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On the Intrinsic Relation of Linear Dynamical Systems and Higher Order Neural Units

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Automation Control Theory Perspectives in Intelligent Systems (CSOC 2016)

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 466))

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Abstract

This paper summarizes the fundamental construction of higher-order-neural-units (HONU) as a class of polynomial function based neural units, which are though non-linear discrete time models, are linear in their parameters. From this a relation will be developed, ultimately leading to a new definition for analysing the global stability of a HONU, not only as a model itself, but further as a means of justifying the global dynamic stability of the whole control loop under HONU feedback control. This paper is organised to develop the fundamentals behind this intrinsic relation of linear dynamic systems and HONUs accompanied by a theoretical example to illustrate the functionality and principles of the concept.

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Acknowledgments

The authors of this paper would like to acknowledge the following study grant for its support SGS12/177/OHK2/3T/12

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Authors and Affiliations

  1. Department of Instrumentation and Control Engineering, Czech Technical University in Prague, Prague, Czech Republic

    Peter Benes & Ivo Bukovsky

Authors
  1. Peter Benes
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  2. Ivo Bukovsky
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Correspondence to Peter Benes .

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Editors and Affiliations

  1. Faculty of Applied Informatics, Tomas Bata University in Zlín, Zlín, Czech Republic

    Radek Silhavy

  2. Faculty of Applied Informatics, Tomas Bata University in Zlín, Zlín, Czech Republic

    Roman Senkerik

  3. Faculty of Applied Informatics, Tomas Bata University in Zlín, Zlín, Czech Republic

    Zuzana Kominkova Oplatkova

  4. Faculty of Applied Informatics, Tomas Bata University in Zlín, Zlín, Czech Republic

    Petr Silhavy

  5. Faculty of Applied Informatics, Tomas Bata University in Zlín, Zlín, Czech Republic

    Zdenka Prokopova

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Benes, P., Bukovsky, I. (2016). On the Intrinsic Relation of Linear Dynamical Systems and Higher Order Neural Units. In: Silhavy, R., Senkerik, R., Oplatkova, Z.K., Silhavy, P., Prokopova, Z. (eds) Automation Control Theory Perspectives in Intelligent Systems. CSOC 2016. Advances in Intelligent Systems and Computing, vol 466. Springer, Cham. https://doi.org/10.1007/978-3-319-33389-2_23

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  • DOI: https://doi.org/10.1007/978-3-319-33389-2_23

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-33387-8

  • Online ISBN: 978-3-319-33389-2

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