Abstract
An optimal control problem for systems of stochastic differential-functional linear equations with past history and Poisson switchings is formulated. The Bellman equation is solved for this problem.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
REFERENCES
E. A. Andreeva, V. B. Kolmanovskii, and L. E. Shaikhet, Control of Hereditary Systems [in Russian], Nauka, Moscow (1992).
P. Billingsley, Convergence of Probabilistic Measures [Russian translation], Nauka, Moscow (1977).
I. I. Gikhman and A. V. Skorokhod, Stochastic Differential Equations and Their Applications [in Russian], Naukova Dumka, Kiev (1982).
A. V. Skorokhod, Asymptotic Methods in Stochastic Differential Equations [in Russian], Naukova Dumka, Kiev (1986).
V. K. Yasinskii, Stochastic Differential-Functional Systems with Past History [in Russian], TViMS, Kiev (2003).
V. I. Zubov, “Stochastic behavior of systems with a finite number of phase states and aftereffect,” Dif. Uravn., 15, No.3, 18–26 (1979).
V. B. Kolmanovskii and T. L. Maizenberg, “Optimal control of stochastic hereditary systems,” Prikl. Mat. Mekh., 41, No.3, 31–38 (1977).
V. B. Kolmanovskii and L. E. Shaikhet, “A method for approximate synthesis of optimal control,” DAN USSR, Ser. A, No. 8, 32–36 (1978).
V. B. Kolmanovskii and L. E. Shaikhet, “Approximate synthesis of optimal control for stochastic quasilinear hereditary systems,” Prikl. Mat. Mekh., 42, No.6, 45–49 (1978).
V. B. Kolmanovskii and L. E. Shaikhet, “Approximate synthesis of quadratic control problems,” Dokl. AN USSR, Ser. A, No. 4, 13–18 (1980).
V. B. Kolmanovskii and L. E. Shaikhet, “Synthesis of optimal control for some mechanical systems under random disturbances,” Izv. AN SSSR, Techn. Kibern., No. 2, 31–43 (1973).
V. B. Kolmanovskii and F. L. Chernous’ko, Optimal Control under Random Disturbances [in Russian], Nauka, Moscow (1978).
L. E. Shaikhet, “Stabilization of controlled stochastic systems with delay by the method of Lyapunov functionals,” Teor. Sluch. Prots., No. 4, 113–118 (1976).
L. E. Shaikhet, “Approximate synthesis of quadratic and nonquadratic control problems,” Teor. Sluch. Prots., No. 9, 125–131 (1981).
L. E. Shaikhet, “Numerical solution of the speed problem under continuous and discrete random disturbances,” Izv. AN SSSR, Techn. Kibern., No. 6, 98–109 (1987).
Author information
Authors and Affiliations
Additional information
Translated from Kibernetika i Sistemnyi Analiz, No. 6, pp. 112–118, November–December 2004.
Rights and permissions
About this article
Cite this article
Korolyuk, V.S., Yasinskii, V.K. & Antonyuk, S.V. Optimal control of stochastic dynamic systems with past history and poison switchings. Cybern Syst Anal 40, 883–888 (2004). https://doi.org/10.1007/s10559-005-0027-6
Received:
Issue Date:
DOI: https://doi.org/10.1007/s10559-005-0027-6