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Robust Discrete-Time Adaptive Control

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Adaptive and Learning Systems

Abstract

This paper proposes a discrete-time model reference adaptive control algorithm which is robust with respect to additive plant uncertainties. The algorithm employs the same controller structure as in [1] but a different adaptive law for adjusting the controller parameters. If the plant uncertainty is “small” the algorithm guarantees the boundedness of all signals in the adaptive loop and “small” residual tracking errors for any bounded initial conditions. In the absence of plant uncertainties the algorithm guarantees zero residual tracking errors.

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References

  1. K.S. Narendra and Y.H. Lin, “Stable Discrete Adaptive Control,“ IEEE Trans. on Automatic Control, AC-25, No. 3, pp. 456–461, 1980.

    Article  Google Scholar 

  2. B. Egardt, “Stability Analysis of Adaptive Control Systems with Disturbances,“ Proc. JA CC, San Francisco, Ca., 1980.

    Google Scholar 

  3. B. Egardt, Stability of Adaptive Controllers Springer-Verlag, Berlin, 1979.

    Google Scholar 

  4. B.B. Peterson and K.S. Narendra, “Bounded Error Adaptive Control,“ IEEE Trans. on Automatic Control, vol. AC-27, No. 6, pp. 1161–1168, 1982.

    Article  Google Scholar 

  5. C.E. Rohrs, L. Valavani, M. Athans and G. Stein, “Robustness of Adaptive Control Algorithms in the Presence of Unmodeled Dynamics,” Preprints 21st IEEE CDC, Orlando, Fl., 1982.

    Google Scholar 

  6. P.A. Ioannou and P.V. Kokotovic, Adaptive Systems with Reduced Models Springer-Verlag, Berlin, 1983.

    Google Scholar 

  7. K.J. Aström, “Analysis of Rohrs Counterexamples to Adaptive Control,” Dept. of Automatic Control, Lund Inst. of Tech. Report, 1983.

    Google Scholar 

  8. B.D. Riedle and P.V. Kokotovic, “Disturbance Instabilities in an Adaptive System,“ IEEE Trans. on Automatic Control,AC-29, pp. 822–824.

    Google Scholar 

  9. P.A. Ioannou and P.V. Kokotovic, “Instability Analysis and Improvement of Robustness of Adaptive Control,” Automatica, vol. 20, No. 5, Sept. 1984.

    Google Scholar 

  10. G. Kreisselmeier and K.S. Narendra, “Stable Model Reference Adaptive Control in the Presence of Bounded Disturbances,” IEEE Trans. on Automatic Control, vol. AC-27, No. 6, pp. 1169–1176, 1982.

    Article  MathSciNet  Google Scholar 

  11. C. Samson, “Stability Analysis of Adaptively Controlled System Subject to Bounded Disturbances,” Automatica, vol. 19, pp. 81–86, 1983.

    MATH  Google Scholar 

  12. S.S. Sastry, “Model Reference Adaptive Control: Stability, Parameter Convergence and Robustness,” I.M.A. Journal of Control and Information, vol. 1, pp. 27–66, 1984.

    Google Scholar 

  13. J.M. Martin-Sanches, “A Globally Stable APCS in the Presence of Bounded Noises and Disturbances,” IEEE Trans. on Automatic Control, vol. AC-29, pp. 461–464, 1984.

    Google Scholar 

  14. K.S. Narendra and A.M. Annaswamy, “Persistent Excitation and Robust Adaptive Algorithms,” Proc. 3rd Yale Workshop on Applications of Adaptive Systems Theory, Yale University, New Haven, Ct., June 15–17, 1983, pp. 11–18.

    Google Scholar 

  15. P.A. Ioannou, “Robust Adaptive Controller with Zero Residual Tracking Errors,” The 24th IEEE Conf. on Decision and Control, Fort Lauderdale, Florida, 1985.

    Google Scholar 

  16. R.L. Kosut and C.R. Johnson, Jr., “An Input-Output View of Robustness in Adaptive Control,” Automatica, vol. 20, No. 5, Sept. 1984.

    Google Scholar 

  17. L. Praly, “Robustness of Model Reference Adaptive Control,” Third Yale Workshop on Applications of Adaptive Systems Theory, Yale University, New Haven, Ct., June 15–17, 1983.

    Google Scholar 

  18. L. Praly, “Robust Model Reference Adaptive Controllers, Part 1: Stability Analysis,” Proc. 23rd IEEE Conf. on Decision and Control, 1984.

    Google Scholar 

  19. G. Kreisselmeier and B.D.O. Anderson, “Robust Model Reference Adaptive Control,” DFVLR - Institut fur Dynamik der Flugsysteme Report, May 1984.

    Google Scholar 

  20. G. Kreisselmeier, “A Robust Indirect Adaptive Control Approach,” The Fourth Yale Workshop on Theory and Applications of Adaptive Control, May 1985.

    Google Scholar 

  21. P.A. Ioannou and K. Tsakalis, “A Robust Direct Adaptive Controller,” University of Southern California, EE–Systems, Report 85–07–1, June 1985.

    Google Scholar 

  22. G. Goodwin, P. Ramadge and P. Caines, “Discrete-Time Multivariable Adaptive Control,” IEEE Trans. on Automatic Control, AC-25, June 1980.

    Google Scholar 

  23. K.S. Narendra, Y.H. Lin and L.S. Valavani, “Stable Adaptive Controller Design, Part II: Proof of Stability,” IEEE Trans. on Automatic Control, AC-25, June 1980.

    Google Scholar 

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© 1986 Springer Science+Business Media New York

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Ioannou, P., Tsakalis, K. (1986). Robust Discrete-Time Adaptive Control. In: Narendra, K.S. (eds) Adaptive and Learning Systems. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-1895-9_5

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  • DOI: https://doi.org/10.1007/978-1-4757-1895-9_5

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4757-1897-3

  • Online ISBN: 978-1-4757-1895-9

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