Non-conventional Control Design by Sigmoid Generated Fixed Point Transformation Using Fuzzy Approximation

Adrienn Dineva, J. Tar, A. Várkonyi-Kóczy, János T. Tóth, Vincenzo Piuri

Research output: Chapter in Book/Report/Conference proceedingChapter


Lyapunov’s 2nd or Direct method is recognized as being the primary tool of adaptive control of nonlinear dynamic systems. The great majority of the adaptive nonlinear control design rest on Lyapunov’s stability theorem. Recent findings have revealed that the Robust Fixed Point Transformation-based method can succesfully replace the Lyapunov technique. Later the “Sigmoid Generated Fixed Point Transformation (SGFPT)” has been introduced. This systematic method has been proposed for the generation of whole families of Fixed Point Transformations. Its extension from Single Input Single Output (SISO) to Multiple Input Multiple Output (MIMO) systems has also been given. In recent times, the great majority of model building issues are replaced by “Soft Computing” techniques. In contrast to the classical mathematical methods the intelligent methodologies are able to cope with ill-defined systems, disturbances and missing information by an efficient and robust way. Especially fuzzy logic has become to be used to model complex systems. This contribution makes an attempt to utilize the advantages of fuzzy approximation in the SGFPT control design. The theoretical investigations are validated by the adaptive control of the inverted pendulum. Comparative analysis have been carried out between the “affine” and the “soft computing-based” models. Results of numerical simulations confirm the applicability and efficiency of the proposed method.

Original languageEnglish
Title of host publicationStudies in Systems, Decision and Control
PublisherSpringer International Publishing
Number of pages15
Publication statusPublished - Jan 1 2018

Publication series

NameStudies in Systems, Decision and Control
ISSN (Print)2198-4182
ISSN (Electronic)2198-4190


  • Fixed point transformation
  • Fuzzy modeling
  • Iterative learning
  • Nonlinear control
  • Sigmoid Generated Fixed Point Transformation

ASJC Scopus subject areas

  • Computer Science (miscellaneous)
  • Control and Systems Engineering
  • Automotive Engineering
  • Social Sciences (miscellaneous)
  • Economics, Econometrics and Finance (miscellaneous)
  • Control and Optimization
  • Decision Sciences (miscellaneous)

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  • Cite this

    Dineva, A., Tar, J., Várkonyi-Kóczy, A., Tóth, J. T., & Piuri, V. (2018). Non-conventional Control Design by Sigmoid Generated Fixed Point Transformation Using Fuzzy Approximation. In Studies in Systems, Decision and Control (pp. 1-15). (Studies in Systems, Decision and Control; Vol. 140). Springer International Publishing.