Observateurs itératifs en horizon fini. Application à la reconstruction de données initiales pour des EDP d'évolution

Abstract

A new iterative algorithm for solving initial data inverse problems from partial observations has been recently proposed in Ramdani, Tucsnak and Weiss (Ramdani et al., 2010). The algorithm, which can be used for finite-dimensional and infinite-dimensional linear systems, is based on the use of two observers (also called Luenberger observers) used iteratively back and forth in time. In this paper, we first present the algorithm in a finite-dimensional context and then generalize it to Partial Differential Equations (PDE). To conclude, the method is applied to the 1D wave equation and numerical results will be given.