Skip to main content
Log in

Comparison of the quantile and guaranteeing approaches to system analysis

  • Stochastic Systems
  • Published:
Automation and Remote Control Aims and scope Submit manuscript

Abstract

The worst value of the quantile of the distribution of the linear loss function which depends on the uncertain stochastic parameters was compared with the maximum value of this function. The stochastic uncertainty is modelled by distributions from the Barmish class.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Kibzun, A.I. and Kan, Yu.S., Stochastic Programming Problems with Probability and Quantile Functions, New York: Wiley, 1996.

    MATH  Google Scholar 

  2. Barmish, B.R. and Lagoa, C.M., The Uniform Distribution: A Rigorous Justification for Its Use in Robustness Analysis, Math. Control Signal Syst., 1997, no. 10, pp. 203–222.

  3. Kan, Yu.S. and Mistrukov, A.A., On the Equivalence in Stochastic Programming with Probability and Quantile Objectives, in Lect. Notes Econom. Math. Syst., Marti, K. and Kall, P., Eds., Berlin: Springer, 1998, pp. 145–153.

    Google Scholar 

  4. Kibzun, A.I., On the Worst Distribution in the Problems of Stochastic Optimization with the Probability Function, Avtom. Telemekh., 1998, no. 11, pp. 104–116.

  5. Kan, Yu.S., On Justification of the Principle of Uniformity in the Problem of OIptimization of the Probabilistic Performance Index, Avtom. Telemekh., 2000, no. 1, pp. 54–70.

  6. Kan, Yu.S. and Kibzun, A.I., Sensitivity Analysis of Worst-Case Distribution for Probability Optimization Problems, in Probabilistic Constrained Optimization: Theory and Applications, Uryasev, S.P., Ed., New York: Kluwer, 2000, pp. 31–46.

    Google Scholar 

  7. Zorich, V.A., Matematicheskii analiz. Ch. II (Mathematical Analysis. Part II), Moscow: Nauka, 1984.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Original Russian Text © Yu.S. Kan, A.V. Sysuev, 2007, published in Avtomatika i Telemekhanika, 2007, No. 1, pp. 57–67.

This work was supported by the Russian Foundation for Basic Research, projects nos. 04-01-00758, 05-08-17963.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kan, Y.S., Sysuev, A.V. Comparison of the quantile and guaranteeing approaches to system analysis. Autom Remote Control 68, 54–63 (2007). https://doi.org/10.1134/S0005117907010055

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0005117907010055

PACS number

Navigation