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Solving inverse source wave problem: From observability to observer design

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DDE - The mathematical and statistical foundation of future data-driven engineering

Tiphaine Delaunay, Sébastien Imperiale, Philippe MoireauThe objective of this work is to propose a practical method using observers to estimate a source term of a wave equation, from internal measurements in a subdomain ω. The first part of the work consists in proving an identifiability result from classical observability conditions for wave equations. We deduce that the source reconstruction is an ill-posed inverse problem of order 2. This inverse problem is solved using a sequential strategy that is proven to be equivalent to a minimization of a cost functional with Tikhonov regularization.

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