The Dead Zone in System Identification

  • K. Forsman
  • L. Ljung

Abstract

A prediction error method for parameter estimation in a dynamical system is studied.
$$ \hat \vartheta = \arg {\mkern 1mu} \mathop {\min }\limits_\vartheta \mathop {\lim }\limits_{N \to \infty } \frac{1}{N}\sum\limits_{t = 1}^N {{\text{E}}l\left( {\varepsilon \left( {t,\vartheta } \right)} \right)} $$
where ε are the prediction errors of a linear regression. A quadratic norm l is zero within an interval [−c, c]. This kind of a dead zone (DZ) criterion is very common in robust adaptive control. The following problems are treated in this chapter:
  • When is the DZ estimate inconsistent, and what is the set of parameters which minimizes the criterion in the case of inconsistency?

  • What happens to the variance of the estimate as the DZ is introduced?

  • Does the DZ give a better estimate than least squares (LS) when there are unmodeled deterministic disturbances present?

  • What are the relations between identification with a dead zone criterion and so called set membership identification?

Keywords

Dead Zone Little Square Estimate Asymptotic Covariance Matrix Adaptive Regulator Robust Adaptive Control 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    B. Egardt, Stability of Adaptive Controllers, volume 20 of Lecture Notes in Control and Information Sciences, Springer (1976).Google Scholar
  2. 2.
    G. C. Goodwin, D. J. Hill, D. Q. Mayne, and R. H. Middleton, Adaptive Robust Control (Convergence, Stability and Performance), Technical Report EE8544, Dept. of Electrical and Computer Engineering, The University of Newcastle, New South Wales, Australia (1985).Google Scholar
  3. 3.
    L. Ljung, System Identification — Theory for the User, Prentice-Hall, Englewood Cliffs, NJ, p. 345 (1987).MATHGoogle Scholar
  4. 4.
    F. B. Hildebrand, Advanced Calculus for Applications, Prentice-Hall, Englewood Cliffs, NJ, p. 359 (1962).Google Scholar
  5. 5.
    L. Ljung, IEEE Control Syst. Mag. 11, 25 (1991).CrossRefGoogle Scholar
  6. 6.
    F. C. Schweppe, Uncertain Dynamical Systems, Prentice-Hall, Englewood Cliffs, NJ (1973).Google Scholar
  7. 7.
    M. Milanese and R. Tempo, IEEE Trans. Aut. Control AC-30, 730 (1985).MathSciNetCrossRefGoogle Scholar
  8. 8.
    E. Walter and H. Piet-Lahanier, in: IEEE Proceedings of the 26th Conference on Decision and Control, pp. 1921-1922 (1987).Google Scholar
  9. 9.
    E. Fogel and Y. F. Huang, Automatica 18, 229 (1982).MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1996

Authors and Affiliations

  • K. Forsman
    • 1
  • L. Ljung
    • 2
  1. 1.ABB Corporate Research, IdeonLundSweden
  2. 2.Department of Electrical EngineeringLinköping UniversityLinköpingSweden

Personalised recommendations