Cybernetics and Systems Analysis

, Volume 49, Issue 5, pp 768–773 | Cite as

A difference stochastic optimization procedure with impulse perturbation

  • U. T. Khimka
  • Ya. M. Chabanyuk


The sufficient conditions are obtained for the convergence of the difference stochastic optimization procedure with impulse perturbations in a Markov environment under the conditions of exponential stability of the averaged system and smooth regression function of the source system. To this end, an asymptotic representation of the perturbed procedure generator is obtained.


stochastic optimization procedure Markov process impulse perturbation 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    M. B. Nevelson and R. Z. Khasminskii, Stochastic Approximation and Recurrent Estimation [in Russian], Nauka, Moscow (1972).Google Scholar
  2. 2.
    L. Ljung, G. Pflug, and H. Walk, Stochastic Approximation and Optimization of Random Systems, Birkhauser Verlag, Basel–Boston–Berlin (1992).CrossRefMATHGoogle Scholar
  3. 3.
    Ya. Z. Tsypkin, Fundamentals of Learning Systems Theory [in Russian], Nauka, Moscow (1970).Google Scholar
  4. 4.
    A. V. Skorokhod, Asymptotic Methods of the Theory of Stochastic Differential Equations [in Russian], Naukova Dumka, Kyiv (1987).Google Scholar
  5. 5.
    V. Koroliuk and N. Limnios, Stochastic Systems in Merging Phase Space, World Sci. Publ., Singapore (2005).CrossRefMATHGoogle Scholar
  6. 6.
    S. A. Semenyuk and Ya. M. Chabanyuk, “Fluctuations of a stochastic system under an asymptotic diffusive perturbation,” Cybern. Syst. Analysis, 44, No. 5, 716–721 (2008).MathSciNetCrossRefMATHGoogle Scholar
  7. 7.
    V. S. Korolyuk and V. V. Korolyuk, Stochastic Models of Systems, Kluwer Acad. Publ., Dordrecht (1999).CrossRefMATHGoogle Scholar
  8. 8.
    Ya. M. Chabanyuk, “Continuous procedure of stochastic approximation with singular perturbation under balance conditions,” Cybern. Syst. Analysis, 42, No. 3, 420–425 (2006).MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.National University “Lviv Polytechnic”LvivUkraine

Personalised recommendations