Journal of Institute of Control, Robotics and Systems (제어로봇시스템학회논문지)

Institute of Control, Robotics and Systems (제어로봇시스템학회)
권호 표지
DOI QR코드

DOI QR Code

Design of an Adaptive Variable Structure Control using Fredholm Integral Formulae for the Uncertainties

불확실성의 Fredholm 적분 수식화를 통한 적응가변구조제어기 설계

  • 유동상 (한경대학교 전기공학과)
  • Published : 2003.09.01
Download PDF
⟨ Previous Next ⟩

Abstract

In deterministic design of feedback controllers for uncertain dynamic systems, the upper bound of the uncertainty is very important to guarantee the stability of the closed loop system. In this paper, we assume that the upper bound of the uncertainty is formulated using a Fredholm integral equation of the first kind, that is, an integral of the product of a predefined kernel with an unknown influence function. We propose an adaptation law that is capable of estimating this upper bound. Using this adaptive upper bound, we design an adaptive variable structure control (AVSC), which guarantees asymptotic stability/ultimate boundedness of uncertain dynamic systems. The illustrative example shows the proposed AVSC is effective for uncertain dynamic systems.

Keywords

References

  1. V. I. Utkin, 'Variable structure systems with sliding modes', IEEE Trans. on Automatic Control, vol. 22, no. 2, pp. 212-222, February, 1977 https://doi.org/10.1109/TAC.1977.1101446
  2. R. A. DeCarlo, S. H. Zak, and G. P. Mathews, 'Variable structure control of nonlinear multivariable systems: A tutorial', IEEE Proceedings, vol. 76, pp. 212-232, 1988 https://doi.org/10.1109/5.4400
  3. S. Gutman, 'Uncertain dynamical systems - A Lyapunov min-max approach', IEEE Trans. on Automatic Control, vol. 24, no. 3, pp. 437-443, March 1979 https://doi.org/10.1109/TAC.1979.1102073
  4. S. Gutman and Z. Palmor, 'Properties of min-max controllers in uncertain dynamical systems', SIAM J. on Control and Optimization, vol. 20, no. 6, pp. 850-861, 1982 https://doi.org/10.1137/0320060
  5. B. R. Barmish, M. J. Corless, and G. Leitmann, 'A new class of stabilizing controllers for uncertain dynamical systems', SIAM J. on Control and Optimization, vol. 21, no. 2, pp. 246-255, 1983 https://doi.org/10.1137/0321014
  6. M. J. Corless and G. Leitman, 'Continuous state feedback guaranteeing uniform ultimate boundedness for uncertain dynamic systems', IEEE Trans. on Automatic Control, vol. 26, no. 5, pp. 1139-1144, May 1981 https://doi.org/10.1109/TAC.1981.1102785
  7. Y. H. Chen, 'Robust control system design: non-adaptive and adaptive', International Journal of Control, vol. 51, no. 6, pp. 1457-1477, 1990 https://doi.org/10.1080/00207179008934146
  8. D. S. Yoo and M. J. Chung, 'A Variable structure control with simple adaptation laws for upper bounds on the norm of the uncertainties', IEEE Trans. on Automatic Control, vol. 37, no. 6, pp. 860-865, June 1992 https://doi.org/10.1109/9.256348
  9. C.-H. Choi and H.-S. Kim, 'Adaptive regulation for a Class of Uncertain Systems with Partial Knowledge of Uncertainty Bounds', IEEE Trans. on Automatic Control, vol. 38, no. 8, pp. 1246-1250, August 1993 https://doi.org/10.1109/9.233160
  10. B. Brogliato and A. Trofino Neto, 'Practical stabilization of a class of nonlinear systems with partially known uncertainties', Automatica, vol. 31. no. 1, pp. 145-150, 1995 https://doi.org/10.1016/0005-1098(94)E0050-R
  11. H. Wu, 'Continuous adaptive robust controllers guaranteeing uniform ultimate boundedness for uncertain nonlinear system', International Journal of Control, vol. 72, no. 2, pp. 115-122, January 1999 https://doi.org/10.1080/002071799221280
  12. G. Artken, Mathematical methods for physicists, Academic Press, New York, 1970
  13. W. Messner, R. Horowitz, W.-W. Kao, and M. Boals, 'A New Adaptive Learning Rule', IEEE Trans. on Automatic Control, vol. 36, no. 2, pp. 188-197, February 1991 https://doi.org/10.1109/9.67294