweg-de Vries equation posed on a bounded interval. The control acts on the left Dirichlet boundary condition. At the right end-point, Dirichlet and Neumann homogeneous boundary conditions are considered. The proposed feedback law forces the exponential decay of the system under a smallness condition on the initial data. Moreover, the decay rate can be tuned to be as large as desired. The feedback control law is designed by using the backstepping method.

Mots clés: Korteweg-de Vries equation; stabilization by feedback; backstepping

Domaines: Optimisation et contrôle [math.OC]

Eduardo Cerpa, Jean-Michel Coron. Rapid stabilization for a Korteweg-de Vries equation from the left Dirichlet boundary condition. IEEE Transactions on Automatic Control, 2013, 58 (7), pp.1688--1695. ⟨10.1109/TAC.2013.2241479⟩. ⟨hal-00730190⟩