A Novel, Abstract Rotation-Based Fixed Point Transformation in Adaptive Control

Peter Galambos, J. Tar, Gyorgy Gyorok, Andrea Serester, Bertalan Csandi

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

3 Citations (Scopus)

Abstract

As an alternative of the Lyapunov function-based design of adaptive controllers the Fixed Point Transformation based Adaptive controller was introduced that in the first step transforms the control task into a Fixed Point Problem then so solves it via iteration that during one digital control step one step of iteration happens. In the actual step this scheme takes into consideration the controlled system's response obtained for the control action in the previous step, therefore it applies delayed feedback that makes it very flexible in the adaptive control of time-delayed systems. In transforming the control problem into a fixed point problem countless mathematical possibilities exist. Till now only a few versions were in use. On the basis of certain old antecedents in this paper a novel version is suggested that creates abstract rotations in the n dimensional space on the basis of the generalization of the Rodrigues formula. Its main advantage is its simplicity, easy geometric interpretation, lucidity, and better fitting to the features of the particular control task. Its applicability is exemplified by simulations for the adaptive control of two mass-points coupled by nonlinear springs.

Original languageEnglish
Title of host publicationProceedings - 2018 IEEE International Conference on Systems, Man, and Cybernetics, SMC 2018
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages2577-2582
Number of pages6
ISBN (Electronic)9781538666500
DOIs
Publication statusPublished - Jan 16 2019
Event2018 IEEE International Conference on Systems, Man, and Cybernetics, SMC 2018 - Miyazaki, Japan
Duration: Oct 7 2018Oct 10 2018

Publication series

NameProceedings - 2018 IEEE International Conference on Systems, Man, and Cybernetics, SMC 2018

Conference

Conference2018 IEEE International Conference on Systems, Man, and Cybernetics, SMC 2018
CountryJapan
CityMiyazaki
Period10/7/1810/10/18

Keywords

  • Abstract Rotations
  • Adaptive Control
  • Delayed Feedback
  • Fixed Point Transformations

ASJC Scopus subject areas

  • Information Systems
  • Information Systems and Management
  • Health Informatics
  • Artificial Intelligence
  • Computer Networks and Communications
  • Human-Computer Interaction

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  • Cite this

    Galambos, P., Tar, J., Gyorok, G., Serester, A., & Csandi, B. (2019). A Novel, Abstract Rotation-Based Fixed Point Transformation in Adaptive Control. In Proceedings - 2018 IEEE International Conference on Systems, Man, and Cybernetics, SMC 2018 (pp. 2577-2582). [8616437] (Proceedings - 2018 IEEE International Conference on Systems, Man, and Cybernetics, SMC 2018). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/SMC.2018.00441