Displaying similar documents to “Controllability theorem for nonlinear dynamical systems”

Exact boundary controllability of a nonlinear KdV equation with critical lengths

Jean-Michel Coron, Emmanuelle Crépeau (2004)

Journal of the European Mathematical Society

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We study the boundary controllability of a nonlinear Korteweg–de Vries equation with the Dirichlet boundary condition on an interval with a critical length for which it has been shown by Rosier that the linearized control system around the origin is not controllable. We prove that the nonlinear term gives the local controllability around the origin.

Exact boundary controllability for the Korteweg-de Vries equation on a bounded domain

L. Rosier (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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The exact boundary controllability of linear and nonlinear Korteweg-de Vries equation on bounded domains with various boundary conditions is studied. When boundary conditions bear on spatial derivatives up to order 2, the exact controllability result by Russell-Zhang is directly proved by means of Hilbert Uniqueness Method. When only the first spatial derivative at the right endpoint is assumed to be controlled, a quite different analysis shows that exact controllability holds...