Skip to main content
SpringerLink
Log in

Some Problems of Robust Control of a Stochastic Object

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

Abstract

Studies are made of a problem of constructing a robust system according to an averaged performance criterion of a stochastic control system. Cases of the parametric and the structural uncertainty are considered. The relation of the notion of the stochastic robustness to the classical definition of deterministic systems is shown. A comparative analysis of the suggested method of developing a robust system and some other approaches is carried out.

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. Jacobs, O.L.R. and Patchell, I.W., Caution and Probing in Stochastic Control, Int. J. Control, 1972, vol. 16, no. 1, pp. 189–199.

    Google Scholar 

  2. Fetisov, V.N. and Shteinberg, Sh.E., Development of Control Algorithms by Engineering Processes in the Case of Inexact Identification Results, Vopr. Prom. Kibernetiki (Tr. TsNIIKA), 1973, issue 36, pp. 64–67.

  3. Fetisov, V.N., To the Problem of Control of an Object with an Unknown Parameter, Avtom. Telemekh., 1973, no. 8, pp. 64–67.

  4. Bar-Shalom, Y., Stochastic Dynamic Programming: Caution and Probing, IEEE Trans. Autom. Control, AC-26, 1981, pp. 1184–1195.

    Google Scholar 

  5. Tsypkin, Ya.Z., Synthesis of Robust Optimal Systems of Control of Objects under Conditions of Limited Uncertainty, Avtom. Telemekh., 1992, no. 9, pp. 139–159.

  6. Polyak, B.T. and Shcherbakov, P.S., Robastnaya ustoichivost' i upravlenie (Robust Stability and Control), Moscow: Nauka, 2002.

    Google Scholar 

  7. Stengel, R.F. and Ray, L.R., Stochastic Robustness of Linear Time-Invariant Control Systems, IEEE Trans. Autom. Control, 1991, vol. 36, pp. 82–87.

    Google Scholar 

  8. Tempo, R. and Dabbene, F., Randomized Algorithms for Analysis and Control of Uncertain Systems: An Overview. Perspectives in Robust Control, London: Springer, 2001.

    Google Scholar 

  9. Vidyasagar, M., Randomized Algorithms for Robust Controller Synthesis Using Statistical Learning Theory, Automatica, 2001, vol. 37(10), pp. 1515–1528.

    Google Scholar 

  10. Patela, V.V., Deodharea, G., and Viswanathb, T., Some Applications of Randomized Algorithms for Control System Design, Automatica, 2002, vol. 38, pp. 2085–2092.

    Google Scholar 

  11. Fisher, R., The Fiducial Argument in Statistical Inference, Ann. Eugenics, 1935, vol. 6, pp. 391–398.

    Google Scholar 

  12. Wilkes, S., Matematicheskaya statistika (Mathematical Statistics), Moscow: Nauka, 1967.

    Google Scholar 

  13. Fetisov, V.N., The Analysis of Sensitivity of Markov Models and its Use for Estimation of the Effect of Identification Errors on the Control Performance Criterion, Proc. 2nd Int. Conf. on Identification of Systems and Control Problems, Moscow, 2003, pp. 614–630.

  14. Fetisov, V.N., An Inequality Related to the Monte Carlo Method, Teor. Veroyat. Primen., 1974, vol. 19, no. 1, pp. 224–226.

    Google Scholar 

  15. Fetisov, V.N., Estimation of the Sample Length in Solving Extremal Problems by the Monte Carlo Method, Zh. Vychisl. Mat. Mat. Fiz., 1976, vol. 16, no. 1, pp. 256–262.

    Google Scholar 

  16. Tsybakov, A.B., Estimation of Accuracy of the Empirical Risk Minimization Method, Probl. Peredachi Inf., 1981, vol. 17, no. 1, pp. 50–61.

    Google Scholar 

  17. Vitushkin, A.G., Otsenka slozhnosti zadachi tabulirovaniya (Estimation of Complexity of a Tabulation Problem), Moscow: Fizmatgiz, 1959.

    Google Scholar 

  18. Gnedenko, B.V., Kurs teorii veroyatnostei (A Course in Probability Theory), Moscow: URSS, 2001.

    Google Scholar 

  19. Chernoff, H., Measure of Asymptotic Efficiency for Test of Hypothesis Based on the Sum of Observations, Ann. Math. Statist., 1952, vol. 23, pp. 493–507.

    Google Scholar 

  20. Vapnik, V.N.,Vosstanovlenie zavisimostei po empiricheskim dannym (Recovery of Relations Using Empirical Data), Moscow: Nauka, 1979.

    Google Scholar 

  21. Tikhomirov, V.M., Nekotorye voprosy teorii priblizhenii (Some Issues of Approximation Theory), Moscow: Mosk. Gos. Univ., 1976.

    Google Scholar 

  22. Fetisov, V.N., Identification of Simplified Mathematical Models in the Problem of Control of a Stochastic Object, Proc. Int. Conf. on Identification of Systems and Control Problems, Moscow, 2000, pp. 2068–2081.

  23. Fetisov, V.N., Accounting for Identification Errors in Control Problems with a Predictor, Proc. 3rd Int. Conf. on Identification of Systems and Control Problems, Moscow, 2004, pp. 1114–1132.

Download references

Author information

Authors and Affiliations

  1. Institute for Information Transmission Problems, Russian Academy of Sciences, Moscow, Russia

    V. N. Fetisov

Authors
  1. V. N. Fetisov
    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

Fetisov, V.N. Some Problems of Robust Control of a Stochastic Object. Automation and Remote Control 65, 594–602 (2004). https://doi.org/10.1023/B:AURC.0000023536.06877.12

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/B:AURC.0000023536.06877.12

Keywords

Search

Navigation