On Function Extrapolation by Fixed Point Iteration for Time-Delayed Systems

Hemza Redjimi, J. Tar, János F. Bitó

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

Abstract

In practical applications the problem of numerical extrapolation of the value of a function over a discrete time-grid so that the previous values can be only "experimentally" observed, often arises. For instance, the extrapolation of the response of a dynamic system that is controlled on the basis of an available approximate dynamic model in adaptive control is a typical example. A quite wide class of controllers e.g. the Optimal Controllers realized by Nonlinear Programming over a discrete time-grid as Receding Horizon Controllers are good examples, too. In 2009 a novel adaptive controller design method was suggested that in the first step transforms the control problem into a fixed point iteration task then it so solves this problem that during one digital control step only one step of the iteration can be realized. This controller adaptively learns from the past. The method widely was investigated for various systems that were free from considerable time-delay, but only preliminary investigations were done how the delay in using the observed data and in exerting the calculated control signal concerns this method. In the present paper systematic investigations restricted to the approximation of known functions are presented in order to better reveal the approximation issues. On the basis of these investigations the usefulness of the suggested iterative method is concluded.

Original languageEnglish
Title of host publicationSAMI 2019 - IEEE 17th World Symposium on Applied Machine Intelligence and Informatics, Proceedings
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages205-210
Number of pages6
ISBN (Electronic)9781728102504
DOIs
Publication statusPublished - Jan 1 2019
Event17th IEEE World Symposium on Applied Machine Intelligence and Informatics, SAMI 2019 - Herl'any, Slovakia
Duration: Jan 24 2019Jan 26 2019

Publication series

NameSAMI 2019 - IEEE 17th World Symposium on Applied Machine Intelligence and Informatics, Proceedings

Conference

Conference17th IEEE World Symposium on Applied Machine Intelligence and Informatics, SAMI 2019
CountrySlovakia
CityHerl'any
Period1/24/191/26/19

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Keywords

  • Banach Space
  • Fixed Point Iteration
  • Function Extrapolation
  • Time Delay

ASJC Scopus subject areas

  • Artificial Intelligence
  • Computer Science Applications
  • Information Systems
  • Control and Optimization
  • Human-Computer Interaction

Cite this

Redjimi, H., Tar, J., & Bitó, J. F. (2019). On Function Extrapolation by Fixed Point Iteration for Time-Delayed Systems. In SAMI 2019 - IEEE 17th World Symposium on Applied Machine Intelligence and Informatics, Proceedings (pp. 205-210). [8782750] (SAMI 2019 - IEEE 17th World Symposium on Applied Machine Intelligence and Informatics, Proceedings). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/SAMI.2019.8782750