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Numerical Schemes of Higher Order for a Class of Nonlinear Control Systems

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Numerical Methods and Applications (NMA 2002)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2542))

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Abstract

We extend a systematic method for the derivation of high order schemes for affinely controlled nonlinear systems to a larger class of systems in which the control variables are allowed to appear nonlinearly in multiplicative terms. Using an adaptation of the stochastic Taylor expansion to control systems we construct Taylor schemes of arbitrary high order and indicate how derivative free Runge-Kutta type schemes can be obtained.

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Author information

Authors and Affiliations

  1. Fachbereich Mathematik, J.W. Goethe-Universität, Postfach 111932, 60054, Frankfurt am Main, Germany

    Lars Grüne & Peter E. Kloeden

Authors
  1. Lars Grüne
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  2. Peter E. Kloeden
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Editor information

Editors and Affiliations

  1. Central Laboratory for Parallel Processing, Bulgarian Academy of Sciences, Acad. G. Bonchev, bl. 25A, 1113, Sofia, Bulgaria

    Ivan Dimov , Ivan Lirkov  & Svetozar Margenov ,  & 

  2. National Environmental Research Institute, Frederiksborgvej 399, P.O. Box 358, 4000, Roskilde, Denmark

    Zahari Zlatev

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Grüne, L., Kloeden, P.E. (2003). Numerical Schemes of Higher Order for a Class of Nonlinear Control Systems. In: Dimov, I., Lirkov, I., Margenov, S., Zlatev, Z. (eds) Numerical Methods and Applications. NMA 2002. Lecture Notes in Computer Science, vol 2542. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36487-0_23

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  • DOI: https://doi.org/10.1007/3-540-36487-0_23

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-00608-4

  • Online ISBN: 978-3-540-36487-0

  • eBook Packages: Springer Book Archive

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