Skip to main content
SpringerLink
Log in

New convergence analysis in adaptive control: Convergence analysis without the barbalat's lemma

  • Published:
KSME Journal Aims and scope Submit manuscript

Abstract

Convergence of the state errore to zero in adaptive systems is shown using the existence and uniqueness of solution and the existence of a Lyapunov function in which the adaptation laws are constructed. Results in the paper are general in the sense that it is applicable to a broad class of adaptive systems of a linear/nonlinear, time-varying or distributed-parameter systems. Since the approach taken in the paper does not require the boundedness of the derivative of the state errore for allt≥0, it is particularly useful in the adaptive control of infinite dimensional systems.

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

  • Bentsman, J., Solo, V. and Hong, K. S. 1992, “Adaptive Control of a Parabolic System with Time-Varying Parameters: An Averaging Analysis,”Proc. 31st IEEE Conf. on Decision and Control, Tucson, AZ, pp. 710–711.

  • Demetriou, M. A. and Rosen, I. G., 1994, “On the Persistence of Excitation in the Adaptive Estimation of Distributed Parameter Systems.”IEEE Transactions on Automatic Control, Vol. 39, No. 5, pp. 1117–1134.

    Article  MATH  MathSciNet  Google Scholar 

  • Friedman, A., 1969,Partial Differential Equations, New York: Holt, Reinhart, and Winston.

    MATH  Google Scholar 

  • Hale, J. K., 1969,Ordinary Differential Equations, New York: Wiley.

    MATH  Google Scholar 

  • Henry, D., 1981,Geometric Theory of Semilinear Parabolic Equations, Lecture Notes in Mathematics, 840, Springer-Verlag.

  • Hong, K. S. and Bentsman, J., 1992a, “Stability Criterion for Linear Oscillatory Parabolic Systems,”ASME J. of Dynamic Systems, Measurement and Control, Vol. 114, No. 1, pp. 175–178.

    Article  MATH  Google Scholar 

  • Hong, K. S. and Bentsman, J., 1992b, “Nonlinear Control of Diffusion Process with Uncertain Parameters Using MRAC Approach,”Proc. 1992 American Control Conference, Chicago, IL, pp. 1343–1347.

  • Hong, K. S., Wu, J. W. and Lee, K. I., 1994, “New Conditions for the Exponential Stability of Evolution Equations,”IEEE Transactions on Automatic Control., Vol. 39, No. 7, pp. 1432–1436.

    Article  MATH  MathSciNet  Google Scholar 

  • Hong, K. S. and Lee, M. H., 1993, “Stability and Tunability of an Adaptive Controller for One-Dimensional Parabolic PDE with Spatially-Varying Coefficients,”KSME Journal, Vol. 7, No. 4, pp. 320–329.

    MathSciNet  Google Scholar 

  • Hong, K. S. and Bentsman, J., 1993. “Averaging for a Hybrid System Arising in the Direct Adaptive Control of Parabolic Systems and its Applications to Stability Analysis,”Prep. of 12th World Congress of IFAC, Sydney, Australia, pp. 177–180.

  • Hong, K. S. and Bentsman, J., 1994a, “Application of Averaging Method for Integro-Differential Equations to Model Reference Adaptive Control of Parabolic Systems,”Automatica., Vol. 30, No. 9, pp. 1415–1419.

    Article  MATH  MathSciNet  Google Scholar 

  • Hong, K. S. and Bentsman, J., 1994b, “Direct Adaptive Control of Parabolic Systems: Algorithm Synthesis and Convergence and Stability Analysis,”IEEE Transactions on Automatic Control, Vol. 39, No. 10, pp. 2018–2033.

    Article  MATH  MathSciNet  Google Scholar 

  • Narendra, K. S. and Annaswamy, A. M., 1989,Stable Adaptive Systems, Englewood Cliffs, NJ: Prentice-Hall.

    Google Scholar 

  • Narendra, K. S., Lin, Y. H. and Valavani, L. S., 1980, “Stable Adaptive Controller Design, Part II: Proof of Stability,”IEEE Transactions on Automatic Control, Vol. AC-25, No. 3, pp. 440–448.

    Article  MATH  Google Scholar 

  • Pazy, A., 1983,Semigroups of Linear Operators and Applications to Partial Differential Equations, New York: Springer-Verlag.

    MATH  Google Scholar 

  • Polycarpou, M. M. and Ioannou, P. A., 1993, “On the Existence and Uniqueness of Solutions in Adaptive Control Systems,”IEEE Transactions on Automatic Control, Vol., 38, No. 3, pp. 474–479.

    Article  MATH  MathSciNet  Google Scholar 

  • Sastry, S. S. and Bodson, M., 1989,Adaptive Control: Stability, Convergence and Robustness, Englewood Cliffs, NJ: Prentice-Hall.

    MATH  Google Scholar 

  • Slotine, J. J. E. and Li, W., 1991,Applied Nonlinear Control, Englewood Cliffs, NJ: Prentice-Hall.

    MATH  Google Scholar 

  • Walker, J. A., 1980,Dynamical Systems and Evolution Equations, New York: Plenum Press.

    MATH  Google Scholar 

  • Wen, J., 1985,Direct Adaptive Control in Hilbert Space, Ph. D. thesis, Electrical, Computer and Systems Engineering Department, Rensselaer Polytechnic Institute, Troy New York.

    Google Scholar 

  • Wu, J. W. and Hong, K. S., 1994, “Delay-Independent Stability Criteria for Time-Varying Discrete Systems,”IEEE Transactions on Automatic Control, Vol. 39, No. 4, pp. 811–814.

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Control and Mechanical Engineering, The Institute of Mechanical Technology, Pusan National University, 30 Changjeon-dong, Kumjeong-ku, 609-735, Pusan, Korea

    Keum-Shik Hong

Authors
  1. Keum-Shik Hong
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Hong, KS. New convergence analysis in adaptive control: Convergence analysis without the barbalat's lemma. KSME Journal 9, 138–146 (1995). https://doi.org/10.1007/BF02953615

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02953615

Key Words

Search

Navigation