On the regularization of dynamic data reconciliation problems

Dynamic data reconciliation problems are discussed from the perspective of the mathematical theory of ill-posed inverse problems. Regularization is of crucial importance to obtain satisfactory estimation quality of the reconciled variables. Usually, some penalty is added to the least-squares objecti...

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Bibliographic Details
Published in:Journal of process control 2002-06, Vol.12 (4), p.557-567
Main Authors: Binder, T., Blank, L., Dahmen, W., Marquardt, W.
Format: Article
Language:English
Subjects:
Adaptive discretization
Dynamic data reconciliation
Dynamic optimisation
Input estimation
Inverse problems
State estimation
Wavelets
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Summary:Dynamic data reconciliation problems are discussed from the perspective of the mathematical theory of ill-posed inverse problems. Regularization is of crucial importance to obtain satisfactory estimation quality of the reconciled variables. Usually, some penalty is added to the least-squares objective to achieve a well-posed problem. However, appropriate discretization schemes of the time-continuous problem act themselves as regularization, reducing the need of problem modification. Based on this property, we suggest to refine successively the discretization of the continuous problem starting from a coarse grid, to find a suitable regularization which renders a good compromise between (measurement) data and regularization error in the estimate. In particular, our experience supports the conjecture, that non-equidistant discretization grids offer advantages over uniform grids.
ISSN:0959-1524
1873-2771
DOI:10.1016/S0959-1524(01)00021-X