Distributed source identification for wave equations: an observer-based approach

TL;DR

This paper presents an observer-based iterative method to identify unknown source terms in wave equations using boundary measurements, achieving minimal observation time.

Contribution

It introduces a novel back-and-forth iterative observer approach for source identification in wave equations, optimizing the observation time.

Findings

Successfully reconstructs source term q(x) from boundary measurements

Achieves minimal observation time for accurate source identification

Demonstrates effectiveness through theoretical analysis and simulations

Abstract

In this paper, we consider a wave equation on a bounded interval where the initial conditions are known (are zero) and we are rather interested in identifying an unknown source term $q(x)$ thanks to the measurement output $y$ which is the Neumann derivative on one of the boundaries. We use a back-and-forth iterative procedure and construct well-chosen observers which allow to retrieve $q$ from $y$ in the minimal observation time.