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Iterative Algorithms for Multiscale State Estimation, Part 1: Concepts

Author

Listed:
  • T. Binder

    (RWTH)

  • L. Blank

    (RWTH)

  • W. Dahmen

    (RWTH)

  • W. Marquardt

    (RWTH)

Abstract

The objective of the present investigation is to explore the potential of multiscale refinement schemes for the numerical solution of dynamic optimization problems arising in connection with chemical process systems monitoring. State estimation is accomplished by the solution of an appropriately posed least-squares problem. To offer at any instant of time an approximate solution, a hierarchy of successively refined problems is designed using a wavelet-based Galerkin discretization. In order to fully exploit at any stage the approximate solution obtained also for an efficient treatment of the arising linear algebra tasks, we employ iterative solvers. In particular, we will apply a nested iteration scheme to the hierarchy of arising equation systems and adapt the Uzawa algorithm to the present context. Moreover, we show that, using wavelets for the formulation of the problem hierarchy, the largest eigenvalues of the resulting linear systems can be controlled effectively with scaled diagonal preconditioning. Finally, we deduce appropriate stopping criteria and illustrate the characteristics of the solver with a numerical example.

Suggested Citation

  • T. Binder & L. Blank & W. Dahmen & W. Marquardt, 2001. "Iterative Algorithms for Multiscale State Estimation, Part 1: Concepts," Journal of Optimization Theory and Applications, Springer, vol. 111(3), pages 501-527, December.
    • Handle: RePEc:spr:joptap:v:111:y:2001:i:3:d:10.1023_a:1012645826935
    DOI: 10.1023/A:1012645826935
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    References listed on IDEAS

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    1. T. Binder & L. Blank & W. Dahmen & W. Marquardt, 2001. "Iterative Algorithms for Multiscale State Estimation, Part 2: Numerical Investigations," Journal of Optimization Theory and Applications, Springer, vol. 111(3), pages 529-551, December.
    2. C. H. Hsiao & W. J. Wang, 1999. "Optimal Control of Linear Time-Varying Systems via Haar Wavelets," Journal of Optimization Theory and Applications, Springer, vol. 103(3), pages 641-655, December.
    3. C. H. Hsiao & W. J. Wang, 1999. "State Analysis and Optimal Control of Time-Varying Discrete Systems via Haar Wavelets," Journal of Optimization Theory and Applications, Springer, vol. 103(3), pages 623-640, December.
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    Cited by:

    1. T. Binder & L. Blank & W. Dahmen & W. Marquardt, 2001. "Iterative Algorithms for Multiscale State Estimation, Part 2: Numerical Investigations," Journal of Optimization Theory and Applications, Springer, vol. 111(3), pages 529-551, December.

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