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Agayeva, Ch. A.

Second order necessary conditions of optimality for stochastic systems with variable delay. (English. Russian original) Zbl 1238.93122

Theory Probab. Math. Stat. 83, 1-12 (2011); translation from Teor. Jmovirn. Mat. Stat. 83, 2-11 (2010).
Summary: 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, a second order necessary optimality condition for the stochastic system with uncontrolled diffusion coefficient is obtained.

Cited in 5 Documents

MSC:

93E20 Optimal stochastic control
49K45 Optimality conditions for problems involving randomness

Keywords:

stochastic differential equations with delay; stochastic control problem; necessary condition of optimality; singular controls; adjoint stochastic differential equations
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\textit{Ch. A. Agayeva}, Theory Probab. Math. Stat. 83, 1--12 (2011; Zbl 1238.93122); translation from Teor. Jmovirn. Mat. Stat. 83, 2--11 (2010)
Full Text: DOI

References:

[1] 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. · Zbl 0785.34005
[2] Случайные возмущения дифференциал\(^{\приме}\)но-функционал\(^{\приме}\)ных уравнений, ”Зинатне”, Рига, 1989 (Руссиан).
[3] 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. · Zbl 0339.49002
[4] 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. · Zbl 0928.93068
[5] 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).
[6] Ch. A. Agayeva, Stochastic optimal control problem with delay, Theory Stoch. Process. 12 (2006), no. 1-2, 3 – 11. · Zbl 1142.93442
[7] Ivar Ekeland, Nonconvex minimization problems, Bull. Amer. Math. Soc. (N.S.) 1 (1979), no. 3, 443 – 474. · Zbl 0441.49011
[8] Agamirza E. Bashirov, Partially observable linear systems under dependent noises, Systems & Control: Foundations & Applications, Birkhäuser Verlag, Basel, 2003. · Zbl 1012.93001
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