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Multi-Scale Aspects in Linear and Nonlinear Estimation and Control

  • Chapter
Nonlinear Model Based Process Control

Part of the book series: NATO ASI Series ((NSSE,volume 353))

Abstract

Multi-scale models of processing systems offer an attractive alternative to models defined in the time- or frequency-domain. They are the outgrowth of a series of developments which came about with the advent of the wavelet decomposition for the analysis of discrete signals. Multi-scale models are defined on dyadic or higher-order trees. The nodes of such trees are used to index the values states, inputs and outputs, modeling errors, and measurement errors. These values are localized in both time and scale (range of frequencies), and thus they offer a hybrid domain that is particularly conducive for estimation and control problems. In this paper we introduce a formal framework for the formulation of multi-scale models on trees, which are consistent with their time-domain counterparts. Such models lead to a multi-scale control theory and the definition of the corresponding transfer functions, stability, controllability, and observability concepts for systems on trees. Fusion of control actions and measurements at different rates as well as their implications on the controllability and observability of dynamic systems are also examined. Of particular significance is the issue of closure between the models in the time- and the time-scale domains, which constrains the type of physico-chemical processes that can be modeled on a tree.

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References

  1. Bakshi, B. R. and Stephanopoulos, G. (1994) Representation of process trends-III. multiscale extraction of trends from process data, Computers Chem. Engng 18, 267–302.

    Article  CAS  Google Scholar 

  2. Bakshi, B. and Stephanopoulos, G. (1993) Wave-net: a multiresolution, hierarchical neural network with localized learning, AICHE Journal 39.

    Google Scholar 

  3. Basseville, M., Benveniste, A., Chou, K.C., Golden, S.A., Nikoukhah, R. and Willsky, A.S. (1992) Modeling and estimation of multiresolution stochastic processes, IEEE Transactions in Information Theory, 38.

    Google Scholar 

  4. Basseville, M., Benveniste, A., and Willsky, A.S. (1992) Multiscale-autoregressive processes, part I: Schur-Levinson parametrizations, IEEE Transactions on Signal Processing, 40.

    Google Scholar 

  5. Basseville, M., Benveniste, A., and Willsky, A.S. (1992) Multiscale-autoregressive processes, part I: Lattice structures for whitening and modeling, IEEE Transactions on Signal Processing, 40.

    Google Scholar 

  6. Bell, M. L., Limebeer, D. J. N., and Sargent, R.W.H. (1996) Robust receding horizon optimal control, CPSE Consortium Meeting.

    Google Scholar 

  7. Benveniste, A., Nikoukhah, R., and Willsky, A. (1994) Multiscale system theory IEEE Transactions on Circuits and Systems-1: Fundamental Theory and Applications, 41.

    Google Scholar 

  8. Beylkin, G. (1991) Wavelets, multiresolution analysis and fast numerical algorithms, Draft of INRIA lecture notes.

    Google Scholar 

  9. Beylkin, G. and Brewster, M.E. (1994) A multiresolution strategy for numerical homogenization, Preprint.

    Google Scholar 

  10. Carrier J. F. and Stephanopoulos, G. (1997) Wavelet-based modulation in control-relevant Process identification, to appear in AIChE Journal.

    Google Scholar 

  11. Cheong. C. K., Aizawa, K., Hatori, M., and Saito, T., (1995) Nonlinear noise reduction on zero-crossing representations of a wavelet transform, Electronics and Communications in Japan, 78.

    Google Scholar 

  12. Chou, K.C., (1991) A stochastic approach to multiscale signal processing, PhD Thesis, Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science.

    Google Scholar 

  13. Chou, K.C., Willsky, A., and Benveniste, A. (1994) Multiscale recursive estimation, data fusion, and regularization, IEEE Transactions on Automatic Control, 39.

    Google Scholar 

  14. Chou, K.C., Willsky, A., and Nikoukhah, R. (1994) Multiscale systems, Kaiman filters, and Ricatti equations, IEEE Transactions on Automatic Control, 39.

    Google Scholar 

  15. Cutler C. R., and Yocum, F.H., (1991) Experience with the DMC inverse for identification, Technical Report.

    Google Scholar 

  16. Daubechies, I., (1992) Ten Lectures on Wavelets, SIAM.

    Google Scholar 

  17. Daubechies, I., (1990) The wavelet transform, time-frequency localization and signal analysis IEEE Trans. Inf. Theory, 36, 961–1005.

    Article  Google Scholar 

  18. Dyer, M., (1997) Multi-scale models for time-varying linear systems, MIT-LISPE, Technical Report, under preparation.

    Google Scholar 

  19. Eaton, J. W., and Rawlings, J.B. (1991) Model predictive control of chemical processes Chemical Engineering Science.

    Google Scholar 

  20. Feng, W., (1996) The application of time-frequency techniques to process control and identification Ph.D. Thesis, Texas A&M Univ.

    Google Scholar 

  21. Fieguth, P.W., (1995) Application of multiscale estimation to large scale multidimensional imaging and remote sensing problems, PhD Thesis, Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science.

    Google Scholar 

  22. Genceli, H., Nikolau, M. (1996) New approach to constrained predictive control with simultaneous model identification, AICHE Journal, 42.

    Google Scholar 

  23. Gilbert, E.G. and Tan, K.T. (1991) Linear systems with state and control constraints: The theory and application of maximal output admissable sets, IEEE Transactions on Automatic Control, 36(9): 1008–1020.

    Article  Google Scholar 

  24. Gopinath, R., and Bequette, B. (1991) Multirate model predictive control, an analysis for single-input single-output systems, Proc of PSE’97 II.5.1.

