JACIII Vol.17 No.3 pp. 418-424
doi: 10.20965/jaciii.2013.p0418


Improved Stabilization for Robust Fixed Point Transformations-Based Controllers

Teréz A. Várkonyi*,**, József K. Tar***, and Imre J. Rudas***

*Doctoral School of Applied Informatics, John von Neumann Faculty of Informatics, Óbuda University, 96/B Bécsi út, Budapest H-1034, Hungary

**Doctoral School of Computer Science, Department of Computer Science, Universitá degli Studi di Milano, Crema Campus, 65 Via Bramante, Crema (CR) I-26013, Italy

***Institute of Intelligent Engineering Systems, John von Neumann Faculty of Informatics, Óbuda University, 96/B Bécsi út, Budapest H-1034, Hungary

February 17, 2013
March 5, 2013
May 20, 2013
nonlinear control, adaptive control, robust fixed point transformations, Van der Pol oscillator, chaos synchronization
Nowadays, dynamical systems are getting increasingly complex because they have to fulfill more expectations and further they have to handle more and more uncertainties. The controllers built in these systems have to face with the same difficulties. Luckily, the applied new controllers are designed to take into account the grown claims and they are able to fit the extreme conditions. The method called Robust Fixed Point Transformations (RFPT) is used to ameliorate existing controllers’ results when an approximate model is used to predict the dynamical system’s behavior. To achieve the stability of RFPT many efforts have been taken in the recent past. In this paper, a new algorithm is proposed that prevents the occurrence of short temporal unstable periods of the RFPT-based controllers, i.e., ensures the continuous stability.
Cite this article as:
T. Várkonyi, J. Tar, and I. Rudas, “Improved Stabilization for Robust Fixed Point Transformations-Based Controllers,” J. Adv. Comput. Intell. Intell. Inform., Vol.17 No.3, pp. 418-424, 2013.
Data files:
  1. [1] A. M. Lyapunov, “A general task about the stability of motion,” Ph.D. thesis, 1892 (in Russian).
  2. [2] J. G. Charney, R. Fjörtoft, and J. von Neumann, “Numerical integration of the barotropic vorticity equation,” Tellus, Vol.2, pp. 237-254, 1950.
  3. [3] R. Courant, K. O. Friedrichs, and H. Lewy, “Über die partiellen Differenzengleichungen der mathematischen Physik,” Mathematische Annalen, Vol.100, pp. 32-74, 1928.
  4. [4] S. Alan, E. Budak, and H. N. Özgüven, “Analytical Prediction of Part Dynamics forMachining Stability Analysis,” Int. J. of Automation Technology, Vol.4, No.3, pp. 259-267, 2010.
  5. [5] T. Furuhashi, H. Yamamoto, J. F. Peters, and W. Pedrycz, “Fuzzy Control Stability Analysis Using a Generalized Fuzzy Petri Net Model,” J. of Advanced Computational Intelligence and Intelligent Informatics, Vol.3, No.2, pp. 99-105, 1999.
  6. [6] R.-E. Precup, S. Preitl, and P. Korondi, “Development of Fuzzy Controllers with Dynamics Regarding Stability Conditions and Sensitivity Analysis,” J. of Advanced Computational Intelligence and Intelligent Informatics, Vol.8, No.5, pp. 499-506, 2004.
  7. [7] J. K. Tar, J. F. Bitó, L. Nádai, and J. A. Tenreiro Machado, “Robust Fixed Point Transformations in Adaptive Control Using Local Basin of Attraction,” Acta Polytechnica Hungarica, Vol.6, No.1, pp. 21-37, 2009.
  8. [8] T. A. Várkonyi, J. K. Tar, and I. J. Rudas, “Fuzzy Parameter Tuning in the Stabilization of an RFPT-based Adaptive Control for an Underactuated System,” Proc. of the 12th Int. Symposium on Computational Intelligence and Informatics (CINTI), pp. 63-68, 2011.
  9. [9] T. A. Várkonyi, J. K. Tar, I. J. Rudas, and I. Krómer, “VS-type Stabilization of MRAC Controllers Using Robust Fixed Point Transformations,” Proc. of the 7th Int. Symposium on Applied Computational Intelligence and Informatics (SACI), pp. 389-394, 2012.
  10. [10] B. Van der Pol, “Forced oscillations in a circuit with non-linear resistance (reception with reactive triode),” The London, Edinburgh, and Dublin Philosophical Magazine and J. of Science, Vol.7, No.3, pp. 65-80, 1927.
  11. [11] L. Xinbin, W. Lamei, and L. Xian, “Synchronization of Van der Pol Oscillators Based on Dynamical Complex Network,” Proc. of the 29th Chinese Control Conference (CCC), pp. 781-785, 2010.
  12. [12] J. Kobayashi, “Entrainment Property Analysis of Van der Pol Oscillator Driving a Spring-Mass System for Large Force Generation by Averaging Method,” Proc. of the 2010 IEEE Conf. on Robotics Automation and Mechatronics (RAM), pp. 498-503, 2010.
  13. [13] A. Bonfanti, F. Pepe, C. Samori, and A. L. Lacaita, “Flicker Noise Up-Conversion due to Harmonic Distortion in Van der Pol CMOS Oscillators,” IEEE Trans. on Circuits and Systems I: Regular Papers, Vol.59, No.7, pp. 1418-1430, 2012.
  14. [14] J. K. Tar, I. J. Rudas, and K. R. Kozłowski, “Fixed Point Transformations-Based Approach in Adaptive Control of Smooth Systems,” In: K. R. Kozłowski (Ed.), Robot Motion and Control 2007: Lecture Notes in Control and Information Sciences 360, Springer Verlag London Ltd., pp. 157-166, 2007.
  15. [15] SCILAB homepage:

*This site is desgined based on HTML5 and CSS3 for modern browsers, e.g. Chrome, Firefox, Safari, Edge, Opera.

Last updated on Apr. 05, 2024