Second order necessary conditions of optimality for stochastic systems with variable delay
Author:
Ch. A. Agayeva
Journal:
Theor. Probability and Math. Statist. 83 (2011), 1-12
MSC (2010):
Primary 93E20, 49K45
DOI:
https://doi.org/10.1090/S0094-9000-2012-00837-5
Published electronically:
February 2, 2012
MathSciNet review:
2768844
Full-text PDF Free Access
Abstract |
References |
Similar Articles |
Additional Information
Abstract: The purpose of this paper is to give necessary conditions of optimality of nonlinear stochastic control systems with variable delay for singular controls. As a result, the second order necessary optimality condition for the stochastic system with uncontrolled diffusion coefficient is obtained.
References
- V. Kolmanovskiĭ and A. Myshkis, Applied theory of functional-differential equations, Mathematics and its Applications (Soviet Series), vol. 85, Kluwer Academic Publishers Group, Dordrecht, 1992. MR 1256486
- E. F. Tsar′kov, Sluchaĭ nye vozmushcheniya differentsial′no-funktsional′nykh uravneniĭ, “Zinatne”, Riga, 1989 (Russian). MR 1036733
- R. Gabasov and F. Kirillova, The qualitative theory of optimal processes, Marcel Dekker, Inc., New York-Basel, 1976. Translated from the Russian by John L. Casti; Control and Systems Theory, Vol. 3. MR 0451082
- N. I. Mahmudov and A. E. Bashirov, First order and second order necessary conditions of optimality for stochastic systems, Statistics and control of stochastic processes (Moscow, 1995/1996) World Sci. Publ., River Edge, NJ, 1997, pp. 283–295. MR 1647306
- Ch. A. Agaeva and Dzh. Dzh. Allakhverdieva, The maximum principle for stochastic systems with variable delay, Dokl. Nats. Akad. Nauk Azerb. 59 (2003), no. 5-6, 61–65 (Russian, with English and Azerbaijani summaries). MR 2186880
- Ch. A. Agayeva, Stochastic optimal control problem with delay, Theory Stoch. Process. 12 (2006), no. 1-2, 3–11. MR 2316281
- Ivar Ekeland, Nonconvex minimization problems, Bull. Amer. Math. Soc. (N.S.) 1 (1979), no. 3, 443–474. MR 526967, DOI https://doi.org/10.1090/S0273-0979-1979-14595-6
- Agamirza E. Bashirov, Partially observable linear systems under dependent noises, Systems & Control: Foundations & Applications, Birkhäuser Verlag, Basel, 2003. MR 1960982
References
- V. B. Kolmanovskiĭ and A. D. Myshkis, Applied Theory of Functional-Differential Equations, Kluwer Academic Publishers, Dordrecht, 1992. MR 1256486 (95f:34092)
- E. F. Tsar’kov, Random Perturbations of Functional-Differential Equations, Riga, 1989. (Russian) MR 1036733 (90m:34164)
- R. Gabasov, The Qualitative Theory of Optimal Processes, Control and Systems Theory, vol. 3, M. Dekker, 1976. MR 0451082 (56:9369)
- N. I. Mahmudov and A. E. Bashirov, First order and second order necessary conditions of optimality for stochastic systems, Statistics and Control of Stochastic Processes, The Liptser Festschrift, Papers of the Steklov Seminar, Moscow 1995/96, pp. 283–295, World Sci. Publ., River Edge, NJ, 1997. MR 1647306 (2000c:49048)
- Ch. A. Agayeva and J. J. Allahverdiyeva, Maximum principle for stochastic systems with variable delay, Reports of NSA of Azerbaijan LIX (2003), 61–65. (Russian) MR 2186880
- Ch. A. Agayeva, Stochastic optimal control problem with delay, Theory of Stochastic Processes (2006), no. 1–2, 3–11. MR 2316281 (2007m:93092)
- I. Ekeland, Nonconvex minimization problem, Bull. Amer. Math. Soc. (NS) (1979), no. 1, 443–474. MR 526967 (80h:49007)
- A. E. Bashirov, Partially Observable Linear Systems under Dependent Noises, Birkhaüser, Basel, 2003. MR 1960982 (2004h:93002)
Similar Articles
Retrieve articles in Theory of Probability and Mathematical Statistics
with MSC (2010):
93E20,
49K45
Retrieve articles in all journals
with MSC (2010):
93E20,
49K45
Additional Information
Ch. A. Agayeva
Affiliation:
Yasar University, Izmir, Turkey, and Institute of Cybernetics, Baku, Azerbaijan
Email:
cher.agayeva@rambler.ru, agaeva.cherkez@yasar.edu.tr
Keywords:
Stochastic differential equations with delay,
stochastic control problem,
necessary condition of optimality,
singular controls,
adjoint stochastic differential equations
Received by editor(s):
December 25, 2007
Published electronically:
February 2, 2012
Article copyright:
© Copyright 2012
American Mathematical Society