    Google Scholar 

  25. Goupillaud, P., Grossman, A., and Morlet, J. (1995) Cycle octave and related transform in seismic signal analysis, Geoexploration, 23, 85–102.

    Article  Google Scholar 

  26. Graps, A. (1995) An introduction to wavelets, IEEE Computational Science and Engineering, 2.

    Google Scholar 

  27. Irving, W. (1995) Multiscale stochastic realization and model identification with applications to large-scale estimation problems, PhD Thesis, Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science.

    Google Scholar 

  28. Jawerth, B., and Sweldens, W. (1991) An overview of wavelet based multiresoiution analyses, Technical Report, University of South Carolina.

    Google Scholar 

  29. Koulouris, A., and Stephanopoulos, G. (1994) On-line empirical learning of process dynamics with Wave-nets, Technical Report, MIT-LISPE.

    Google Scholar 

  30. Koung, C., and Macgregor, F.J. (1994) Identification for robust multivariable control: the design of experiments, Automatica, 30,1541–1554.

    Article  Google Scholar 

  31. Kreinovich, V., Sirisaengtaksin, O., and Cabrera, S. (1993) Wavelet neural networks are optimal approximators for functions of one variable, Technical Report, MIT-LISPE.

    Google Scholar 

  32. Lee, J., (1995) Model predictive control: A tutorial, to appear in CRC Industrial Electronics Handbook, Department of Chemical Engineering, Auburn University, Auburn, AL.

    Google Scholar 

  33. Lee, L. H., Chikkula, Y., Yu, Z., and Kantor, J.C. (1995) Improving computational efficiency of model predictive control algorithm using wavelet transformation, Int. J. Control, 61 859–883.

    Article  Google Scholar 

  34. Luettgen, M. (1993) Image processing with multiscale stochastic models, PhD Thesis, Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science.

    Google Scholar 

  35. Lindsey, A. (1994) The non-existence of a wavelet function admitting a wavelet transform convolution theorem of the Fourier type, preprint, Ohio Univeristy, Athens, OH.

    Google Scholar 

  36. Mallat, S. G. (1989) A theory for multiresoiution signal decomposition: The wavelet representation, IEEE Transactions on Pattern Analysis and Machine Intelligence, II, 674–693.

    Article  Google Scholar 

  37. Mayne, D. (1996) Nonlinear model predictive control: An assessment, Preprints of Chemical Process Control-V, Tahoe City, CA.

    Google Scholar 

  38. Mayne, D. and Michalska, H. (1990) Receding horizon control of nonlinear systems, IEEE Transactions on Automatic Control AC-35: 814–824.

    Article  Google Scholar 

  39. Morari, M. (1993) Model predictive control: Multivariable control technique of choice in 1990’s ? Preprint, California Institute of Technology.

    Google Scholar 

  40. Morari, M., Garcia, C.E., Lee, J., and Prett, D.M., (1994) Model predictive control, Book preprint.

    Google Scholar 

  41. Muske K. R., Rawlings, J.B. (1992) Model predictive control with linear models”, accepted to be published in AICHE Journal, 1992.

    Google Scholar 

  42. Nikolau, M. (1995) Multiscale model predictive control, Memorandum, MIT-LISPE.

    Google Scholar 

  43. Ohshima, M., and Hashimoto I. (1992) Multi-rate multivariable model predictive control and its application to a semi-commercial polymerization reactor, Technical Report.

    Google Scholar 

  44. Qin, S. J., and Badgwell, T.A. (1995) An overview of industrial model predictive control technology, Preprint, University of Texas at Austin.

    Google Scholar 

  45. Ramirez, W. F. (1985) Process control and identification, Academic Press, Boston.

    Google Scholar 

  46. Rauch, H., Tung, F., and Striebel, C. (1965) Maximum likelihood estimates of linear dynamic systems, AIAA Journal, 3.

    Google Scholar 

  47. Rawlings, J. B., Muske, K.R. (1993) The stability of constrained receding horizon control, IEEE Transactions on Automatic Control, 38.

    Google Scholar 

  48. Robertson, D., Lee, J.H., and Rawlings, J.B. (1994) A moving horizon-based approach for least squares state estimation, AICHE Journal, 42, 2209–2223.

    Article  Google Scholar 

  49. Strang, G., and Nguyen, T. (1996) Wavelets and filter banks, Wellesley.

    Google Scholar 

  50. Stephanopoulos, G., (1989) The Shell Process Control Workshop, D. Prett and C. Garcia Butterworth Publishers, Stoneham, MA.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA

    G. Stephanopoulos, O. Karsligil & M. S. Dyer

Authors
  1. G. Stephanopoulos
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  2. O. Karsligil
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  3. M. S. Dyer
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Editor information

Editors and Affiliations

  1. Department of Chemical Engineering, Ankara University, Tandoğan, Ankara, Turkey

    Ridvan Berber

  2. Department of Chemical Engineering, The University of Michigan, Ann Arbor, Michigan, USA

    Costas Kravaris

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© 1998 Springer Science+Business Media Dordrecht

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Stephanopoulos, G., Karsligil, O., Dyer, M.S. (1998). Multi-Scale Aspects in Linear and Nonlinear Estimation and Control. In: Berber, R., Kravaris, C. (eds) Nonlinear Model Based Process Control. NATO ASI Series, vol 353. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-5094-1_22

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  • DOI: https://doi.org/10.1007/978-94-011-5094-1_22

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-6140-7

  • Online ISBN: 978-94-011-5094-1

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