Successive approximations to the optimal control of stochastic systems with after-effect. II

Successive approximations to the optimal control of stochastic systems with after-effect. II Random Oper. & Stock, Eqs., Vol. 1, No. 4, pp. 375-392 (1993) O VSP 1993 V. B. KOLMANOVSKIJ1 and L. E. SHAIKHET2 Moscow institute of Electronic industry, 109028 Moscow, Russia Donetsk State Academy of Management, 340015 Donetsk, Ukraine Received for ROSE 11 May 1991 Abstract--This paper is a continuation of [1]. The method of successive approximations to the optimal control of stochastic differential equations with after-effect is considered. 4. SYSTEMS WITH A NOISE UNDER CONTROL In this section the problem of an approximate synthesis for the system with a small noise under control is considered. The Bellman equation and the optimal control which define an exact solution of the problem are given. By means of the algorithm developed in the previous sections the successive approximations to the optimal control are constructed. 4.1. Formulation of the problem We consider the controllable system with random obstacles under control \ B(t) + VS5>(t,*:f)e<(t) Udt i=l / Here a process () is the same as in (3.1). Denote by f;(t), i = 1, . . . , JV, independent scalar standard Wiener processes which do not depend on 77(2), the ( /) matrices B(t) and ,·(£, </?), i = 1, . . http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Random Operators and Stochastic Equations de Gruyter

Successive approximations to the optimal control of stochastic systems with after-effect. II

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Publisher
de Gruyter
Copyright
Copyright © 2009 Walter de Gruyter
ISSN
0926-6364
eISSN
1569-397X
DOI
10.1515/rose.1993.1.4.375
Publisher site
See Article on Publisher Site

Abstract

Random Oper. & Stock, Eqs., Vol. 1, No. 4, pp. 375-392 (1993) O VSP 1993 V. B. KOLMANOVSKIJ1 and L. E. SHAIKHET2 Moscow institute of Electronic industry, 109028 Moscow, Russia Donetsk State Academy of Management, 340015 Donetsk, Ukraine Received for ROSE 11 May 1991 Abstract--This paper is a continuation of [1]. The method of successive approximations to the optimal control of stochastic differential equations with after-effect is considered. 4. SYSTEMS WITH A NOISE UNDER CONTROL In this section the problem of an approximate synthesis for the system with a small noise under control is considered. The Bellman equation and the optimal control which define an exact solution of the problem are given. By means of the algorithm developed in the previous sections the successive approximations to the optimal control are constructed. 4.1. Formulation of the problem We consider the controllable system with random obstacles under control \ B(t) + VS5>(t,*:f)e<(t) Udt i=l / Here a process () is the same as in (3.1). Denote by f;(t), i = 1, . . . , JV, independent scalar standard Wiener processes which do not depend on 77(2), the ( /) matrices B(t) and ,·(£, </?), i = 1, . .

Journal

Random Operators and Stochastic Equationsde Gruyter

Published: Jan 1, 1993

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