2011
DOI: 10.1007/s00211-011-0408-x
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Reconstructing initial data using observers: error analysis of the semi-discrete and fully discrete approximations

Abstract: International audienceA new iterative algorithm for solving initial data inverse problems from partial observations has been recently proposed in Ramdani et al. (Automatica 46(10), 1616-1625, 2010). Based on the concept of observers (also called Luenberger observers), this algorithm covers a large class of abstract evolution PDE's. In this paper, we are concerned with the convergence analysis of this algorithm. More precisely, we provide a complete numerical analysis for semi-discrete (in space) and fully disc… Show more

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Cited by 27 publications
(35 citation statements)
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“…Using the proposed algorithm to construct open loop controls for stable systems is more practical. The rigorous numerical analysis of the back and forth algorithm contained in [5] (for exact controllability) and in Haine and Ramdani [13] (for exact observability) could be useful while implementing our algorithm.…”
Section: The Time-varying Controllermentioning
confidence: 99%
“…Using the proposed algorithm to construct open loop controls for stable systems is more practical. The rigorous numerical analysis of the back and forth algorithm contained in [5] (for exact controllability) and in Haine and Ramdani [13] (for exact observability) could be useful while implementing our algorithm.…”
Section: The Time-varying Controllermentioning
confidence: 99%
“…System (14)- (16). For the sake of clarity we will use the same notation for the estimation error, namelyx…”
Section: Convergence Estimate Using Interpolated Observationsmentioning
confidence: 99%
“…(48) In the previous equation we denoted by I the interpolation operator which, in the case of linear interpolation, is given by (16) and by ε n+1 d the interpolation error of the observations without noise, as presented in Theorem 3.6. In a general case, assuming that I ∈ L(Z, Z) is a bounded linear operator, the proof of Theorem 3.6 remains valid, so that the estimate (41) reads…”
Section: Convergence Estimate Using Interpolated Observationsmentioning
confidence: 99%
See 1 more Smart Citation
“…This fact provides a first example of the use of these non-uniform grids in the context of inverse problems. We also refer to the works [15] for another strategy (based on the used of back and forth observers) in a situation in which the observability property does not necessarily hold uniformly with respect to the discretization parameters.…”
Section: Further Comments and Open Problemsmentioning
confidence: 99%