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Null-controllability, exact controllability, and stabilization of hyperbolic systems for the optimal time

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Abstract

In this paper, we discuss our recent works on the null-controllability, the exact controllability, and the stabilization of linear hyperbolic systems in one dimensional space using boundary controls on one side for the optimal time. Under precise and generic assumptions on the boundary conditions on the other side, we first obtain the optimal time for the null and the exact controllability for these systems for a generic source term. We then prove the null-controllability and the exact controllability for any time greater than the optimal time and for any source term. Finally, for homogeneous systems, we design feedbacks which stabilize the systems and bring them to the zero state at the optimal time. Extensions for the non-linear homogeneous system are also discussed

Dates and versions

hal-03070478 , version 1 (15-12-2020)

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Jean-Michel Coron, Hoai-Minh Nguyen. Null-controllability, exact controllability, and stabilization of hyperbolic systems for the optimal time. CDC 2020 - 59th Conference on Decision and Control, Dec 2020, Jeju Island / Virtual, South Korea. ⟨hal-03070478⟩
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