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Instabilities in Adaptive Control Systems

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Analysis and Optimization of Systems

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 83))

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Abstract

An exposition of some of the results in continuous-time adaptive control systems in stability is given. We study instabilities that arise due to: high adaptation gain and/or large reference signals, interplay between unmodeled dynamics and output dis turbances and crosscoupling in decentralized controllers. In all cases simple worked examples are included to illustrate the phenomena. In the disturbance-free case, the causes of instability are rigorously explained via instability theorems. The basic purpose of the paper is to establish criteria for instability, however, conditions for stability are also formulated concurrently.

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References

  1. Liberzon, M.R., “New results on absolute stability of nonstationary controlled systems” Autom. i Telemekh Vol. 40, N°- 8, Aug., 1979.

    Google Scholar 

  2. Rohrs, CE “Adaptive control in the presence of unmodeled dynamics” Ph. D. Thesis, Dept. of Elect. Engg. and Comp. Sc., MIT, 1982.

    Google Scholar 

  3. Ioannou, P., Kokotovic P., “Instability analysis and improvement of robustness of adaptive control”, Automatica Vol 20, N° 5, pp. 583–594, 1984.

    MathSciNet  Google Scholar 

  4. Riedle, B, Kokotovic P. “A stability-instability boundary for disturbance free slow adaptation and unmodeled dynamics. Proc. 23rd IEEE CDC 1984.

    Google Scholar 

  5. Rohrs C.E. “Stability mechanisms and adaptive control” Proc. 23rd. IEEE Conf. Dec. Contr. 1984.

    Google Scholar 

  6. Kosut R. Friedlander B. “Robust adaptive control: conditions for global stabil ity”, IEEE Trans. on Aut. Cont. Vol AC-30, No. 7, July 1985.

    Google Scholar 

  7. Ortega R, Praly L, Landau I. “Robustness of discrete-time adaptive controllers”, IEEE Trans. on Aut. Cont. Vol AC-30, N° 12, Dec. 1985.

    Google Scholar 

  8. Kosut R. Anderson B.D.O., “Robust adaptive control: conditions for local stabil ity”, IEEE Trans. on Aut. Cont. Vol AC-31, N° 1, Jan. 1986.

    Google Scholar 

  9. Kosut R. Anderson B.D.O., Mareels, I. “Stability theory for adaptive systems: methods of averaging and persistency of excitation”, Proc 24th IEEE CDC 1985.

    Google Scholar 

  10. Fu, L, Bodson, M., Sastry, S., “New stability theorems for averaging and their application to the convergence analysis of adaptive identification and control schemes”, Proc. 24rd IEEE CDC 1985.

    Google Scholar 

  11. Astrom, K. “Interactions between excitation and unmodeled dynamics in adaptive control”, Proc. 23rd IEEE CDC 1984.

    Google Scholar 

  12. Lehtomaki, N., et. al. “Robustness and modeling error characterization”, IEEE Trans. on Aut. Cont. Vol AC-29, N° 3, March 1984.

    Google Scholar 

  13. Ortega R., Kelly, R. “On the destabilizing effect of crosscoupling in decentral ized adaptive control”, Syst. & Cont. Letters. 6, pp. 99–102, July 1985.

    Google Scholar 

  14. Ortega, R. “On the stability of continuous-time adaptive controllers for delay systems” 1986 American Cont. Conf. (Submitted)

    Google Scholar 

  15. Ortega, R., Kelly R. “On stability-instability condition of a simple robust adaptive servo controller”, Proc 24th IEEE CDC 1985.

    Google Scholar 

  16. Riedle, B. Cyr, B., Kokotovic, P. “Disturbance instabilities in an adaptive sys tem”, IEEE Trans. on Aut. Cont. Vol. AC-29, N° 9, Sept. 1984.

    Google Scholar 

  17. Willems, J.C., Byrnes, C.I. “Global adaptive stabilization in the absence of information on the sign of the high frequency gain”, 6th Intl. Conf. on Anal. & Opt. of Syst. INRIA. Nice, France, June 19–22, 1984.

    Google Scholar 

  18. Astrom, K.J. “Analysis of Rohr’s counterexamples to adaptive control”, Proc. 22nd IEEE CDC 1983.

    Google Scholar 

  19. Yakubovich, V.A. “Absolute instability on nonlinear control systems” Avtomatika i Telemekhanika No. 12, pp. 5–14, 1971.

    Google Scholar 

  20. Ioannou, P. “Decentralized adaptive control of interconnected systems” IEEE Trans. on Aut. Cont. (To be published).

    Google Scholar 

  21. Narendra, K.S., Annaswamy, A.M. “Robust adaptive control” Report No. 8601 Yale Univ. Jan. 1986.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Facultad de Ingeniería Apdo, División de Estudios de Posgrado, Postal 70-256, 04510, México, D.F., Mexico

    Romeo Ortega & Tang Yu

Authors
  1. Romeo Ortega
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  2. Tang Yu
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Editor information

Editors and Affiliations

  1. Institut National de Recherche en Informatique et en Automatique, INRIA, Domaine de Voluceau, Rocquencourt, B.P. 105, 78153, Le Chesnay, France

    A. Bensoussan  & J. L. Lions  & 

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© 1986 Springer Science+Business Media Dordrecht

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Ortega, R., Yu, T. (1986). Instabilities in Adaptive Control Systems. In: Bensoussan, A., Lions, J.L. (eds) Analysis and Optimization of Systems. Lecture Notes in Control and Information Sciences, vol 83. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0007553

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  • DOI: https://doi.org/10.1007/BFb0007553

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-16729-7

  • Online ISBN: 978-3-540-39856-1

  • eBook Packages: Springer Book Archive

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