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Dynamics, Bifurcations, and Control pp 241–254Cite as

Longtime Dynamics in Adaptive Gain Control Systems

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Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 273))

Abstract

We study the longtime dynamics of a nonlinear adaptive control system introduced by Mareels et al. [10] to control the behavior of a plant which can be described by a finite dimensional SISO linear time invariant system stabilizable by a high gain output feedback. We apply frequency domain methods to derive conditions for global stability, to approximate the region containing the global attractor and to estimate its Hausdorff dimension.

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References

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Author information

Authors and Affiliations

  1. Department of Mathematics and Mechanics, St. Petersburg State University, Petrodvoretz, Bibliotechnaya pl. 2, 198904, St. Petersburg, Russia

    Gennady A. Leonov

  2. Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstraße 39, D-10117, Berlin, Germany

    Klaus R. Schneider

Authors
  1. Gennady A. Leonov
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  2. Klaus R. Schneider
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Editor information

Editors and Affiliations

  1. Institut für Mathematik, Universität Augsburg, Universitätsstraße, 86150, Augsburg, Germany

    Fritz Colonius

  2. Fachbereich Mathematik, J.W. Goethe-Universität, Postfach 11 19 32, 60054, Frankfurt am Main, Germany

    Lars Grüne

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© 2002 Springer-Verlag Berlin Heidelberg

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Leonov, G.A., Schneider, K.R. (2002). Longtime Dynamics in Adaptive Gain Control Systems. In: Colonius, F., Grüne, L. (eds) Dynamics, Bifurcations, and Control. Lecture Notes in Control and Information Sciences, vol 273. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45606-6_17

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  • DOI: https://doi.org/10.1007/3-540-45606-6_17

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42890-9

  • Online ISBN: 978-3-540-45606-3

  • eBook Packages: Springer Book Archive

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