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

Abstract : 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.
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Philippe Martin, Ivonne Rivas, Lionel Rosier, Pierre Rouchon. Exact controllability of a linear Korteweg-de Vries equation by the flatness approach. SIAM Journal on Control and Optimization, Society for Industrial and Applied Mathematics, 2019, 57 (4), pp.2467-2486. ⟨10.1137/18M1181390⟩. ⟨hal-01767971v2⟩

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