Skip to main content
SpringerLink
Log in

A note on the model reference adaptive control of linear parabolic systems with constant coefficients

  • Published:
Journal of Systems Science and Complexity Aims and scope Submit manuscript

Abstract

The problem of constructing a model reference adaptive control law for an uncertain 1-dimensional parabolic system with one constant coefficient is considered in this paper. Adaptive control law are obtained by Lyapunov redesign method. The energy method for parabolic systems and the Agmon’s inequality are applied in the analysis, which leads to a stronger result than that of Hong and Bentsman (Automatica, 1994).

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. K. S. Hong and J. Bentsman, Application of averaging method for integro-differential equations to model reference adaptive control of parabolic system, Automatica, 1994, 30(9): 1415–1419.

    Article  MATH  MathSciNet  Google Scholar 

  2. K. J. Astrom and B. Wittenmark, Adaptive Control, Addison-Wesley, Reading, MA, 1989.

    Google Scholar 

  3. P. A. Ioannou and J. Sun, Robust Adaptive Control, Prentice-Hall, Englewood Cliffs, N. J., 1996.

    MATH  Google Scholar 

  4. S. Sastry and M. Bodson, Adaptive Control: Stability, Convergence and Robustness, Prentice-Hall, Englewood Cliffs, N. J., 1989.

    MATH  Google Scholar 

  5. G. Tao, Adaptive Control Design and Analysis, John Wiley and Sons, Hoboken, 2003.

    Book  MATH  Google Scholar 

  6. Y. Miyasato, Model reference adaptive control for distributed parameter systems of parabolic type by finite dimensional controller, Proc. 29th IEEE Conference on Decision and Control, Honolulu, Hawaii, 1990.

  7. M. Böhm, A. A. Demetriou, S. Reich, and I. G. Rosen, Model reference adaptive control of distributed parameter systems, SIAM J. Control Optim., 1998, 36(1): 33–81.

    Article  MATH  MathSciNet  Google Scholar 

  8. K. S. Hong and J. Bentsman, Direct adaptive control of parabolic systems: Algorithm synthesis and convergence and stability analysis, IEEE Trans. Automat. Control, 1994, 39(10): 2018–2033.

    Article  MATH  MathSciNet  Google Scholar 

  9. K. S. Hong, K. J. Yang, and D. H. Kang, Model reference adaptive control of a time-varying parabolic system, KSME International Journal, 2000, 14(2): 168–176.

    Google Scholar 

  10. K. J. Yang and K. S. Hong, Robust MRAC of a nonautonomous parabolic system with spatiotemporally varying coefficients and bounded disturbance, Asian Journal of Control, 2003, 5(3): 350–363.

    Article  Google Scholar 

  11. T. Kobayashi, Adaptive regulator design for a class of parabolic distributed parameter system with disturbed outputs, IMA J. Math. Control Inf., 2007, 24: 461–471.

    Article  MATH  Google Scholar 

  12. M. Krstic and A. Smyshlyaev, Adaptive boundary control for unstable parabolic PDEs-Part I: Lyapunov design, IEEE Trans. Automat. Control, 2008, 53(7): 1575–1591.

    Article  MathSciNet  Google Scholar 

  13. L. C. Evans, Partial Differential Equations, Graduate Studies in Mathematics, Vol. 19, American Mathematical Society, 1998.

  14. R. Temam, Infinite-Dimensional Dynamical Systems in Mechanics and Physics, Applied Mathematical Science, Vol. 68, Springer-Verlag, New York, 1988.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Mathematics and Systems Science, Beihang University, Beijing, 100191, China

    Chaohua Jia

Authors
  1. Chaohua Jia
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Chaohua Jia.

Additional information

This research is supported by the National Natural Science Foundation of China under Grant No. 10626002, and the Fundamental Research Funds YWF-10-01-A15 for the Central Universities.

This paper was recommended for publication by Editor Dexing FENG.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Jia, C. A note on the model reference adaptive control of linear parabolic systems with constant coefficients. J Syst Sci Complex 24, 1110–1117 (2011). https://doi.org/10.1007/s11424-011-0042-9

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11424-011-0042-9

Key words

Search

Navigation