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On the efficient computation of higher order maps ad kf g(x) using Taylor arithmetic and the Campbell-Baker-Hausdorff formula

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Nonlinear and Adaptive Control

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 281))

Abstract

The computation of ad kf g requires derivatives of f and g up to order k. For small dimensions, the Lie brackets can be computed with computer algebra packages. The application to non-trivial systems is limited due to a burden of symbolic computations involved. The author proposes a method to compute function values of ad kf g using automatic differentiation.

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Author information

Authors and Affiliations

  1. Institut für Regelungs- und Steuerungstheorie, TU Dresden, Mommsenstr. 13, D-01062, Dresden, Germany

    Klaus Röbenack

Authors
  1. Klaus Röbenack
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Editor information

Editors and Affiliations

  1. Departement of AppliedMathematics, The University of Sheffield, Western Bank, Sheffield, S10 2TN, UK

    Alan Zinober

  2. Dept. of Automatic Control and Systems Engineering, The University of Sheffield, Mappin Street, Sheffield, S1 3JD, UK

    David Owens

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© 2003 Springer-Verlag Berlin Heidelberg

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Röbenack, K. (2003). On the efficient computation of higher order maps ad kf g(x) using Taylor arithmetic and the Campbell-Baker-Hausdorff formula. In: Zinober, A., Owens, D. (eds) Nonlinear and Adaptive Control. Lecture Notes in Control and Information Sciences, vol 281. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45802-6_26

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  • DOI: https://doi.org/10.1007/3-540-45802-6_26

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-43240-1

  • Online ISBN: 978-3-540-45802-9

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