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.
This is a preview of subscription content, access via your institution.
Buy single article
Instant access to the full article PDF.
Price includes VAT (USA)
Tax calculation will be finalised during checkout.
M. B. Nevelson and R. Z. Khasminskii, Stochastic Approximation and Recurrent Estimation [in Russian], Nauka, Moscow (1972).
L. Ljung, G. Pflug, and H. Walk, Stochastic Approximation and Optimization of Random Systems, Birkhauser Verlag, Basel–Boston–Berlin (1992).
Ya. Z. Tsypkin, Fundamentals of Learning Systems Theory [in Russian], Nauka, Moscow (1970).
A. V. Skorokhod, Asymptotic Methods of the Theory of Stochastic Differential Equations [in Russian], Naukova Dumka, Kyiv (1987).
V. Koroliuk and N. Limnios, Stochastic Systems in Merging Phase Space, World Sci. Publ., Singapore (2005).
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).
V. S. Korolyuk and V. V. Korolyuk, Stochastic Models of Systems, Kluwer Acad. Publ., Dordrecht (1999).
Ya. M. Chabanyuk, “Continuous procedure of stochastic approximation with singular perturbation under balance conditions,” Cybern. Syst. Analysis, 42, No. 3, 420–425 (2006).
Translated from Kibernetika i Sistemnyi Analiz, No. 5, September–October, 2013, pp. 145–151.
About this article
Cite this article
Khimka, U.T., Chabanyuk, Y.M. A difference stochastic optimization procedure with impulse perturbation. Cybern Syst Anal 49, 768–773 (2013). https://doi.org/10.1007/s10559-013-9564-6
- stochastic optimization procedure
- Markov process
- impulse perturbation