Abstract
The synthesis of optimal control over nonlinear stochastic systems that are described by the Itô equations is reduced to the solution of recurrence relations derived from the Bellman stochastic equation.
Similar content being viewed by others
References
I. I. Gikhman and A. V. Skorokhod,Introduction to the Theory of Random Processes [in Russian], Nauka, Moscow (1965).
L. N. Raitenberg,Automatic Control [in Russian], Fizmatgiz, Moscow (1978).
M. V. Trigub, “Synthesis of suboptimal control over stochastic systems of a certain class,”Avtomat. Telemekh., No. 6, 43–54 (1994).
E. G. Al'brekht, “Optimal stabilization of nonlinear systems,”Prikl. Mat. Mekh.,25, No. 5, 836–844 (1961).
M. V. Trigub, “Approximately optimal stabilization of a certain class of nonlinear systems,”Avtomat. Telemekh., No. 1, 34–43 (1987).
M. V. Trigub, “Optimal control over quasilinear systems,”Ukr. Mat. Zh.,47, No. 9, 1280–1295 (1995).
V. V. Golubev,Lectures on the Analytic Theory of Differential Equations [in Russian], Gostekhteorizdat, Moscow-Leningrad (1950).
F. M. Kirillova, “Analytic construction of regulators,”Prikl. Mat. Mekh.,25, No. 3, 433–439 (1961).
Additional information
Kharkov Technical University of Radioelectronics, Kharkov. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 51, No. 4, pp. 532–541, April, 1999.
Rights and permissions
About this article
Cite this article
Trigub, M.V. Optimal control over nonlinear stochastic systems. Ukr Math J 51, 592–603 (1999). https://doi.org/10.1007/BF02591761
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02591761