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Convergence of Åström-Wittenmark’s Self-Tuning Regulator and Related Topics

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New Directions in Time Series Analysis

Part of the book series: The IMA Volumes in Mathematics and its Applications ((IMA,volume 46))

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Abstract

In this paper we consider adaptive tracking purely based on the ELS algorithm for the ARMAX system that may be unstable in open loop but is of minimum phase. 1) The Åström-Wittenmark’s self-tuning tracker is shown to be convergent and optimal and the convergence rate of the tracking error is established as well. 2) When the first coefficient for the system input is unknown the adaptive control is designed so that the ELS-based adaptive tracker is convergent and optimal.

Project supported by the National Natural Science Foundation, the TWAS RG MP 898–117 and the K.C. Wang Education Foundation

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Authors and Affiliations

  1. Institute of Systems Science, Academia Sinica, Beijing, 100080, P.R. China

    Lei Guo & Han-Fu Chen

Authors
  1. Lei Guo
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  2. Han-Fu Chen
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Editor information

Editors and Affiliations

  1. Department of Statistics, University of California, Berkeley, CA, 94720, USA

    David Brillinger

  2. Department of Electrical Engineering, McGill University, Montreal, Quebec, H3A 2A7, Canada

    Peter Caines

  3. Department of Economics, University of Minnesota, Minneapolis, MN, 55455, USA

    John Geweke

  4. Department of Statistics, Texas A&M University, College Station, TX, 77843-3143, USA

    Emanuel Parzen

  5. Mathematics Department, University of California, San Diego, La Jolla, CA, 92093, USA

    Murray Rosenblatt

  6. Department of Mathematics, Boston University, Boston, MA, 02215, USA

    Murad S. Taqqu

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© 1993 Springer-Verlag New York, Inc.

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Guo, L., Chen, HF. (1993). Convergence of Åström-Wittenmark’s Self-Tuning Regulator and Related Topics. In: Brillinger, D., Caines, P., Geweke, J., Parzen, E., Rosenblatt, M., Taqqu, M.S. (eds) New Directions in Time Series Analysis. The IMA Volumes in Mathematics and its Applications, vol 46. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-9296-5_13

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  • DOI: https://doi.org/10.1007/978-1-4613-9296-5_13

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4613-9298-9

  • Online ISBN: 978-1-4613-9296-5

  • eBook Packages: Springer Book Archive

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