Abstract
Process monitoring via state estimation is accomplished by the solution of an appropriately posed optimization problem on a receding horizon. The need of a fast solution of the optimization problem is additionally restricted by the a priorily unknown available computation time. Therefore, we propose a multiscale approach with the following features. It provides a coarse approximation after a very short time and upgrades iteratively approximations from coarser levels through further refinement steps. At each refinement step the error is to be reduced by a fixed fraction according to the discretization error while the corresponding computational cost is to remain proportional to the current number of degrees of freedom. Our multiscale discretization is based on suitable wavelet bases. It will be presented along with numerical results as well as with open questions.
Article Note
This work has been supported by the “Deutsche Forschungsgemeinschaft” under grant no. MA1188/6.
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Binder, T., Blank, L., Dahmen, W., Marquardt, W. (2001). Iterative Multiscale Methods for Process Monitoring. In: Hoffmann, KH., Hoppe, R.H.W., Schulz, V. (eds) Fast Solution of Discretized Optimization Problems. ISNM International Series of Numerical Mathematics, vol 138. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8233-0_2
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DOI: https://doi.org/10.1007/978-3-0348-8233-0_2
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