Adaptive controller for systems of fractional dynamics based on robust fixed point transformations

J. K. Tar, I. J. Rudas, J. F. Bitó, J. A.Tenreiro Machado, K. Kozlowski

Research output: Chapter in Book/Report/Conference proceedingConference contribution

6 Citations (Scopus)

Abstract

In this paper a discrete time approximation of Caputo's fractional order derivatives is used for modeling the dynamic behavior of hypothetical fractional order systems the appropriate responses of which that can directly be manipulated by some physical agents are some fractional order time-derivatives of their state variables. A possible generalization of the concept of "initial conditions" of the integer order systems is proposed as "preceding history" for fractional order ones. It is shown that the number of the independent data characteristic to the "preceding history" can be made independent of the order of derivation. It is shown that the discrete time approximation proposed makes it possible to interpret the order of derivation in a higher range than in the case of the original integral form of Caputo's definition. By providing a simple analysis of the so obtained time-sequences it is shown that by manipulating the order of differentiation in this model both dissipative and unstable behavior can be modeled. The dissipative case corresponds to the presence of unmodeled internal degrees of freedom that are dynamically coupled to the directly controlled ones but cannot directly be controlled. The unstable case seems to be appropriate for modeling the behavior of systems coupled to some directly unmodeled exciting environment. For this purpose very simple mathematical estimations can be applied. The paradigm controlled is a fractional order F6 type Van der Pol oscillator that already obtained certain attention in the literature. It is shown that the simple fixed point transformations based adaptive control elaborated for integer order systems can be applied without any modification for fractional order ones.

Original languageEnglish
Title of host publicationSAMI 2009 - 7th International Symposium on Applied Machine Intelligence and Informatics, Proceedings
Pages117-123
Number of pages7
DOIs
Publication statusPublished - 2009
Event7th International Symposium on Applied Machine Intelligence and Informatics, SAMI 2009 - Herl'any, Slovakia
Duration: Jan 30 2009Jan 31 2009

Publication series

NameSAMI 2009 - 7th International Symposium on Applied Machine Intelligence and Informatics, Proceedings

Other

Other7th International Symposium on Applied Machine Intelligence and Informatics, SAMI 2009
CountrySlovakia
CityHerl'any
Period1/30/091/31/09

ASJC Scopus subject areas

  • Artificial Intelligence
  • Information Systems
  • Electrical and Electronic Engineering

Fingerprint Dive into the research topics of 'Adaptive controller for systems of fractional dynamics based on robust fixed point transformations'. Together they form a unique fingerprint.

  • Cite this

    Tar, J. K., Rudas, I. J., Bitó, J. F., Machado, J. A. T., & Kozlowski, K. (2009). Adaptive controller for systems of fractional dynamics based on robust fixed point transformations. In SAMI 2009 - 7th International Symposium on Applied Machine Intelligence and Informatics, Proceedings (pp. 117-123). [4956622] (SAMI 2009 - 7th International Symposium on Applied Machine Intelligence and Informatics, Proceedings). https://doi.org/10.1109/SAMI.2009.4956622