Exponential convergence of an observer based on partial field measurements for the wave equation

Abstract : We analyze an observer strategy based on partial --~i.e.~in a subdomain --~measurements of the solution of a wave equation, in order to compensate for unknown initial conditions. We prove the exponential convergence of this observer under a non-standard observability condition, whereas using measurements of the time-derivative of the solution would lead to a standard observability condition arising in stabilization and exact controlability. Nevertheless, we directly relate our specific condition to the classical geometric control condition. Finally, we provide some numerical illustrations of the effectiveness of the approach.
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Submitted on : Tuesday, December 4, 2012 - 5:25:27 PM
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Dominique Chapelle, Nicolae Cîndea, Maya de Buhan, Philippe Moireau. Exponential convergence of an observer based on partial field measurements for the wave equation. Mathematical Problems in Engineering, Hindawi Publishing Corporation, 2012, 2012, pp.12. ⟨10.1155/2012/581053⟩. ⟨inria-00619504v2⟩

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